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Stochastic Set-Based Particle Swarm Optimization Based on Local Exploration for Solving the Carpool Service Problem Sheng-Kai Chou, Ming-Kai Jiau, and Shih-Chia Huang, Senior Member, IEEE

Abstract—The growing ubiquity of vehicles has led to increased concerns about environmental issues. These concerns can be mitigated by implementing an effective carpool service. In an intelligent carpool system, an automated service process assists carpool participants in determining routes and matches. It is a discrete optimization problem that involves a system-wide condition as well as participants’ expectations. In this paper, we solve the carpool service problem (CSP) to provide satisfactory ride matches. To this end, we developed a particle swarm carpool algorithm based on stochastic set-based particle swarm optimization (PSO). Our method introduces stochastic coding to augment traditional particles, and uses three terminologies to represent a particle: 1) particle position; 2) particle view; and 3) particle velocity. In this way, the set-based PSO (S-PSO) can be realized by local exploration. In the simulation and experiments, two kind of discrete PSOs—S-PSO and binary PSO (BPSO)—and a genetic algorithm (GA) are compared and examined using tested benchmarks that simulate a realworld metropolis. We observed that the S-PSO outperformed the BPSO and the GA thoroughly. Moreover, our method yielded the best result in a statistical test and successfully obtained numerical results for meeting the optimization objectives of the CSP. Index Terms—Carpool service problem (CSP), intelligent carpool system (ICS), set-based particle swarm optimization (S-PSO).

I. I NTRODUCTION HE GROWING ubiquity of vehicles has increased concern about environmental issues such as traffic congestion, oil consumption, air pollution emissions, fuel dependency, and so on [1]. Carpooling has significant evolutions from past decade to now [2] and has been long discussed as an effective strategy for reducing these concerns by effectively increasing usage of empty car seats to improve the occupancy rate of private vehicles [3]. The vehicle is shared between the driver and one or more riders whose itineraries are similar. Technological advancements regarding mobile communication and mobile devices allow the broadening of carpooling’s appeal, and better enables the practicality of the platform.

T

Manuscript received November 10, 2015; accepted January 18, 2016. This work was supported by the Ministry of Science and Technology, Taiwan, under Grant MOST 103-2221-E-027-030-MY2 and Grant MOST 103-2221E-027-031-MY2. This paper was recommended by Associate Editor J. Zhang. (Corresponding author: Shih-Chia Huang.) The authors are with the Department of Electronic Engineering, National Taipei University of Technology, Taipei 106, Taiwan (e-mail: [email protected]). Digital Object Identifier 10.1109/TCYB.2016.2522471

As such, the push service to carpooling is available via mobile devices and this allows carpooling to be used by participants more frequently, easily, and flexibly [4]. Currently, a few organizations and companies have been involved in developing a system that offers fundamental carpool services accessed over the Web or mobile phone applications, referred to as the intelligent carpool system (ICS). Developers include Flinc,1 Carma,2 Zimride,3 sidecar,4 and go2gether.5 In this system, each participant who is either a driver or rider can easily deliver the required information like a source and a destination to the system platform and subsequently receive a list of trips that is available for desired (or planned) ride-share trip. However, in this system, users must independently make the effort to find the favorite trip as the current systems are profoundly deficient in automated processing that would facilitate effective matching. This automated process is a route and matching service that can be formulated as a problem in combinatorial optimization called the carpool service problem (CSP). The problem consists of a collection of carpool participants, including driver and rider, and a set of origin-destination pairs owned by each participant. The CSP is very complicated because the itineraries of the drivers and riders must be resolved optimally as well as simultaneously. In the study of [10], the carpool problem is resolved in a specific case that encourages a company’s employees to carpool with their colleagues. The purpose of [10] is to identify what role should be assigned to each employee who is willing to join the carpool activity. However, this situation is impossible for implementation in a practical ICS system because users prefer to explicitly determine what a participant’s role will be. Besides, many studies of combinational optimization have proved that the complexity of an exact-type method increases exponentially as the number of instances (i.e., participants) increases [12], [28]. Therefore, the method based on integer programming in [10] and [11] is inefficient for application to large-scale problems. Note that Agatz et al. [11] provided a rolling horizon approach based on batch to cope with consistent requests. Evolutionary computations have been robust and effective tools in many optimization industries, such as transportation, 1 https://flinc.org/ 2 https://car.ma/ 3 http://www.zimride.com/ 4 http://www.side.cr/ 5 http://www.go2gether.ca/

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management, scheduling, and so on [13]–[18]. A prominent example is particle swarm optimization (PSO) that has had startling growth as a research paradigm in recent years [19]–[24], [27]–[34]. The development of PSO is based on a simple concept that imitates the social behavior of animals to determine effective solutions. Although the benefits of PSO include easy implementation and effective solution convergence due to its gained characteristics, it is natively developed for continuous problems and is also known as continuous PSO (CPSO) [19]. Most existing PSOs developed to solve discrete problems are operated in the continuous domain by converting continuous real values into discrete integer solutions. Some of these PSOs are used for well-known combinational problems such as task assignment problems, vehicle routing problem (VRP), permutation flow shop scheduling, and so on [22]–[24], [27], [28]. Nevertheless, the mathematical properties originally implied in values could be inordinately sacrificed during the process of continuous–discrete conversion, making these CPSOs inadequate in regard to discrete optimization problems. Another approach to use the binary coding scheme for discrete problems extends PSO to binary PSO (BPSO) [25], [26]. However, the binary coding conducts the particle to a sparse matrix in which most of the elements are zero and causes the evolution in a stagnant way to not effectively change the dimension value in binary domain. Therefore, the BPSO has limitations in many discrete optimization applications. Significantly, the work of [27] proposed a new DPSO called set-based PSO (S-PSO) that relies on two theorems of set and probability and treats the search space as a universal set. As such, this S-PSO uses a crisp subset contained in the universal set to equivalently represent the position of each particle (i.e., candidate solution) in discrete space. The S-PSO has succeeded in solving discrete problems like traveling salesman problem, multidimensional knapsack problem, and VRP, and its efficiency has been proved in [27] and [28]. Although the PSO has exhibited good performance in many test problems, it suffers from the problem of easily being trapped in local optimums while solving more complicated problems. Some researchers have introduced the addition of mutation operators into CPSO to improve performance by adopting different mutations for CPSO such as Cauchy mutation and Gaussian mutation [29]–[34]. These improvements to CPSO have been empirically investigated by testing the mathematical function optimizations and the constrained optimization problems that are more complex and closer to real-world requirements. These studies have made contributions that show that the CPSO combined with the mutation operators can aid the optimization performance and thereby avoid untimely CPSO stagnancy due to premature convergence. However, few studies exist that efficiently added the mutation into DPSO for solving discrete optimization problems, and no studies exist concerning the application of the concept of mutation to the novel S-PSO. In this paper, an improved S-PSO, called stochastic S-PSO (SS-PSO), is proposed to solve the combinational optimization problem in discrete space. We wisely develop the mutation operator formerly used for CPSOs by which to present the hybrid of S-PSO and mutation in discrete space, as well as alter the mutation operator as a robust scheme for particle

