Entropy-based bare bones particle swarm for dynamic constrained optimization

Abstract

This paper proposes an entropy-based bare bones particle swarm for solving dynamic constrained optimization problems. The Shannon’s entropy is established as a phenotypic diversity index and the proposed algorithm uses the Shannon’s index of diversity to aggregate the global-best and local-best bare bones particle swarm variants. The proposed approach applies the idea of mixture of search directions, using the index of diversity as a factor to balance the influence of the global-best and local-best search directions. High diversity promotes the search guided by the global-best solution, with a normal distribution for exploitation. Low diversity promotes the search guided by the local-best solution, with a heavy-tailed distribution for exploration. A constraint-handling strategy is also proposed, which uses a ranking method with selection based on the technique for order preference by similarity to ideal solution (TOPSIS) to obtain the best solution within a specific population of candidate solutions. Mechanisms to detect changes in the environment and to update particles’ memories are also implemented into the proposed algorithm. All these strategies do not act independently. They operate related to each other to tackle problems such as: diversity loss due to convergence and outdated memories due to changes in the environment. The combined effect of these strategies provides an algorithm with ability to maintain a proper balance between exploration and exploitation at any stage of the search process without losing the tracking ability. An empirical study was carried out to evaluate the performance of the proposed approach. Experimental results show the suitability of the algorithm in terms of effectiveness to find good solutions for the benchmark problems investigated. Finally, an application is developed where the proposed algorithm is applied to solve the dynamic economic dispatch problem in power systems.