A simple hyper-heuristic approach for a variant of many-to-many hub location-routing problem

This paper addresses a variant of the many-to-many hub location-routing problem. Given an undirected edge-weighted complete graph G=(V,E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G = (V, E)$$\end{document}, this problem consists in finding a subset of V designated as hub nodes, partitioning all the nodes of V into cycles such that each cycle has exactly one hub node, and determining a Hamiltonian cycle on the subgraph induced by hub nodes. The objective is to minimize the total cost resulting from all these cycles. This problem is referred to as Many-to-Many p-Location-Hamiltonian Cycle Problem (MMpLHP) in this paper. To solve this problem, one has to deal with aspects of subset selection, grouping, and permutation. The characteristics of MMpLHP change according to the values of its constituent parameters. Hence, this problem can be regarded as a general problem which encompasses a diverse set of problems originating from different combinations of values of its constituent parameters. Such a general problem can be tackled effectively by suitably selecting and combining several different heuristics each of which cater to a different characteristic of the problem. Keeping this in mind, we have developed a simple multi-start hyper-heuristic approach for MMpLHP. Further, we have investigated two different selection mechanisms within the proposed approach. Experimental results and their analysis clearly demonstrate the superiority of our approach over best approaches known so far for this problem.