Adaptive probabilistic harmony search for binary optimization problems

Harmony search (HS) is an optimization technique that uses several operators such as pitch adjustments to provide local improvement to candidate solutions during the optimization process. A standard pitch adjustment operator is known to be inefficient for binary domain optimization problems. A novel adaptive probabilistic harmony search (APHS) algorithm for binary optimization problems is proposed in this paper. APHS combines the power of the standard harmony search with the modelling capability of probabilistic search algorithms, with almost no extra user-tuned parameters. In APHS, the expected value of the search probability distribution is adapted using a sample of "good" vectors among the population to minimize the cross entropy between the actual distribution and the measured one. Moreover, Bernoulli probability distribution was used to enhance the pitch adjustment operator to fit the binary optimization domain. The effectiveness and the robustness of the proposed algorithm are shown by a thorough comparison with state-of-the-art existing techniques in a number of binary space optimization problems with variant complexities and sizes. The set of binary space optimization problems investigated in this paper include: Max-One problem, Order-3 deceptive problem, Bipolar Order-6 deceptive problem, Muehlenbein's Order-5 problem, Knapsack problem, Multi-Knapsack problem, and finally a real-world problem of the satellite broadcast scheduling. Experimental results show that our proposed algorithm is indeed very effective and outperforms the existing algorithms by finding optimal solutions for almost all tested benchmarks.