Solve VRPPD with Improved Bacteria Optimization Algorithm

In this paper, an improved bacteria foraging optimization algorithm based on different constraint conditions is proposed to solve the vehicle routing problem with pickup and delivery (VRPPD). At first, the mathematical model is established aiming at minimizing the dispatching time and the total cost. Secondly, the paper proposes the method with dynamic variable step factor, as well as propagation threshold and death threshold to copy the excellent individuals and eliminate the inferior individuals. Finally, the improved method is applied to the CMTnX and CMTnY, and its effectiveness is verified from the result of comparison with some existing algorithms. Introduction In the VRP with Pickup and Delivery, the heterogeneous vehicle fleet based on multiple terminals must meet a set of transportation requests. Each request is defined by a pickup point and the corresponding delivery point. The objective function(s) is generally minimizing the delivery cost. The previous work on VRPPD was conducted for dial-a-ride scenarios [1]. It was first examined by Wilson and Weissberg [2], and motivated by the demand-responsive transportation systems. A parallel insertion heuristic was proposed by Roy et al [3] for the multiple VRPPD in the context of the transportation of disabled persons. Since a fair amount of requests are known in advance, these are used by means of time-spatial proximity criteria to create initial routes for all vehicles starting at the beginning of the day. Madsen, Ravn, and Rygaard [4] implemented a generalized version of this approach for a partly dynamic dial-a-ride problem. Their algorithm can minimize the waiting time for the vehicle as well as the break time. Local search for the VRPPD was first considered by Psarafits [5], who extended the ideas of Lin and Kernighan. A decade later, Bent R and Hentenryck presented another local search heuristic for the VRPPD [6]. The algorithm involves two phases, both using arc exchange procedures. In the construction phase, it tries to find an initial feasible route allowing infeasibility and penalizing the violation of restrictions in the objective function [7]. There are a variety of practical applications about VRPPD, including the transport of the disabled and elderly, sealift and airlift of cargo, as well as the pickup and delivery for overnight carriers. Perspectives on this growing field were offered by Solomon and Desrosiers, et al [8]. An improved bacterial foraging optimization algorithm (IBFOA) based on different constraint condition is proposed in this paper. The effectiveness is verified through the application to the CMTnX and CMTnY. Here, the above efforts can be extended by reviewing important recent developments and offering our view for future directions. Model of VRPPD Identify request by two nodes of i and n+i, respectively, correspond to the pickup and delivery. It is possible for different nodes to represent the same geographical location. Next, denote the set of pickup nodes by P={1,...,n} and the set of delivery nodes by D={n+1,..., 2n }. Further, define N=PD. If request i consists of transporting di units from i to n+i, let li=di and ln+i=-di. K represents the set of vehicles. Because not all the vehicles can serve all request points, each 2nd International Conference on Materials Science, Machinery and Energy Engineering (MSMEE 2017) Copyright © 2017, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Advances in Engineering Research, volume 123