On the Use of Second Order Neighbors to Escape from Local Optima

Abstract

Designing efficient local search based algorithms requires to consider the specific properties of the problems. We introduce a simple and efficient strategy, the Extended Reach, that escapes from local optima obtained from a best improvement local search and apply it to the linear ordering problem (LOP), the traveling salesperson problem (TSP) and the quadratic assignment problem (QAP). This strategy is based on two landscape properties observed in the literature. First, it considers that a local optimum is usually located in the frontier of its own attraction basin, and thus, it is enough to inspect the second order neighbors to reach a (better) solution inside an attraction basin of a better local optimum. Second, taking into account that for the LOP and specific neighborhoods it is possible to discard solutions without the need of being evaluated, we extend this result to the TSP with the 2-opt neighborhood to avoid the unnecessary evaluation of solutions. Efficient ways of evaluating the second order neighbors are also presented, based on the cost differences, reducing significantly the computation cost. Experimental results on random and benchmark instances show that our strategy, indeed, escapes from local optima despite its simplicity.