Changdar, C., Maiti, M., Maiti, M. (2013). A CONSTRAINED SOLID TSP IN FUZZY ENVIRONMENT:
TWO HEURISTIC APPROACHES. Iranian Journal of Fuzzy Systems, 10(1), 1-28. doi: 10.22111/ijfs.2013.153

Chiranjit Changdar; Manas Kumar Maiti; Manoranjan Maiti. "A CONSTRAINED SOLID TSP IN FUZZY ENVIRONMENT:
TWO HEURISTIC APPROACHES". Iranian Journal of Fuzzy Systems, 10, 1, 2013, 1-28. doi: 10.22111/ijfs.2013.153

Changdar, C., Maiti, M., Maiti, M. (2013). 'A CONSTRAINED SOLID TSP IN FUZZY ENVIRONMENT:
TWO HEURISTIC APPROACHES', Iranian Journal of Fuzzy Systems, 10(1), pp. 1-28. doi: 10.22111/ijfs.2013.153

Changdar, C., Maiti, M., Maiti, M. A CONSTRAINED SOLID TSP IN FUZZY ENVIRONMENT:
TWO HEURISTIC APPROACHES. Iranian Journal of Fuzzy Systems, 2013; 10(1): 1-28. doi: 10.22111/ijfs.2013.153

A CONSTRAINED SOLID TSP IN FUZZY ENVIRONMENT:
TWO HEURISTIC APPROACHES

^{1}Department of Computer Science, Raja N.L. Khan Women's
College, Midnapore, Paschim- Medinipur, West Bengal, India-721102

^{2}Department of Mathematics, Mahishadal Raj College, Mahishadal,
Purba- Medinipur, West Bengal, India-721628

^{3}Department of Mathematics, Vidyasagar University, Midnapore,
Paschim- Medinipur, West Bengal, India-721102

Abstract

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 di erent conveyances to travel from one city to another. Costs and environmental e ect factors for travelling between the cities using di erent conveyances are di erent. Goal of the problem is to nd 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 e ect factors, cost function as well as environment constraints become fuzzy. As optimization of a fuzzy objective function is not well de ned, fuzzy possibility approach is used to get optimal decision. To test the eciency of the algorithm, the problem is solved considering only one conveyance facility ignoring the environmental e ect constraint, i.e., a classical two dimensional TSP (taking standard data sets from TSPLIB for solving the problem). Di erent numerical examples are used for illustration.

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