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view to advance the local exploration of particles. Lastly, our experiments were examined via various CSP benchmarks generated from actual traffic situations, and analyzed in respect to the performance and efficacy of the improved S-PSO. The rest of this paper is organized as follows. Section II presents background information including an overview of the ICS and problem formulation of the CSP. In Section III, the particle swarm-based carpool service algorithm (PSCSA) is proposed. Section IV includes the experimental results, comparisons, discussions, and analysis of the PSCSA. Finally, the conclusions are given in Section V. II. D ESCRIPTION OF S YSTEM AND P ROBLEM A. Overview of Intelligent Carpool System The ICS adopts the Web application hybrid, which establishes an automated system so that participants may effortlessly construct arrangements of drivers and riders by accessing the system via mobile device or terminal [5]–[8]. The fundamental resources used for the metrics of carpool matching can be retrieved from integrated services such as the geographic information, route planning, social reputation, and so on. A user has the option of assuming either the role of driver (carpool provider) or the role of rider (carpool demander). At anytime and any place, users who are active in the carpool system are allowed to announce ride offers and ride requests by submitting carpool inquiries to the carpool service in the ICS. The representation of each carpool inquiry (Q) has four parameters specifically defined as follows: Q = (qT , qO , qD , qN )

(1)

where qT indicates the type of identity this inquiry can be categorized as (driver or rider), qO is the original location of the driver (or passenger), qD is the destination of the driver (or passenger), and qN is the number of seats offered by the driver (or requested by the rider). In order to facilitate the usability of ride-share, the ICS is based on the automated matching mechanism and assists drivers and riders to find proper matches in a way that minimize user effort. This is an optimization process by which to organize the assignment, and is a difficult challenge, often referred to as the CSP. From a system-wide perspective, the optimization approach focuses on optimizing the entire community cost, taking into consideration factors like total vehicle miles, total reputation to each assignment, and so on. The travel cost savings of all assignments are considered individually, as well. The definitions of the CSP will be described in detail in the following section. B. Mathematical Formulation of Carpool Service Problem A ride-share assignment considering both driver–rider relationships and route planning for each vehicle is determined as the solution output to the CSP, which is a discrete optimization problem. The CSP can be described as follows: let D = {1, 2, . . . , m} denote a set of m drivers and R = {2m + 1, 2m + 2, . . . , 2m + n} denote a set of n riders. Each of the m drivers provides a given seat capacity (Ci , i ∈ D) and each of the n riders also has a given seat demand (sj , j ∈ R).

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Each driver owns a pair of two nodes that includes the original location and destination as follows: {vi , vi+m }, i ∈ D and a set of nodes owned by all drivers is: ND = ∪i∈D {vi , vi+m }. Each rider also has two nodes including the pick-up location and drop-off location as follows: {vj , vj+n }, j ∈ R and a set of nodes owned by all riders is: NR = ∪j∈R {vj , vj+n }. All drivers are to responsibly serve the allocated rider(s) by systematically traveling to all rider pick-up and drop-off locations. There is implied a natural constraint that each driver must depart from the original location to the destination, and in a manner that allows the driver to pick-up riders first and then drop them off later. A collection of vehicle routes for each driver can be defined as a graph problem, given an undirected network denoted as G = (N, E), where N = ND ∪ NR is the aggregations of all drivers’ nodes and all riders’ nodes, and E = {a, b| a = b, a ∈ N, b ∈ N} is the set of edges in which the travel distance of an edge is denoted as cab and cab = cba . The optimization of CSP has five objectives, and the objective functions are represented by two binary decision variables and an integer decision variable, which are defined as follows:  1, if i (i ∈ D) traverses the edge a, b i xab = (2) 0, otherwise  1, if j ( j ∈ R) is allocated to i (i ∈ D) (3) yij = 0, otherwise ziv : the order of traveling nodev by i (i ∈ D).

and

⎞ i j   1 E ·E ⎠ 1 f2 = α · ⎝EH − yij i m Mi E + Ej jR

1  i +β· · cab · xab m iD aN bN 1  1  i  i +β· · yj cab · xab m Mi i i iD

jR

aAj bAj

1  1  i  i +β· · yj cab · xab m Mi i i iD

jR

jR





yij ≤ 1,

iD yij · zivj

≤ yij · zivj+n ,

∀j ∈ R

(8)

∀i ∈ D, ∀j ∈ R

(9)

i xvv = 0, i

∀i ∈ D

(10)

xvi i+m v = 0,

∀i ∈ D

(11)

i xvv = yij , j

∀i ∈ D, ∀j ∈ R

(12)

xvi j v = yij ,

∀i ∈ D, ∀j ∈ R

(13)

i xvv = yij , j+n

∀i ∈ D, ∀j ∈ R

(14)

xvi j+n v = yij ,

∀i ∈ D, ∀j ∈ R

(15)

vNR ∪{vi+m }



vNR ∪{vi }



vNR ∪{vi ,vi+m }



vNR ∪{vi ,vi+m }



vNR ∪{vi ,vi+m }



vNR ∪{vi ,vi+m }







i∈D v {vj | j∈R}



i∈D v {vj+n | j∈R}

xvi i v = m

i = m. xvv i+m

(16) (17)

(5)

⎛

iD

 i Bij = {v|zivr ≤ ziv ≤ zivj+n , n ∈ NR }, M = jR yj , and the objective functions are subject to a collection of constraints that are: 1) the number of seats requested by riders is small or equal to the seats offered by drivers because capacity constraint; 2) each rider can only can be served by one driver; 3) drivers drop off allocated riders after picking them up; 4) drivers must start from their own original locations; 5) drivers always finish the carpool ride at their own destinations; and 6) vehicle routes that match each driver are required to be complete. After briefly describing the constraints, they are accurately denoted in mathematical form shown as follows:  sj yij ≤ Ci , ∀i ∈ D (7)

(4)

The prior optimal decision ( f1 ) is to maximize the total amount of matched riders (MRs) to drivers. Subsequent optimizations ( f2 ) maximize evaluation scores (ESs) to all driver– rider matches and minimize all distance terms that include an average driver travel distance (TDD), the average rider waiting distance (WDR), and the average rider travel distance (TDR). The conflicting nature of the match number and distance metrics in the CSP gives rise to sacrifices f2 for maximizing amount of MRs. The formulations that describe the optimal objectives for the CSP are shown as follows: f1 = φ

3

(6)

aBj bBj

where α and β are the tunable weights for balance of reliancerelated and distance-related terms in the importance decisions, φ is the total amount of MRs, and Ei expresses the user’s evaluation of the reliance of a ride-share match in which the value is ranged in a scale of 0 to EH ; the remaining variables are defined as: Aij = {v|ziv ≤ zivj , v ∈ NR ∪ ND },

