Completion of FCVRP using Hybrid Particle Swarm Optimization Algorithm

Recently, the government and business players have increased their awareness of green logistics in the industrial sector [1]. The background of concern is based on the fact that logistics activities cause significant negative impacts on the environment [2]. Transportation is the most critical element in logistics and infrastructure fundamental to economic growth [3]. However, transportation also contributes to a large part of overall pollution [4]. In the last few decades, scientists have revealed that transportation activity causes an increase in Green House Gas (GHG) in the atmosphere [5]. Thus, the industrial sector's logistic policies need to consider environmental and ecological effects and focus on economic aspects. According to Poonthalir and Nadarajan [6], fuel consumption in transportation activities is an essential parameter in controlling GHG. One of the main parameters affecting fuel consumption is the weight of load [7]. According to the US Department of Energy, Wang and Kuo [8] stated that fuel consumption increased by 2% for each additional 100-pound capacity. So that in this situation, logistics activities require a ARTICLE INFO ABSTRACT

The issue of green logistics has received full attention from the government and business people. It is closely related to the increase in Green House Gas (GHG) by transportation activities in the logistics sector. Controlling fuel consumption in transportation activities is fundamental in dealing with GHG. Therefore, the Fuel Consumption Vehicle Routing Problem (FCVRP) is proposed as a solution model in optimizing fuel consumption in the logistics sector. This study aims to develop a Hybrid Particle Swarm Optimization (HPSO) algorithm to solve the FCVRP problem. The proposed algorithm is the development of the PSO algorithm with local procedures search. Several experiments were carried out to determine the HPSO parameter's effect on minimizing fuel consumption in the FCVRP. The experiment results show that increasing the population and iteration parameters can produce minimum fuel consumption. Furthermore, the smaller the total fuel consumption produced when the kilometers per liter (KPL) high.

Assumptions, Notations, and Problem Descriptions
The problem assumptions in the FCVRP problem are as follows; (1) Each customer is only served by one vehicle, (2) Each vehicle departs and returns to the depot (3) Fuel consumption is affected by the weight of the load, KPL, and distance (4) Vehicles for distribution activities are homogeneous (4) Demand for every customer is a regular.
To describe the FCVRP problem, this study uses the notations described as follows: KPL : distance traveled per unit of fuel : fuel consumption increases with each additional load : increase in load capacity : load : collection of vehicles at the depot, with = {1,2, … , : set of routes traveled by the vehicle , with = { 1 , 2 , . . , } : set node : distance from to nodes : route index : operational costs for vehicle k traveling the route r : constant, value 1 if vehicle k with route r to customer i and value 0 for other conditions : time taken for the vehicle to travel the route r : maximum allowable travel time ∶ Fuel Consumption : th node in th route, for example 2 4 = 4 can be interpreted as the 4th node on the 2nd route is 4 (0-5-2-3-4-0) In this study, the problem description was described in a mathematical model. The objective function of this FCVRP problem was to minimize fuel consumption. The mathematical model that described the problem description is described as follows: Objective function: (3) With the decision variables: Equation (1) was the objective function to minimize fuel consumption. The constraint in Equation (2) was ensuring that all customers can be visited. Equation (3) guaranteed that each customer was served once by a vehicle. The limitation in equation (4) was to guarantee that K vehicles could carry out distribution activities. The constraint in equation (5) ensured that customer demand did not exceed the vehicle capacity on each route. Equation (6) was ensuring that every vehicle passed at least one lane/route. The constraint in equation (7) was to ensure that the vehicle travel time did not exceed the allowable travel time. Equation (8) was a constraint that guaranteed the decision variable was a binary integer.

FCVRP Completion with Hybrid Particle Swarm Optimization (HPSO) Algorithm
This study suggested the use of the HPSO algorithm to minimize fuel consumption. The HPSO algorithm is a model development of the Particle Swarm Optimization (PSO) algorithm. The proposed algorithm combines PSO with a local search strategy. The PSO algorithm was initially proposed by Trelea [33] in 2003. Each particle has characteristics that distinguish PSO from other algorithms, namely position and velocity. NP-hard problems such as FCVRP require high computation time in line with the complexity of the study. The hybrid process in an algorithm can increase the effectiveness of finding a solution. Therefore, Hybrid PSO (HPSO) was proposed in this study to minimize fuel consumption in FCVRP problems.
HPSO has stages in its journey, such as (1) Converting particle positions into travel routes using the Short Rank Value (SRV) method (2) Updating inertia weight (3) Updating cognitive acceleration (4) Updating social acceleration (5) Updating velocity (6) Updating particle position (7) Conducting local search. The local search procedure used to develop the algorithm was the swap and flip procedure. The following is an explanation regarding the stages of HPSO in completing the FCVRP.

