A COMPARATIVE ANALYSIS OF MULTI OBJECTIVE SHORTEST PATH PROBLEM

Abstract For a Multi objective shortest path problem (MOSPP) of a network, there may be several pareto optimal solutions. Among them, the decision maker can select the best one or the most satisfactory solution depending upon the priority and nature of the problem. In this paper, a comparative study was made for two different set of objectives based on the pareto optimal solutions. Keywords: Shortest path problem, Multi objective shortest path problem, Fuzzy triangular number. 1. Introduction The problem of finding the best or shortest path in a network from source node to destination is called shortest path problem (SPP). The objectives used in finding out the best or shortest path in a network may be one or more, such as minimization of cost, minimization of time, minimization of risk etc. When only one objective is considered in SPP, it is called single objective shortest path problem. In most of the cases, the consideration of one objective function for a SPP does not lead to any realistic solution. A Multi objective shortest path problem (MOSPP) of a network consists of more than one objective of either maximization type or minimization type or of mixed type. In the case of single objective, the best path indicates the optimal path. The concept of optimality is replaced by pareto optimality in multi objective case due to conflicting nature of the objectives. A pareto optimal solution [1] or non dominated solution for a multi objective problem is one for which no objective function can be improved without a simultaneous detriment to atleast one of the other objectives. Hence for a MOSPP, there may be several pareto optimal solutions. Among them, the decision maker can select the best one or the most satisfactory solution depending upon the priority and nature of the problem. ISSN: 0975-5462 3241