III. P ROPOSED PARTICLE S WARM -BASED C ARPOOL S ERVICE A LGORITHM In this section, the SS-PSO for discrete space is proposed. The SS-PSO is an extension of the S-PSO, and includes a local search region by which to cleverly solve the CSP. It is referred to as the PSCSA. Our proposed PSCSA is comprised of two important modules, as shown in Fig. 1. These include: 1) swarm initialization (SI) and 2) swarm evolution (SE). The SI module consists of two procedures: 1) particle representation (PR) and 2) particle initialization (PI), and is designed to characterize the CSP as a candidate solution that indicates carpool match relationships between drivers and riders via a novel encoding scheme. This encoding scheme is a kind of stochastic coding that facilitates the representation of set-based particles with a regional view, also referred to the stochastic region. As such, the advantage of using this scheme is that each particle is endowed with a self-improvement ability. The SI module initializes the collection of candidate solutions to form a flock of particles called a swarm, which the SE module is manipulates via five

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Fig. 2. view.

Fig. 1.

Flowchart of the proposed PSCSA based on SS-PSO.

procedures: 1) particle conversion (PC); 2) particle evaluation (PE); 3) a set-based velocity update (SVU); 4) a global position update (GPU); and 5) a local position update (LPU). Initially, the SE module evaluates the particles in the form of a route, whereupon it imitates the behavior of bird-flocking to search for approximate optimal solutions to the CSP by rectifying the movements and velocities of all particles of the swarm during each iteration. Instead of the arithmetic operators used in a continuous domain, the set-based operators are applied to perform the particle updates. In particular, we propose a local search mechanism for set-based representation to improve the optimization results of primitive S-PSO. These processes are continually repeated, after which the proposed PSCSA will obtain a satisfactory matching solution for the drivers and riders in the ICS. A. Swarm Initialization 1) Particle Representation: Ride provision and requisition in the ICS are established on demand. The carpool inquiries in the pool of requests are characterized as a potential solution to the CSP via the PR that involves two set-based vectors: 1) particle position and 2) particle velocity, along with a real number vector: particle view. The representation of a particle’s position indicates a match solution to the CSP, and is comprised of a set of rider elements for each dimension. In order to portray the particle with the regional view, the particle’s position is associated with the variance vector in the PR. Hence, the position vector is viewed as a mean vector, which is called the particle position and is expressed as follows:

Particle Position: μk = μ1k , μ2k , . . . , μdk , . . . , μm (18) k μdk = {r | riderr is served by driverd } (19) where μk is a mean vector in discrete space with m dimensions that is derived from the number of drivers, each dimension

Visual illustration of the search process of a swarm with particle

μdk is a set of elements that belong to the universal rider set (UR ) containing all riders, and μdk denotes a carpool group composed of the riders served by driverd . The numerical representation of the variance vector denotes the regional view of the particle, which is called the particle view and is characterized by a multivariate normal distribution. Each component of the mean vector has a respective corresponding variance value in the variance vector. As such, the variance vector is expressed as follows:

Particle View: σk = σk1 , σk2 , . . . , σkd , . . . , σkm (20) where σk is a vector of m-dimensional real numbers, the variance value (σkd ) for each dimension is ranged from 0 to 1. A visual illustration of particle view is shown in Fig. 2. Regional view allows each particle to search a wider perspective during local exploration while the swarm is responsible for global exploration. This will allow the neighbor particles around the current optimum of each particle to be searched more thoroughly in each iteration. The set-based velocity vector, which is called the particle velocity, is very important for the conduction of the movement direction and evolution of a particle. For the update of a particle in a set-based formation, each velocity dimension represents the set in which each element is added with a probability. The expression of this velocity vector is shown as follows:

Particle Velocity: Vk = Vk1 , Vk2 , . . . , Vkd , . . . , Vkm (21) Vkd = {r/p(r)|r ∈ UR }

(22)

where Vk represents the velocity vector in the m-dimensional discrete space, and p(·) ∈ [0, 1] is a probabilistic function that indicates the probability that the rider element is selected from the UR during the process of velocity updating. 2) Particles Initialization: At the beginning of the optimization process, a collection of solutions representing the match result is initialized as a swarm. The initial position of each particle in the swarm is constructed by using both random and predetermined approaches in order to suitably cover the

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Fig. 3.

PR of the matching relationship.

Fig. 4.

PR of the route of a vehicle.

solution space of the CSP while the swarm gains high diversity. The random or predetermined selection is determined by a probability (ψp ). This initialization process of each particle consists of two steps: 1) the origin-destination pair for the driver is used for the driver’s route first and then 2) the origindestination pair of pickup and delivery locations of riders is inserted into the carpool route. For allocating the proper riders to the driver, it must be ensured that the two constraints of duplication and load restriction are not violated. As such, the other assignments are sequentially continued until all drivers reach maximum load. For the construction of the predetermined particle in particular, tour-building heuristics are employed to generate a highly promising solution by using the insertion heuristics [35] modified to suit the CSP, in which the specific insertion criteria is expressed as follows: c1 (r) = d(dO , rO ) + d(rO , dD ) − μ · d(dO , dD ) c2 (r) = d(rO , rD ) + d(rD , dD ) − η · d(rO , dD ) c3 (r) = d(dO , rO )

(23) (24) (25)

where d(a, b) indicates the distance from a to b, dO and dD are the origin-destination location of the driver, rO and rD denote the origin-destination location of the rider, μ ≥ 0 and η ≥ 0 are the saving strengths of distance, and c1 , c2 , and c3 are summed up in a weight equation as: c( j) = α1 c1 ( j) + α2 c2 ( j) + α3 c3 ( j), α1 + α2 + α3 = 1. The random approach is utilized to initialize each dimension of velocity owned by each particle of the swarm as the initialization of a particle’s velocity does not affect the performance of an S-PSO [27]. As such, the velocity initialization includes random selection of a set of riders from the universal rider set (UR ) in which each rider has a random probability that is subject to [0, 1] and the probability of the others in the UR is set to 0.