Convert particle position into travel route
The search for a solution began with initializing the position through a random number with an upper limit (ub) and a lower limit (lb). The upper limit (ub) and the lower limit (lb) were used to determine each particle's position. In this process, there should be no repetition of values in each position dimension. This illustration is presented in Fig. 1. The position value (continuous) was then converted into a trip sequence (discrete) using the SRV method. The way these method works was to sort the position values from the smallest to the largest value. Fig. 2 shows a representation of the SRV process. The procedure for calculating fuel consumption can be seen in Fig. 3. The formula for calculating the fuel consumption was carried out by reversing the sequence of the subroutes formed. Fig. 3 describes the sum of all customer requests distributed from the customer ( ) and followed by the next customer in reverse until customer ( ) and the last one visited was the distribution center.

Update inertia weight, cognitive acceleration, dan social acceleration
One of the factors that affect an algorithm's performance in solving an optimization problem is determining the right combination of parameters. The particle size used refers to Eberhart and Yuhui [34], namely 30-50 particles.
2.2.3 Update velocity, particle position Each particle was assumed to have two characteristics; position and velocity. Each particle moves in a certain space and remembers the best position ever traveled or found against a food source or objective function value. Each particle conveys information or its good position to the other particles and adjusts each position and velocity.
The following is a mathematical formulation that describes the position and velocity of particles in a search space.
, … , ( ) represents the local best of the i(th) particle. Whereas , … , ( ) represents the global best of all particles. 1 and 2 are the acceleration coefficients which are positive, then 1 and 2 is a random number whose value is between 0 and 1.

Local search
To improve the PSO algorithm's performance, this study proposed PSO with the local search procedure. Some of the procedures used to maximize the efficiency of the PSO were the swap and flip procedures. Fig. 4 b illustrates the stages of the swap procedure. The swap procedure begins by selecting two positions or nodes randomly and then swapping positions. On the other hand, the flip procedure has steps where two nodes are randomly selected. Then the selected nodes are reversed in order. The stages of the flip procedure are described in Figure 4a. The implementation of the hybrid in PSO with swap and flip procedures was carried out in each iteration t as many as the number of nodes. Algorithm 1 and Algorithm 2 show the pseudocode for the PSO and HPSO algorithms.  w 1 , c 1max , c 1min , c 2max , c 1min , v max , n, max iteration (t)) Initialize the routes with a random way [position=rand. * (ub − lb) + lb] Convert particle' position in continuous form Initialize the position and velocity of each particle Convert particle' position into routing division (section 2.2.2) Calculate the initial fitness function of each particle in section 2.4.1 and eq (11) while (t < t max ) do for each particle for each task do calculate the particle's fitness value according to equation (11) do if fitness value < P best then P best = fitness end if do if fitness value < G best then G best = fitness end if do updating inertia weight according to equation (9) do updating cognitive acceleration c 1 according to equation (10) do update the social acceleration c 2 according to equation (11) do update the particle's velocity according to the equation (12) do update the particle's position according to the equation (13) end for end for end while

