Orthogonal learning competitive swarm optimizer for economic dispatch problems

Power system economic dispatch (ED), mathematically, is a typical complex nonlinear multivariable strongly coupled optimization problem with equality and inequality constraints, especially considering the valve-point effects. In this paper, a novel variant of competitive swarm optimizer (CSO) referred to as OLCSO is proposed to solve both convex and non-convex ED problems. In the canonical CSO, the loser particle in each pair updates its position by learning from the winner particle. Such a learning strategy is easy to implement, but is not efficient enough because even a bad particle can contain useful information while a good particle may have misleading features. To solve this issue, an orthogonal learning (OL) strategy based on orthogonal experimental design is developed for CSO to quickly discover more useful information that contained in the winner and the loser particles. The OL strategy can easily construct a more promising solution to provide a more systematic search strategy for OLCSO. A set of 24 numerical benchmark functions and three ED cases with diverse complexities and characteristics are used to comprehensively verify the performance of OLCSO. The experimental results and comparison results consistently indicate that OLCSO can be used as a competitive alternative for ED problems.