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B. Swarm Evolution 1) Particle Conversion: Based on the representation of the proposed particle, the structure of the particle’s position is depicted by means of visual illustration to take the example shown in Fig. 3, which depicts a match solution for each component of the m-dimensional position vector. It demonstrates that a ride-share driver is matched with riders where rider3 , rider13 , and rider18 are assigned to driver1 , and rider27 and rider32 are assigned to driver2 , and so on. In CSP, the objective of all carpool participants concentrates on minimization of the total travel distance to get satisfactory match. For this reason, the particle’s position is extended from the driver–rider matching relation to include supplementary representation of the travel route. As such, the particle’s position provides exact information about the vehicle route necessary for picking up and dropping off riders. Fig. 4 is an advanced illustration of the particle used in the previous example (see Fig. 3), and illustrates the vehicle route guidance where the first dimension of the particle demonstrates that driver1 will rely on the sequence of rider18 and rider13 to pick up all MRs, and drop off same group of riders in accordance with the sequence of rider13 and rider18 . Finally, driver1 picks up and drops off rider3 to complete the assigned task. In regard to a route from the particle, the Bellman optimality is capable of locating a good routing solution [36]. The routing resolution process for each driver is broken down into a collection of simply recursive subforms, the mathematical expression of which is shown as follows: Td (ω) = min {c(nω , nω−1 ) + Td (ω − 1)} nω

nω ∈ O(ω) ∪ D(ω)

(26) (27)

and the initial condition is Td (0) = min {c(n0 )} n0 ∈O(0)

(28)

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where Td (ω) is a recursive function by which to estimate the travel distance from nodes n0 to nω , c(h, k) is used as a cost function of travel distance of edge(h, k), ω ∈ {1, . . . , 2·|MRd |} is a positive integer that indexes the node, and MRd represents the group of riders matched with driver, O(ω) is a set of the locations at which the driver picks up the allocated riders, and D(ω) is also a set of the destinations of riders allocated to driver. The resolution process starts from the initial condition Td (0) in which the function c(n) returns the travel distance that spans from the origin of driver to node n. The procedure for route generation involves moving the origin-destination pair of riders and the resultant route (RNd ) to conduct en-route the driver through the ride-share process. 2) Particle Evaluation: After obtaining the route information from a particle’s position via PC, each particle is then quantified into a fitness (Fk ) that will reflect the optimization quality upon both respective dimensions and entire particle. As such, the objective function for the fitness is defined as follows: Fk = fks + fku fks = |UR | − |MR| 1  fku =

d + d + d |D|

(29) (30) (31)

d∈D

where fks is expected to be minimized in order to boost the total number of MRs from system-wide perspective, i.e., the prior objective ( f1 ), MR ⊆ UR is a set that possesses a flock of MRs, fku optimizes each dimension from user perspective and improves not only the sequent objective ( f2 ) but also prior objective, d improves user reputation to be maximized; d contributes to the distance-related terms of the CSP to be minimized, in addition to optimization of the sequent objective ( f2 ), d considers the number of seats offered by driver to make sure the car is occupied efficiently to facilitate f1 to be optimized further, and the expressions and explanations of d ,

d , and d are shown as follows: ⎧ 1, if |MR ⎪ ⎪ ⎛d | = 0 ⎞ ⎨ d · Ep  2 E 1 (32)

d = ⎠ · tan−1 ⎝EH − ⎪ ⎪ ⎩π |MRd | Ed + Ep pMRd ⎧ 2 ⎪ ⎪ · tan−1 (Td + Tbase ), if |MRd | = 0 ⎪ ⎨π ⎤ ⎡  d = 2 (33)   1 ⎪ −1 ⎣T + w + Tt ⎦ ⎪ · tan T d ⎪ p p ⎩ |MRd | π p∈MRd

d = Cd − |MRd |

(34)

where D = {d1 , . . . , dm } has all driver entities, MRd contains all MRs in regard to driver, Cd is the number of seats offered by driverd , Ei denotes user reputation to either driver or rider, Td , Tpw , and Tpt ∈ R is computed by using RNd and represents the total travel distance of driverd , and the waiting distance and the riding distance of each MR, i.e., passenger p,  Tbase is subject to the condition: Tbase (1/MRd ) p∈MRd (Tpw +Tpt ), ∀d ∈ D to penalize a situation that driver is matched without any riders because it causes an exception of treating rider-related distances to be shortened, and both d and d

uses an arctangent function that normalizes all user reputations and distances in the interval [0, 1], note that the d and d via normalization reduce degree of change compared with d and fks . As such, the particle search has high priority for f1 and then makes improvement in f2 . The PE procedure is performed in order to ensure optimization of all objectives of the CSP based on both match and routing results implied in the particle. 3) Set-Based Velocity Update: Particle velocity updating uses the comprehensive learning PSO (CLPSO) [37] and is a standard PSO with modified search behavior. The CLPSO learns from different dimensions of other particles in order to increase the population diversity of the swarm, so that it can avoid becoming trapped in the local solution. The velocity update of the CLPSO to apply in S-PSO is shown as follows:   Vkd = w · Vkd + c · randd · pbestdindexk (d) − Xkd (35) where w is the inertia weight, c is the acceleration coefficient, randd is the random numbers of the dth dimension the is uniformly distributed in the interval [0, 1], pbestdk represents the dth dimension of the best particlek so far, Vkd and Xkd are the velocity and the position of particle, respectively, and indexk (d) is a function by which is returned the index of that particle or another particle. The dimension of the particle will learn from its own pbest if the random number is larger than the decision probability (Pc ); otherwise, it will learn from the pbest of the other particles determined by the tournament selection. In addition, since the proposed SS-PSO is based on an S-PSO, all arithmetic operators of standard velocity equation are replaced with new operators so that it can exert the velocity update on a particle. As such, the particles are able to find the optimal solution to the CSP in the discrete search space. In the S-PSO, the operators related to velocity are performed by updating the probability. Similarly, the operators related to position are performed by using set subtraction and appending a probability to the element. The set-based operational rules are defined as follows: ω · Vkd = { r/pω (r)|r ∈ UR }  Vωd (36)     / Xbd  Vcd c · randd · Xad − Xbd = r/pc (r)|r ∈ Xad and r ∈ (37)     Vωd + Vcd = r/max pω (r), pc (r) r ∈ UR (38) where pω (r) is equal to 1 if ω · pω (r) > 1; otherwise, it is directly set to ω · pω (r); pc (r) is equal to 1 if c · randd > 1; otherwise, it is directly set to c·randd . Eventually, the addition of two terms, which are Vωd and Vcd , remains the maximal probability of accomplishing the velocity update on the dth dimension. 4) Global Position Update: After the particle velocity is updated, it proceeds to update the particle’s position by the update formula that is denoted as μ˜ dk = μdk + Vkd in our form of symbolic notation. As such, the operation will perform on every individual dimension to update the velocity vector (μk ) as a new vector (μ˜ k ). To update of set-based position on a global scale of search space, three crisp sets are used and

