Abstract
Problem statement: The shipment of goods from manufacturer to the consumer is a focal point of distribution logistics. In reality, the demand of consumers is not known a priori. This kind of distribution is dealt by Stochastic Vehicle Routing Problem (SVRP) which is a NP-hard problem. In this proposed work, VRP with stochastic demand is considered. A probability distribution is considered as a random variable for stochastic demand of a customer. Approach: In this study, VRPSD is resolved using Meta heuristic algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Hybrid PSO (HPSO). Dynamic Programming (DP) is used to find the expected cost of each route generated by GA, PSO and HPSO. Results: The objective is to minimize the total expected cost of a priori route. The fitness value of a priori route is calculated using DP. In proposed HPSO, the initial particles are generated based Nearest Neighbor Heuristic (NNH). Elitism is used in HPSO for updating the particles. The algorithm is implemented using MATLAB7.0 and tested with problems having different number of customers. The results obtained are competitive in terms of execution time and memory usage. Conclusion: The computational time is reduced as polynomial time as O(nKQ) time and the memory required is O(nQ). The ANOVA test is performed to compare the proposed HPSO with other heuristic algorithms.
Highlights
The VRP was first introduced by (Dantzig and Ramset, 1958), where the objective is to find the optimal set of routes for a fleet of vehicles in order to serve a given set of customers
This study focuses on designing Particle Swarm Optimization (PSO) incorporated with Genetic Algorithm (GA) operators such as mutation and crossover to solve VRPSD and Dynamic Programming (DP) is used to solve the objective function of stochastic program
The performance of Meta heuristic algorithms for VRPSD is shown in the Fig. 7
Summary
The VRP was first introduced by (Dantzig and Ramset, 1958), where the objective is to find the optimal set of routes for a fleet of vehicles in order to serve a given set of customers. A VRP in a broad sense is a generic name given to whole class of problems in which a set of routes for a fleet of vehicles based at one or several depots must be determined for a number of geographically dispersed cities or customers. It is easy to describe the VRP problem, but difficult to solve. VRP usually takes exponential time for finding the optimal solution, is a NP-hard problem. There are many solutions are proposed to solve VRP but finding a globally minimum solution is computationally complex
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