Data Collection
In this study, several numbers nodes were used as a numerical experiment. The coordinates of customer position, number of customer requests, and capacity were based on the problems of Gaskell [36] and Dantzig and Ramser [37]. Nodes 21 and 22 were taken from Gaskell's data set [36], and node 12 was derived from the Dantzig and Ramser problem [37]. The distance between customers and the distance from the depot to the customer ( ( )( +1 ) ) were calculated by the euclidian distance formula in equation (14).  c 1max , c 1min , c 2max , c 1min , v max , n , max iteration (t)) Initialize the routes with a random way [position=rand. * (ub − lb) + lb] Convert particle' position in continuous form Initialize the position and velocity of each particle Convert particle' position into routing division (section 2.2.2) Calculate the initial fitness function of each particle in section 2.4.1 and eq (11) while (t < t max ) do for each particle for each task do calculate the particle's fitness value according to equation (11) do if fitness value < P best then P best = fitness end if do if fitness value < G best then G best = fitness end if do updating inertia weight according to equation (9) do updating cognitive acceleration c 1 according to equation (10) do update the social acceleration c 2 according to equation (11) do update the particle's velocity according to the equation (12) do update the particle's position according to the equation (13) end for end for Apply local search For i = 1; node Perform swap on the X * . Ensure No. repeated swap in the X * If Xt < X * X * < Xt end if end for For j = 1 ; node Perform flips on the X * . Ensure No. repeated flip in the X * If Xt < X * X * < Xt end if end for end while Here, r-th was the route consisting of node s to node s + 1. KPL calculation or distance per unit of fuel refers to Kuo's research [19]. The increase in fuel consumption (ρ) at each additional load per 100 pounds or 45.35 kilograms was 2%. This study was conducted in 9 variations; three variations in the number of nodes and three variations in   0  145  215  0  1  151  264  1100  2  159  261  700  3  130  254  800  4  128  252  1400  5  163  247  2100  6  146  246  400  7  161  242  800  8  142  239  100  9  163  236  500  10  148  232  600  11  128  231  1200  12  156  217  1300  13  129  214  1300  14  146  208  300  15  164  208  900  16  141  206  2100  17  147  193  1000  18  164  193  900  19  129  189  2500  20  155  185  1800  21  139  182

Setup the experiment
In this study, an experiment was conducted to determine the vehicle's fuel consumption's HPSO parameters' performance. The calculation experiment was carried out with variations in the number of populations and iterations. Variations in population parameters used were 30, 40, and 50 populations. Meanwhile, the iteration parameters used in the experiment varied with a range of 10-300 iterations. The calculation experiment was carried out in as many as 54 experiments. Each calculation result was performed a recapitulation of the fuel consumption results. The recapitulation of the overall experimental results was analyzed to determine population variations and iterations on numerical experiments with variations in the number of nodes.
In this study, an analysis of the Kilometers Per Liter (KPL) effect on fuel consumption was also conducted. KPL was tested with a value of 9.35, 12.8, and 16.25. Each experimental result was recorded and analyzed for the effect of the changes on the fuel consumption result. All calculation experiments were carried out using Matlab 2014a software on Windows 10 AMD A12 with x64-64 8GB RAM processor.

Solution Using HPSO
In this section, the results of the experimental calculation of the FCVRP study using the Hybrid Particle Swarm Optimization (HPSO) approach were explained. The fuel consumption calculation was carried out in 3 different cases. Table 4, Table 5, and Table  6 portray the experiment calculation results with variations in the number of nodes, population, and iteration.  Table 4, Table 5, and Table 6 indicate that the optimal fuel consumption in the case of node 12 was obtained in an experiment with a population of 50 iterations of 300. Like node 12, the optimal fuel consumption in nodes 21 and 22 was obtained during the experiment on population 50 and iterations 300. Based on Table 6, it is concluded that the optimal fuel consumption tends to be obtained in experiments with large population parameters and iterations. The greater the population parameter and the iteration, the greater the probability of getting optimal fuel consumption. Therefore, to minimize fuel consumption in this FCVRP case study, it is highly recommended to use various high parameters. Population parameters and high iterations appear to be more effective in generating minimum fuel consumption.

Analysis of the Effect of Changes in KPL on Fuel Consumption
The analysis was carried out on changes in the KPL variable on the fuel consumption. The procedure used was to experiment with calculating the KPL value, which varies from 9.35 to 16.25 liters. This process functioned to find the effect of changes in the value of the KPL variable on fuel consumption value. Fig. 5 shows that the greater the KPL variable's value, the smaller the total fuel consumption produced. On the other hand, the total fuel consumption was observed to get more significant when the KPL value gets smaller.

Conclusion
This study discussed the problem of the Fuel Consumption Vehicle Routing Problem (FCVRP). The Hybrid Particle Swarm Optimization (HPSO) algorithm was developed to minimize fuel consumption in transportation activities. The experiment showed that to obtain a more optimal fuel consumption, the population and iteration parameters need to be increased. The effect of changes in KPL on energy consumption was also investigated. The results indicated that the greater the KPL variable's value, the smaller the total fuel consumption produced. Some of the limitations of this study included not considering the pick-up load at each node. The suggestion for further research is to investigate FCVRP problems by considering the pick-up and delivery load. 25