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symbolized by the velocity crisp set (Cv ), the position crisp set (Cp ), and the universal crisp set (CU ), respectively. The CU is produced by using all elements of the UR . It is apparent that CU contains whole rider elements to have random variations because the new elements are not derived from the established elements in Cv and Cp . The CU is defined as follows: CU = {r|r ∈ UR }. All elements of μk are assigned to Cp and play a critical role in maintaining the contribution of the previous  particle’s position. The Cp is defined as follows: Cp = μd ∈μk {r|r ∈ μdk }. In addition, the particle’s k velocity is also involved in the position progression update via Cv . However, the Cv differs from the CU and the Cp and thus cannot be directly taken as the set inclusion of new particle’s velocity. Instead, the Cv can probabilistically determine its elements by using the probability of each element that is in the Vk . The special process for constructing the Cv is conducted in a way in which the element will be placed in the Cv if a random number, which is limited to the interval [0, 1], is larger than the probability of the element. As a result, the definition of the Cv is shown as follows:     r ∈ Vkd and rand > p(r) . (39) r  p(r) d Vk ∈Vk

Due to the representation of a set-based particle’s position, the “+”-operator in the formula for the position update is operationally modified as the pseudo-code shown in Fig. 5. The update is performed by applying three principal steps: 1) an empty position set (μ˜ dk ) is first built; 2) several elements (r ∈ UR ) are chosen from among three crisp sets; and 3) these elements are added into the μ˜ dk so that a new group of riders is organized to generate potential carpool matches. Selection priority of the crisp sets has a hierarchical configuration specified as follows: Cv , Cp , and CU . New elements are selected from the Cv until the Cv is empty. After the Cv is completely exhausted, it will turn to choose elements of the Cp . If a new element is unobtainable from the Cv and the Cp , then the elements are chosen from the CU . Note that this process of set-based position update could meet its end as soon as the load restriction of the driver in the CSP is met. Moreover, we apply an additional scheme called superior component selection to confirm the effectiveness of the particle update. According to the measurement of the dimension’s fitness via (31), the particle’s position may or may not be renewed. If the μ˜ dk is superior to the μdk , the μ˜ dk is chosen instead; otherwise, the original position μdk is maintained in this update process. Therefore, this scheme is able to reduce the movement drift of particles in each dimension by passing the good traits (i.e., dimensional component) to next iteration of the PSO. That is to say, it ensures that the driver–rider matches implied in each particle do not revert to inferior results. 5) Local Position Update: After the global update adjusts a particle toward the best position found by it or other particles, the LPU is allowed to continue the process of self-improvement. After the global update, each dimension, μ˜ dk , of a particle’s position in the new vector (μ˜ k ) is used in the local

Fig. 5.

Pseudo-code of the GPU in a given dimension.

update phase. The random variable vector (Xk ), which is distributed normally with the mean vector and the variance vector, represents a feasibly promising particle as follows:

Xk = Xk1 , Xk2 , . . . , Xkd , . . . , Xkm (40)   Xk ∼ N μ˜ k , σk 2 (41) where μ˜ dk denotes the mean vector, and σk is the variance vector that facilitates the particle exploration of the neighborhood inside its own view, and Xk is a multivariate random variable whose components are set-based random variables distributed 2 on Xkd ∼ N(μ˜ dk , σ dk ); μ˜ dk ∈ μ˜ k is a position set that represents a driver–rider match produced by the GPU procedure, and σkd ∈ σk is a variance. The normal distribution extends from continuous space to discrete space in order to use it for set-based representation. Fig. 6 describes the different loci of a bell curve while retaining normal distribution. In this case, “ABC” is arrowed by the locus of the middle point has the highest probability; this is because we wish the position set (i.e., μ˜ dk ) to be maintained with high probability. With a decreasing curve on either side, the number of possible maintained elements are reduced; these include “AB∗ ” that maintains two elements, “A∗∗ ” that maintains one element only, and so on. When the distribution reaches the end of curve, all possible elements become unfixed and can be arbitrary. As such, the idea of normal distribution is available for each dimension of a particle’s position in the set-based space. A random variable will be generated from each corresponding distribution and will be regarded as a new promising dimension of position by the generating function. The operators of

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Fig. 8. Fig. 6. Normal distribution tailored to the discrete set-based space (the asterisk is a wildcard that represents a set containing zero elements or more).

Three spatial structures and nine spatial transitions in a metropolis.

in μ˜ dk and the complement set, SRc , and is initialized to a difference set of UR and all μ˜ dk . Then, the diversity of SRc will be determined according to random number and variance and its diversity is high if variance value is large; otherwise is low. The operation will select the candidate elements from SRc , SR and UR one by one and added to the μ¯ dk to form a new d-dimensional position set of the particle until μ¯ dk finally reaches the load restriction. By repeating the process of function generation, a collection of promising dimensions enters a fitness competition and determines the final result. Then, the best dimension will become a new component in the position of the d-dimensional particle, as follows: Xkd = arg min f (x) x ∈ Cd

  Cd = {xτ | 1 ≤ τ ≤ τmax } ∪ μ˜ dk

(43) (44)

where Cd denotes a set that includes a collection of dimensions generated from normal distribution and the original dimension (μ˜ dk ) is generated from the GPU, τmax is a predefined parameter that sets the maximum number of produced dimension entities that in turn controls the intention of a particle’s exploration, and f (·) is the fitness function dedicated to the dimension evaluation of (31). Fig. 7. Pseudo-code of the generating function tailored to the S-PSO of the LPU procedure.

the generating function are redefined in order to be applicable to the set-based particle, and we rewrite the generating function as follows: μ¯ dk = μ˜ dk + Dk · σkd

(42)

where μ˜ dk is the mean of normal distribution in the dth dimension, and σkd is the variance of normal distribution in the dth dimension to determine the diversity of the new element set. The Dk uniformly ranges from 0 to 1, and accomplishes the normal distribution; in other words, the new element set will diverge from the mean set if the randk is closer to one. The pseudo-code of this procedure is shown in Fig. 7, and two sibling sets, SR and SRc , are involved; SR contains all elements

IV. E XPERIMENTAL S TUDIES A. Tested Benchmarks of CSP Problem Under Actual Environment Our experimentation was performed using benchmarks that feature human behavior in metropolitan areas. The behavior of transit movement within a metropolis can be represented by the metropolitan movement model. As shown in Fig. 8, the movement model can be distinguished as three spatial structures: 1) the urban core; 2) the intermediate area; and 3) the suburban area, and contains nine spatial transitions to specify the commuting modes of residents and movement behaviors in the metropolis [38], [39]. These spatial transitions have varied directionalities illustrated by arrow shape and described as follows. T1: Inner transition. T2: Intermediate transition. T3: Outer transition.

