Abstract
In this paper, a novel multiobjective lightning flash algorithm (MOLFA) is proposed to solve the multiobjective optimization problem. The charge population state of the lightning flash algorithm is defined, and we prove that the charge population state sequence is a Markov chain. Since the convergence analysis of MOLFA is to investigate whether a Pareto optimal solution can be reached when the optimal charge population state is obtained, the development of a charge population state is analyzed to achieve the goal of this paper. Based on the martingale theory, the MOLFA convergence analysis is carried out in terms of the supermartingale convergence theorem, which shows that the MOLFA can reach the global optimum with probability one. Finally, the effectiveness of the proposed MOLFA is verified by a numerical simulation example.
Highlights
Lightning flash algorithm (LFA), a new heuristic algorithm proposed by Kheshti [1], has been successfully applied to large-scale nonconvex economic dispatch [2], nonconvex combined emission economic dispatch [3], protective relay coordination [4], and intelligent inertial control of wind turbines for grid frequency control [5, 6]
Generational distance (GD) [37] is to estimate the gap between the nondominated vectors produced by algorithm and true Pareto optimal front, which can be defined as GD ni 1 d2i, n where n is the number of nondominated solutions obtained by the algorithm and di is the Euclidean distance between the i-th solution and the nearest member of the Pareto optimal front
It can be seen that most of solutions are close to the true Pareto front and are unevenly distributed. erefore, it is demonstrated that the proposed multiobjective lightning flash algorithm (MOLFA) method is able to solve these standard multiobjective optimization problems, which provide an effective nondominated solution set and cover the full Pareto front
Summary
Lightning flash algorithm (LFA), a new heuristic algorithm proposed by Kheshti [1], has been successfully applied to large-scale nonconvex economic dispatch [2], nonconvex combined emission economic dispatch [3], protective relay coordination [4], and intelligent inertial control of wind turbines for grid frequency control [5, 6]. Despite of all these efforts, the convergence analysis of LFA and MOLFA has not been fully studied To shorten such a gap, this study proposes a multiobjective lightning flash algorithm and analyzes the global convergence of LFA. (2) e Markov chain of LFA is modelled, and martingale theory is applied to the optimal fitness value of population state discussing the convergence of the algorithm.
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