A dual local search framework for combinatorial optimization problems with TSP application

Jamal Ouenniche (), Prasanna K. Ramaswamy and Michel Gendreau
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Jamal Ouenniche: University of Edinburgh
Prasanna K. Ramaswamy: University of Edinburgh
Michel Gendreau: CIRRELT and MAGI, École Polytechnique de Montréal

Journal of the Operational Research Society, 2017, vol. 68, issue 11, 1377-1398

Abstract: Abstract In practice, solving realistically sized combinatorial optimization problems to optimality is often too time-consuming to be affordable; therefore, heuristics are typically implemented within most applications software. A specific category of heuristics has attracted considerable attention, namely local search methods. Most local search methods are primal in nature; that is, they start the search with a feasible solution and explore the feasible space for better feasible solutions. In this research, we propose a dual local search method and customize it to solve the traveling salesman problem (TSP); that is, a search method that starts with an infeasible solution, explores the dual space—each time reducing infeasibility, and lands in the primal space to deliver a feasible solution. The proposed design aims to replicate the designs of optimal solution methodologies in a heuristic way. To be more specific, we solve a combinatorial relaxation of a TSP formulation, design a neighborhood structure to repair such an infeasible starting solution, and improve components of intermediate dual solutions locally. Sample-based evidence along with statistically significant t-tests support the superiority of this dual design compared to its primal design counterpart.

Keywords: dual local search; relaxation; optimization; traveling salesman; routing and scheduling (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1057/s41274-016-0173-4

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