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TABLE I B ENCHMARK DATASETS FOR P ERFORMANCE C OMPARISON

T4: Outbound transition from the urban core to the intermediate area. T5: Inbound transition from the intermediate area to the urban core. T6: Outbound transition from the intermediate area to the suburban area. T7: Inbound transition from the suburban area to the intermediate area. T8: Outbound transition from the urban core to the suburban area. T9: Inbound transition from the suburban area to the urban core. In most advanced countries, metropolises usually feature three moving configurations and peripheral zones, which we used in our experimental scenarios in order to accurately represent the real world. Via the utilization of the movement model, three representative configurations are described as follows. C1: Inward radiating movement (CI) configuration is typified by the following situation: commuters, such as employees and students, usually leave for work or school from their own homes each work day. Thus this configuration features transitions of the T5 and the T9 in relatively high proportions relative to others. C2: Lateral drifting movement (CL) configuration is typified by the following situation: employees in some industries like salesmen and delivery men often move to different places throughout their work-days. Thus, this configuration has a high proportion of T1 and T2 in comparison to the others, and the T1 tends to preponderate over the T2. C3: Outward radiating movement (CO) configuration is typified by the following situation: commuters in the evening or at night return to residential areas commonly surrounding the urban core. Thus, the proportion of the two outbound transitions of the T4 and the T8 are higher than the others in this configuration. In our experiment, we examined all compared methods by testing their respective performances via benchmarks captured from the actual environment in Taipei, the capital

city of Taiwan. The Taipei City Government Department of Transportation (TCDOT) gathers traffic statistics continuously for Taipei and performs statistical analysis that reveals the monthly conditions regarding all transportation usage [40]. We referred to the historical traffic records provided by TCDOT to produce the tested benchmarks used for the metropolitan movement model. For the experimental scenarios, three aforementioned moving configurations were used. Each type of configuration has special prefixes—CI, CL, and CO—which represent the inward radiating movement, lateral drifting movement, and outward radiating movement, respectively. As shown in Table I, all the benchmarks include both large instances (i.e., participant) to simulate peak hours and small instances by which to evaluate the different levels of problem. Two categories of additional benchmarks with varied attributes also are provided: 1) F-class and 2) V-class. The V-class benchmarks were chosen to have simulations with specific attributes in which participants’ seats feature high variance relative to the F-class. B. Experimental Settings of Comparison Methods All implemented algorithms were programmed in C# language executed under Microsoft .Net Framework 4.0 and on a server-level machine with an Intel Xeon 2.27-GHz CPU, 6-GB RAM, and a Windows Server 2008 operating system. Both PSO and genetic algorithm (GA) are two well-known algorithms and are examined in-depth in this paper. Two types of discrete PSOs, including BPSO and S-PSO, are used in discrete space. It is a novel approach for reliance on the theorem of an S-PSO in our proposed PSCSA, was compared with BPSO and GA, and is the focus of our investigation and observation. The following parameters are used in both discrete PSOs, including our PSCSA and BPSO: swarm size = 20, ψp is set to 0.5 to initialize the swarm with both predetermined and random traits, w = 0.9, c = 2.0, and tmax is set to 1000 to ensure that all discrete PSOs are not terminated until the

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TABLE II C OMPARISONS OF A LL M ETHODS FOR THE M AJOR O BJECTIVE OF MR

1000th iteration. The implementation of BPSO to solve the CSP problem is based on state-of-art BPSO research [20], [21], the details and characteristics of which are briefly described as follows: the velocity is updated by the conventional rule as V ← w · V + c1 · rand · (pbest − X) + c2 · rand · (gbest − X), in which it can be noted that the global optimal particle is reserved and utilized in the optimization process. In BPSO, the transfer function is a concept based on probability to update the positions in a binary space, and a sigmoid function, called S-shaped transfer, is employed to map velocity values to probability values for updating the positions. To represent a complete solution of CSP in binary, an m ∗ n matrix is used to indicate which passengers are matched with each driver, respectively. The driver–passenger mapping matrix is denoted as follows: ⎡ ⎤ M0,0 ··· M0,n−1 ⎢ .. ⎥ .. .. (45) ⎣ . ⎦ . . Mm−1,0

···

Mm−1,n−1

m×n

where Mi,j , which forms a match of driver i and passenger j, is 1 if it is true and 0, otherwise. As such, the matrix is linearly sketched as an m∗n dimensional particle to achieve BPSO evolution in binary space. In addition, the GA is generally used to solve discrete problems. The parameters and genetic operations are applied in the GA as follows: population size = 30 to allow a comparatively large size in contrast to the compared PSO-based methods, ψp = 0.5, uniform crossover is assigned a probability of 0.9, single-point and swap mutations are assigned probabilities of 0.5, and the maximal generation = 1000. Also, all operational procedures of the population initialization, chromosome representation, and solution evaluation in GA are accomplished as described in the section of this paper defining the proposed PSCSA. It is worth noting that the chromosome is similar with our particle structure that is well-suited representation to aid the carpool solution within the search operation. C. Discussion of the Results to Two Optimal Objectives In this section, we describe the results of the experiments and perform comparisons between all compared methods as

follows: 1) PSCSA; 2) BPSO; and 3) GA, with the parameters as described in the previous section. The statistical performances of the 30 independent test-runs are listed in Tables II and III. The tables demonstrate the numerical analyses, including the comparison metrics of the five optimal objectives to the CSP problem as: the prior optimization maximizes the total number of MRs to drivers (MR); the subsequent optimization maximizes the ESs of all driver–rider matches and minimizes all distance terms such as the average TDD, the average WDR, and the average TDR. Through our analyses, it can be seen that our proposed method achieves excellent results for the CSP problem. 1) Optimization of Major Objectives: The major objective of the CSP is MR (i.e., the number of MRs), which is expected to be maximized in a system-wide perspective in order to effectively find all promising carpool matches. From the results presented in Table II, the effectiveness of the S-PSO concept is demonstrated by comparing it to BPSO and GA; as such, it is very evident that the our PSCSA is superior to BPSO and GA. During BPSO evolution, the binary representation usually conducts the solution to a sparse matrix in which most of the elements are zero, and it causes the evolution in a stagnant way to not effectively change the dimension value of particle solution in binary domain. As a result, BPSO has more difficulty maximizing the number of MRs compared with our PSCSA and GA because of binary representation for suitability of a CSP solution. Considering PSCSA and GA contrast in contrast to BPSO, they employ well-suited representation for CSP to achieve highly effective evolution operation. However, GA, operating on an element set given in initialization phase for evolved population, confines itself to the recombination of immutable elements, and thus it will reduce GA exploration of new and promising genomes. For these reasons, we chose to apply the S-PSO to solve the complicated problem that is the focus of this paper. Thus, it can be seen that the proposed PSCSA exhibits the best optimization performance and yields the maximal MR consistently regardless of the number of instances in a given dataset. Furthermore, there is a particular benchmark and it features 500 users consisting of 200 drivers and 300 passengers, mean seat number of 5 with variance of 3, and a CI-type pattern to simulate a harder scenario for markedly presenting the self-comparison of PSCSA. A comparison of the results obtained using our SS-PSO and the S-PSO demonstrate the outstanding capacity of MR to supersede the original S-PSO. As shown in Table IV, it can be observed that the original S-PSO has difficulty maximizing the number of MRs compared with SS-PSO regarding to the benchmark, the offered seats-property of which has high an STD value and a large number of carpoolers. In our LPU procedure, the sampling set, SR , facilitates stochastic exploration of local particles that contain partial modifications of the original particle, and an SR tailored to the CSP to help avoid the application of duplicate rider elements that have existed in other matches so that it will make an attempt on the usage of unexploited rider elements. Therefore, the LPU procedure can produce more promising solutions. Moreover, the experimental results prove

