Abstract-Vehicle Routing Problem (VRP) is a NP-Complete and a multi-objective problem. The problem involves optimizing a fleet of vehicles that are to serve a number of customers from a central depot. Each vehicle has limited capacity and each customer has a certain demand. Genetic Algorithm (GA) maintains a population of solutions by means of a crossover and mutation operators. For crossover and mutation best cost route crossover techniques and swap mutation procedure is used respectively. In this paper, we focus on two objectives of VRP i.e. number of vehicles and total cost (distance). The proposed Multi Objective Genetic Algorithm (MOGA) finds optimum solutions effectively.Index Terms-Vehicle routing problem, genetic algorithm, multi-objective optimization, pareto ranking procedure, bestcost route crossover (BCRC).

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Non-dominated Sorting Genetic Algorithm (NSGA) has established itself as a benchmark algorithm for Multi objective Optimization. The determination of pareto-optimal solutions is the key to its success. However the basic algorithm for big problem gives less efficient results, which renders it less useful for practical applications. Among the variants of NSGA, several attempts have been made to reduce the complexity. Though successful in giving good results but, there is scope for further improvements, especially considering that the populations involved are frequently of large size. We propose a variant which gives better efficient results. The improved algorithm is applied to the transportation problem: vehicle routing problem (VRP). Results of comparative tests are presented showing that the improved algorithm performs well on large populations.

The increasingly conspicuous problems of energy crisis and environmental pollution are paid attention to by governments and people all over the world since they seriously affect the sustainable development of the human society. As the automotive industry is developing and the quantity of vehicles is dramatically increasing, the emission gas is discharging more and more pollutant into the environment. Correlation between uncertain parameters is possibly a major stumbling block in many application areas. Assigning and scheduling vehicle routes in an uncertain environment are a crucial management problem. The assumption that in a real life environment everything goes according to a priori determined static schedule. The paper considers a version of vehicle routing problem which not only optimise travel time, distance and number of vehicles but also reduces fuel consumption and green house gas emission. In this paper, a variant of predator prey evolutionary strategy (variant-I) is proposed. We modified existing cross over and mutation technique and named as index-based crossover technique and insert random mutation technique. The performance of the algorithm is discussed under a variety of problem settings and parameters value by the numerical experiments and sensitivity analysis. A comparative study of proposed and classical predator prey evolutionary strategy algorithm is specified in this paper.Keywords: environmental multi objective uncertain transport trail model; EMOUTTM; index-based crossover technique; insert random mutation technique; IRMT; green house gas; GHG; vehicle routing problem; VRP; predator prey evolutionary strategy; PPES; VRP with uncertain tours; VRPTours; VRP with uncertain travel time; VRPUTT; VRP with uncertain customers; VRPUC; VRP with uncertain demand; VRPUD.Reference to this paper should be made as follows: Chand, P. and Mohanty, J.R. (2015) 'Environmental multi objective uncertain transport trail model using variant of predator prey evolutionary strategy', Int. . He has published in a number of international journals and conferences proceedings. He is a reviewer for several international conferences. His research interest includes queuing networks, computational intelligence, and data mining.