Abstract
In this paper, an effective multi-objective evolutionary algorithm is proposed to solve the multiple travelling salesman problem. In order to obtain minimum total visited distance and minimum range between all salesmen, some novel representation, crossover and mutation operators are designed to enhance the local and global search behaviours, then NSGA-II framework is applied to find well-convergent and well-diversity non-dominated solutions. The proposed algorithm is compared with several state-of-the-art approaches, and the comparison results show the proposed algorithm is effective and efficient to solve the multiple travelling salesman problems.
Highlights
Multiple Travelling Salesman Problem (MTSP) is an extension of the famous Travelling Salesman Problem (TSP) that visiting each city exactly once with no sub-tours (Gerhard, 1994)
Lots of real-life problems can be modelled as MTSP, such as printing press scheduling problem (Gorenstein, 1970), distribution of emergence materials problem (Liu & Zhang, 2014), vehicle routing problem (Angel, Caudle, Noonan, & Whinston, 1972), UAVs planning problem (Ann, Kim, & Ahn, 2015) and hot rolling scheduling problem (Tang, Liu, Rong, & Yang, 2000)
An estimation of distribution algorithm (EDA) with a gradient search is used to solve MOmTSP which objective function is set as the weighted sum of the total travelling costs of all salesmen and the highest travelling cost of any single salesman (Shim, Tan, & Tan, 2012), in which the author considers minimizing the longest cost to balance the workload between salesmen
Summary
Multiple Travelling Salesman Problem (MTSP) is an extension of the famous Travelling Salesman Problem (TSP) that visiting each city exactly once with no sub-tours (Gerhard, 1994). An estimation of distribution algorithm (EDA) with a gradient search is used to solve MOmTSP which objective function is set as the weighted sum of the total travelling costs of all salesmen and the highest travelling cost of any single salesman (Shim, Tan, & Tan, 2012), in which the author considers minimizing the longest cost to balance the workload between salesmen. An effective evolutionary algorithm, reinforced by a post-optimization procedure based on path-relinking (PR), is used to deal with a bi-objective multiple travelling salesman problem with profits (Labadie, Melechovsky, & Prins, 2014). In the research on MTSP, most of the problems are treated as a single-objective problem, or considered from two separate perspectives For the latter, there are usually two objective functions that are used: minimizing the total distance travelled and minimizing the travel distance of the longest traveller.
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