Genetic Algorithms for Binary Quadratic Programming

In this paper, genetic algorithms for the unconstrained binary quadratic programming problem (BQP) are presented. It is shown that for small problems a simple genetic algorithm with uniform crossover is sufficient to find optimum or best-known solutions in short time, while for problems with a high number of variables (n 200) it is essential to incorporate local search to arrive at high-quality solutions. A hybrid genetic algorithm incorporating local search is tested on 40 problem instances of sizes containing between n = 200 and n = 2500. The results of the computer experiments show that the approach is comparable to alternative heuristics such as tabu search for small instances and superior to tabu search and simulated annealing for large instances. New best solutions could be found for 14 large problem instances. 1 INTRODUCTION In the unconstrained binary quadratic programming problem (BQP), a symmetric rational n \Theta n matrix Q = (q ij ) is given, and a binary vector of leng..