On fundamental design of parthenogenetic algorithm for the binary quadratic programming problem

The aims of this paper are to develop a heuristic called Parthenogenetic Algorithm (PA) for the binary quadratic programming problem (BQP) and to show empirical performance of PA on large test instances of the BQP. The PA may be interpreted as iterated local search where a population consists of a single individual and a mutation operator rather than a crossover is fully used to generate new offspring, which is used as a starting solution for a local search process in each iteration. Due to the first attempt of PA approach to the BQP, we investigate several PA implementations to choose the best PA. Each of them incorporates each of four local search heuristics (deterministic 1-opt, randomized 1-opt, deterministic k-opt, and randomized k-opt) known for the BQP so far and has a random mutation controlled by a probability parameter. Computational results after extensive experiments show that search abilities of PAs with k-opt are not as sensitive in the parameter values as PAs with 1-opt. Moreover, it turns out that the PA incorporating the randomized k-opt local search and with the near-optimal parameter value of the mutation is superior or at least competitive to the other existing powerful heuristics