Dynamic Reduction-Expansion Operator to Improve Performance of Genetic Algorithms for the Traveling Salesman Problem

Santiago-Omar Caballero-Morales,Diana Sanchez-Partida,Jose-Luis Martinez-Flores

doi:10.1155/2018/2517460

Santiago-Omar Caballero-Morales, Diana Sanchez-Partida + Show 1 more

Open Access

https://doi.org/10.1155/2018/2517460

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Abstract

The Traveling Salesman Problem (TSP) is an important routing problem within the transportation industry. However, finding optimal solutions for this problem is not easy due to its computational complexity. In this work, a novel operator based on dynamic reduction-expansion of minimum distance is presented as an initial population strategy to improve the search mechanisms of Genetic Algorithms (GA) for the TSP. This operator, termed as RedExp, consists of four stages: (a) clustering to identify candidate supply/demand locations to be reduced, (b) coding of clustered and nonclustered locations to obtain the set of reduced locations, (c) sequencing of minimum distances for the set of reduced locations (nearest neighbor strategy), and (d) decoding (expansion) of the reduced set of locations. Experiments performed on TSP instances with more than 150 nodes provided evidence that RedExp can improve convergence of the GA and provide more suitable solutions than other approaches focused on the GA’s initial population.

Highlights

As defined by [1], routing is the process of selecting “best” routes in a graph G = (V, A), where V is a node set and A is an arc set
The main test was performed with 41 Traveling Salesman Problem (TSP) instances which were selected from the TSPLIB95 [9], National TSP, and VLSI TSP [17] libraries to evaluate the statistical significance of the Reduction-Expansion Operator (RedExp) operator on the Genetic Algorithms (GA)’s convergence
While the operator is based on clustering as in [2], only pairs of the closest nodes were considered for clustering, and the number of clusters was dynamically defined by an acceptance threshold which considers the distance variation between all nodes in the network

Summary

Introduction

“expansion” of the clustered nodes is performed to represent the route considering the original N nodes This strategy was evaluated with a selection of 41 symmetric TSP instances (with N = [51 − 1432], mean = 474 nodes) and considering six scenarios where RedExp could be used alone or in conjunction with other standard processes to generate an initial population. In order to avoid significant variability between the original and reduced sets, a criterion of minimum distance was defined for the clustering candidates This can be explained with the following example: consider that pairs (4,6), (6,20), and (12,6) comply with the restriction of dc and the distances between the nodes of each pair are 100, 150, and 120, respectively. Note that this process ensures that close pairs of nodes (within a distance dc) of minimum distance are kept together

Sequencing Stage

Assessment

B Rp Sh Reject Reject Accept

Discussion and Future