Quantum firefly swarms for multimodal dynamic optimization problems

Abstract Optimization problems have attracted attention of researchers for decades. Commonly, problem related data and problem domain are assumed to be exactly known beforehand and to remain stationary. However, numerous real life optimization problems are dynamic. In practice, unpredictable events like due date changes, arrivals of new jobs or cancellations yield to changes in parameters, constraints or variables. In addition to the challenges of traditional stationary optimization problems, diverse parts of the problem space should also be monitored to keep track of moving optima in dynamic problems. Therefore, dividing a population (swarm) into smaller sized sub-swarms is a promising strategy particularly for multi-modal problems. In this context, the present work extends Firefly Algorithm (FA) as a multi-population based algorithm to solve multi-modal dynamic optimization problems due to its popularity and demonstrated competitive performance. Quantum particles are employed to monitor the neighborhoods of the best solutions of each sub-swarm in order to overcome the loss of diversity problem. Quantum strategy is also used to respond to dynamic events. Moreover, economical FA along with a simpler move function is introduced in order to consume fitness evaluations more efficiently. Most of the previous approaches ignore prioritizing sub-swarms which can be advantageous. For example, sub-swarms can either be evolved sequentially, randomly or they can be prioritized via some learning-based techniques. Thus, more promising regions might be discovered at earlier evaluations. In this context, the proposed FA extension is further enhanced with such prioritizing strategies, which are based on the feedback from sub-swarms. The experiments are conducted on the well-known Moving Peaks Benchmark along with comparisons with well-known methods. The proposed FA is found as promising and competitive according to the outcomes of the comprehensive experimental study.