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TABLE III C OMPARISON OF A LL M ETHODS R EGARDING THE M INOR O BJECTIVES OF ES, TDD, WDR, AND TDR

that the proposed LPU procedure enhances the performance of the S-PSO in solving the CSP benchmarks. 2) Optimization of Minor Objectives: The minor objectives to be maximized are ES for high reliance of ride-share matches; TDD, WDR, and TDR will be minimized to provide distances for participants that are as short as possible. The optimization of major objectives minimizes the collections of minor objectives due to conflicts between major and minor objectives. It causes all distance results of all compared methods to increase if their results regarding major objective are improved. Based on observations of major objectives for all benchmarks, the F-class benchmarks can be properly used for our PSCSA. Therefore, we first focus on the comparison of the F-class benchmarks to eliminate the conflicting impacts on the numerical results produced by optimizing all the minor objectives. From the results tabulated in Table III, it can be seen that the statistical performance metrics for the F-class reveal that BPSO and GA do not reflect desirable results for the minor objectives in contrast with PSCSA. For the comparison of F-class between our PSCSA, BPSO, and GA, it can be observed that all the distance-related metrics of the PSCSA has lower values than do BPSO and GA. And the users’ reliance score of the PSCSA has a higher value than do those of the BPSO and GA. In addition, Table III also includes a V-class dataset and other benchmarks. Its results regarding CI102V1, CI303V2, CL107V1, CL306V2, CO104V1, and CO309V2 show that BPSO and GA have smaller values than our PSCSA in respect to distance-related metrics; and unfortunately, neither BPSO nor GA effectively optimize the CSPs major objective regarding these above benchmarks. We also observed the same CI500 benchmark as mentioned in last section. As shown in Table IV, the self-comparison of our PSCSA reveals that, for all minor objectives, the values of SS-PSO had lightly larger than S-PSO does, but SS-PSO still were close to S-PSO while S-PSO has inferior value of major objective. 3) Nonparametric Statistical Test to Show the Significance of SS-PSO: A nonprobability scheme to compare the overall performance of any two methods involves using the

TABLE IV S ELF -C OMPARISON OF O UR SS-PSO AND S-PSO IN A M ORE D IFFICULT S CENARIO T HAT F EATURES H IGH U SER I NSTANCE AND H IGH S EAT VARIATION

TABLE V S TATISTICAL T EST FOR I MPROVING S IGNIFICANCE B ETWEEN SS-PSO AND OTHER M ETHODS FOR M AJOR O BJECTIVE OF CSP

nonparametric statistical test in which the difference between the performance scores of the two algorithms via each benchmark is ranked according to their absolute values [41]. This section discusses the fitness values derived through statistical tests, as well as major and minor objectives, for verification of the significance of the performance results of our PSCSA. Tables V and VI summarize the performance of all compared methods in terms of the major and minor objectives, as determined in a nonparametric statistical test using the same dataset. Table V shows that the rank-sum (i.e., R+ and R− ) and significance levels (see p-values and α) based on the major objective are calculated for pairwise comparisons of PSCSA and the other methods. Regarding the major objective, R+ represents the sum of ranks for the benchmarks in which PSCSA is better than the method with which it is compared, and R− represents the sum of ranks for the benchmarks where PSCSA performs worse than the method with which it is compared owing to maximization of f1 . It can be seen that PSCSA achieves significantly better results, with levels of significance at α = 0.1 and α = 0.2. Moreover, Table VI lists the rank-sum and significance levels of all compared methods in terms of performance in computing the minor objective.

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TABLE VI S TATISTICAL T EST FOR I MPROVING S IGNIFICANCE B ETWEEN SS-PSO AND OTHER M ETHODS FOR M INOR O BJECTIVES OF CSP

TABLE VII S TATISTICAL T EST FOR I MPROVING S IGNIFICANCE B ETWEEN SS-PSO AND OTHER M ETHODS FOR F ITNESS VALUE

Note that for the minor objective, R− indicates that PSCSA is superior, and R+ indicates that PSCSA is inferior. This is because f2 is always expected to be minimized. In our case, judging by the results of PSCSA versus GA, R− was higher than R+ , and thus, we concluded that PSCSA outperforms GA by α = 0.7. As already indicated, PSCSA is superior to BPSO in terms of the significance level (α) of f1 ; therefore, it takes into account the fact that R− was lower than R+ in terms of comparison of PSCSA to BPSO. Table VII summarizes the results of a global performance comparison of fitness values for both major and minor objectives. The identical statistical tests entail comparison of the fitness values computed by all methods for the major objectives. The search processes of all methods aim at minimizing the expected fitness value. PSCSA has an extremely significant performance advantage over BPSO and GA. The fitness function defined in (29)–(34) considers two optimal decisions with dissimilar priorities where the importance of the major objective is greater than that of the minor objective during the search process. A comparison of the fitness values of all methods confirms that our fitness function is well suited for optimizing the major and minor objectives. V. C ONCLUSION This paper proposes a proposed method by which to solve the CSP that is an automated process built into the ICS. Our method is called the PSCSA and offers appropriate ridematches to carpool participants in which all matches have low distance costs and high user reputation. Improved S-PSO (improved S-PSO), called SS-PSO, is proposed to solve the CSP in the discrete domain, and includes two main modules as follows: 1) SI characterizes the solution of the CSP by the representation of set-based particles and uses both random and predetermined approaches to strategically initialize the swarm and 2) SE evaluates the whole swarm by which to search for the CSP optima iteratively. It is worth noting that the SI introduces the concept of stochastic coding to enhance the particle’s endowment by adding a variance vector to simulate the particle view. The particle position is thus viewed as a mean vector to collaborate with particle view.

