Multi-objective Combinatorial Optimisation with Coincidence algorithm

Most optimization algorithms that use probabilistic models focus on extracting the information from good solutions found in the population. A selection method discards the below-average solutions. They do not contribute any information to be used to update the models. This work proposes a new algorithm, combinatorial optimization with coincidence (COIN) that makes use of both good and not-good solutions. A generator represents a probabilistic model of the required solution, is used to sample candidate solutions. Reward and punishment schemes are incorporated in updating the generator. The updating values are defined by selecting the good and not-good solutions. It has been observed that the not-good solutions contribute to avoid producing the bad solutions. The multi-objective version of COIN is also introduced. Several benchmarks of multi-objective problems of real world industrial applications are reported.