A Constrained Solid TSP in Fuzzy Environment: Two Heuristic Approaches

A solid travelling salesman problem (STSP) is a travelling salesman problem (TSP) where the salesman visits all the cities only once in his tour using different conveyances to travel from one city to another. Costs and environmental effect factors for travelling between the cities using different conveyances are different. Goal of the problem is to find a complete tour with minimum cost that damages the environment least. An ant colony optimization (ACO) algorithm is developed to solve the problem. Performance of the algorithm for the problem is compared with another soft computing algorithm, Genetic Algorithm(GA). Problems are solved with crisp as well as fuzzy costs. For fuzzy cost and environmental effect factors, cost function as well as environment constraints become fuzzy. As optimization of a fuzzy objective function is not well defined, fuzzy possibility approach is used to get optimal decision. To test the efficiency of the algorithm, the problem is solved considering only one conveyance facility ignoring the environmental effect constraint, i.e., a classical two dimensional TSP (taking standard data sets from TSPLIB for solving the problem). Different numerical examples are used for illustration.