Rough Genetic Algorithm for Constrained Solid TSP with Interval Valued Costs and Times

Abstract

This paper presents new rough set based genetic algorithms (RSGAs) to solve constrained solid travelling salesman problems (CSTSPs) with restricted conveyances (CSTSPwR) having uncertain costs and times as interval values. To grow the impreciseness in soft computing (SC), the proposed RSGAs, a rough set based age-dependent selection technique and an age-oriented min-point crossover are used along with three types of probability, p (Formula presented.) -dependent random mutations. A number of benchmark problems from standard data set, TSPLIB are tested against the proposed algorithms and existing simple GA (SGA). CSTSPwRs are formulated as constrained linear programming problems and solved by both proposed RSGAs and SGA. These are illustrated numerically by some empirical data and the results from the above methods are compared. Statistical significance of the proposed algorithms are demonstrated through statistical analysis using standard deviation. Moreover, the non-parametric test, Friedman test, is performed with the proposed algorithms. In addition, a post hoc paired comparison is applied and the out performance of the RSGAs. � 2018, � 2018 The Author(s). Published by Taylor & Francis Group on behalf of the Fuzzy Information and Engineering Branch of the Operations Research Society of China & Operations Research Society of Guangdong Province.