Oscillation, heuristic ordering and pruning in neighborhood search

Abstract

This paper describes a new algorithm for combinatorial optimization problems and presents the results of our experiments. HOLSA — Heuristic Oscillating Local Search Algorithm- is a neighborhood search algorithm using an evaluation function f inspired from A*, a best-first strategy, a pruning of states as in B&B and operators performing variable steps. All these caracteristics lead to an oscillation principle whereby the search alternates between improving the economic function and satisfying the constraints. We specify how to compute the start state, the evaluation function and the variable steps in order to implement the general outline of HOLSA. Its performance is tested on the multidimensional knapsack problem, using randomly generated problems and classical test problems of the litterature. The experiments show that HOLSA is very efficient, according to the quality of the solutions as well as the search speed, at least on the class of problems studied in this paper. Moreover with large problems, and a limited number of generated nodes, we show that it is better than Branch & Bound, simulated annealing, tabu search and GRASP, both for the quality of the solution and the computational time.