Multiobjective scatter search for a commercial territory design problem

In this paper, a multiobjective scatter search procedure for a bi-objective territory design problem is proposed. A territory design problem consist of partitioning a set of basic units into larger groups that are suitable with respect to some specific planning criteria. These groups must be compact, connected, and balanced with respect to the number of customers and sales volume. The bi-objective commercial territory design problem belongs to the class of NP-hard problems. Previous work showed that large instances of the problem addressed in this work are practically intractable even for the single-objective version. Therefore, the use of heuristic methods is the best alternative for obtaining approximate efficient solutions for relatively large instances. The proposed scatter search-based framework contains a diversification generation module based on a greedy randomized adaptive search procedure, an improvement module based on a relinked local search strategy, and a combination module based on a solution to an assigment problem. The proposed metaheuristic is evaluated over a variety of instances taken from literature. This includes a comparison with two of the most successful multiobjective heuristics from literature such as the Scatter Tabu Search Procedure for Multiobjective Optimization by Molina, Mart́ı, and Caballero, and the Non-dominated Sorting Genetic Algorithm by Deb, Agrawal, Pratap, and Meyarivan. Experimental work reveals that the proposed procedure consistently outperforms both existing heuristics from literature on all instances tested.