# A CONSTRAINED SOLID TSP IN FUZZY ENVIRONMENT: TWO HEURISTIC APPROACHES

Document Type : Research Paper

Authors

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 eciency 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.

Keywords

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