As such, each particle can feature self-improvement to locally explore the neighborhood. In SE, each particle in the swarm is evaluated in terms of PR that expresses the ride-matches for each dimension so that it is able to consider not only the fitness of its respective dimensions but also the fitness of its entirety. Next, each particle is updated both globally and locally via two particle update procedures. The first update utilizes population information to perform a global update that uses set-based operators to enable the update of set-based particles. The second update makes each particle induce self-improvement via local exploration, which introduces the thought of mutation to S-PSO and the two aforesaid vectors: 1) mean vector (i.e., particle position) and 2) variance vector. These are applied to support the local particle update in S-PSO. Also, the exploring intension of the local update of the particle can be optionally adjusted under the constraints of the problem. Two discrete PSOs, S-PSO and BPSO, along with a GA are compared in this paper, and all of which had similar set-up in order for fair comparison. All the tested benchmarks feature a metropolitan area with actual transportation movement, and have three representative configurations demonstrated by the metropolitan movement model. From the results of actual simulations with the tested benchmarks, our PSCSA proves superior not only in regard to the major objectives of the CSP, but also its minor objectives. The performance of our method effectively maximizes and minimizes the major and minor objectives, respectively. R EFERENCES [1] B. Brunekreef and S. T. Holgate, “Air pollution and health,” Lancet, vol. 360, pp. 1233–1242, Oct. 2002. [2] N. D. Chan and S. A. Shaheen, “Ridesharing in North America: Past, present, and future,” Transp. Rev., vol. 32, no. 1, pp. 93–112, 2012. [3] J. Saranow, “Carpooling for grown-ups high gas prices, new services give ride-sharing a boost, rating your fellow rider,” Wall Street J., 2006. [Online]. Available: http://www.wsj.com/ articles/SB113884611734062840 [4] A.-J. Fougeres, P. Canalda, A. Samaali, T. Ecarot, and L. Guglielmetti, “A push service for carpooling,” in Proc. IEEE Conf. Green Comput. Commun., Besançon, France, Nov. 2012, pp. 685–691. [5] M.-K. Jiau and S.-C. Huang, “Services-oriented computing using the compact genetic algorithm for solving the carpool services problem,” IEEE Trans. Intell. Transp. Syst., vol. 16, no. 5, pp. 2711–2722, Oct. 2015. [6] M.-K. Jiau, S.-C. Huang, J.-N. Hwang, and A. V. Vasilakos, “Multimedia services in cloud-based vehicular networks,” IEEE Intell. Transp. Syst. Mag., vol. 7, no. 3, pp. 62–79, Sep. 2015. [7] S.-C. Huang, M.-K. Jiau, and C.-H. Lin, “Optimization of the carpool service problem via a fuzzy-controlled genetic algorithm,” IEEE Trans. Fuzzy Syst., vol. 23, no. 5, pp. 1698–1712, Oct. 2015. [8] S.-C. Huang, M.-K. Jiau, and C.-H. Lin, “A genetic-algorithm-based approach to solve carpool service problems in cloud computing,” IEEE Trans. Intell. Transp. Syst., vol. 16, no. 1, pp. 352–364, Feb. 2015. [9] N. Agatz, A. Erera, M. Savelsbergh, and X. Wang, “Optimization for dynamic ride-sharing: A review,” Eur. J. Oper. Res., vol. 223, no. 2, pp. 295–303, 2012. [10] R. Baldacci, V. Maniezzo, and A. Mingozzi, “An exact method for the car pooling problem based on Lagrangian column generation,” Oper. Res., vol. 52, no. 3, pp. 422–439, 2004. [11] N. A. H. Agatz, A. L. Erera, M. W. P. Savelsbergh, and X. Wang, “Dynamic ride-sharing: A simulation study in metro Atlanta,” in Proc. 19th Elsevier Int. Symp. Transp. Traffic Theory, vol. 17, Berkeley, CA, USA, Jul. 2011, pp. 532–550. [12] B.-B. Li, L. Wang, and B. Liu, “An effective PSO-based hybrid algorithm for multiobjective permutation flow shop scheduling,” IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 38, no. 4, pp. 818–831, Jul. 2008.

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[37] J. J. Liang, A. K. Qin, P. N. Suganthan, and S. Baskar, “Comprehensive learning particle swarm optimizer for global optimization of multimodal functions,” IEEE Trans. Evol. Comput., vol. 10, no. 3, pp. 281–295, Jun. 2006. [38] B. Meng, L. Zheng, H. Yu, and G. Me, “Spatial characteristics of the residents’ commuting behavior in Beijing,” in Proc. IEEE Int. Conf. Geoinformat., Shanghai, China, Jun. 2011, pp. 1–5. [39] M. O. Asikhia and F. N. Nkeki, “Polycentric employment growth and the commuting behaviour in Benin metropolitan region, Nigeria,” J. Geogr. Geol., vol. 5, no. 2, pp. 1–17, 2013. [40] Taipei City Traffic Engineering Office. [Online]. Available: http://www.bote.gov.taipei/, accessed Feb. 3, 2016. [41] J. Derrac, S. García, D. Molina, and F. Herrer, “A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms,” Swarm Evol. Comput., vol. 1, no. 1, pp. 3–18, 2011. Sheng-Kai Chou received the B.S. degree from the National Taipei University of Technology, Taipei, Taiwan, in 2014, where he is currently pursuing the Ph.D. degree with the Department of Electronic Engineering. His current research interests include evolutionary computations and digital image processing.

Ming-Kai Jiau received the B.S. and Ph.D. degrees in electronic engineering from the National Taipei University of Technology, Taipei, Taiwan, in 2012 and 2015, respectively. He is currently a Post-Doctoral Researcher and an Adjunct Assistant Professor with the National Taipei University of Technology, and also the CEO of BlueNet Technology Inc., Sunnyvale, CA, USA. His current research interests include evolutionary computations, fuzzy systems, artificial intelligence, social network, computer vision, embedded systems, and applications of cloud technology. Dr. Jiau was a recipient of the Sayling Wen Doctoral Dissertation Award in 2015 by the Service Science Society of Taiwan. Shih-Chia Huang (SM’14) received the doctorate degree in electrical engineering from National Taiwan University, Taipei, Taiwan, in 2009. He is a Full Professor with the Department of Electronic Engineering, National Taipei University of Technology, Taipei, and an International Adjunct Professor with the Faculty of Business and Information Technology, University of Ontario Institute of Technology, Oshawa, ON, Canada. He has published over 40 journal and conference papers and holds over 30 patents in the U.S., Europe, Taiwan, and China. His current research interests include image and video coding, wireless video transmission, video surveillance, error resilience and concealment techniques, digital signal processing, cloud computing, mobile applications and systems, embedded processor design, and embedded software and hardware codesign. Dr. Huang was a recipient of the Kwoh-Ting Li Young Researcher Award in 2011 by the Taipei Chapter of the Association for Computing Machinery, the Dr. Shechtman Young Researcher Award in 2012 by the National Taipei University of Technology, and the Outstanding Research Award from the National Taipei University of Technology in 2014 and the College of Electrical Engineering and Computer Science, National Taipei University of Technology in 2014–2015. He is an Associate Editor of the Journal of Artificial Intelligence, and a Guest Editor of the Information Systems Frontiers and the International Journal of Web Services Research. He is also the Applications Track Chair and the Program Committee Chair of the IEEE BigData Congress and the IEEE BigData Taipei Satellite Session in 2015, and was the Program Committee Chair of the IEEE BigData Taipei Satellite Session in 2014. He is currently the Chair of the IEEE Taipei Section Broadcast Technology Society. He is a Review Panel Member of the Small Business Innovation Research Program for the Department of Economic Development of Taipei City and New Taipei City, respectively.