An Improved Multi-Objective Particle Swarm Optimization With TOPSIS and Fuzzy Logic for Optimizing Trapezoidal Labyrinth Weir

Labyrinth Weir (LW) is a popular control structure that passes a significantly higher flow rate compared to the linear weirs. In order to approach the optimal design of a trapezoidal LW, a multi-objective problem is defined to concurrently minimize the LW consumed concrete volume and maximize its discharge capacity. Simultaneously, a Radial Basis function Neural Networks (RBFNN) is designed and used for estimating LW discharge coefficient (C-d) according to the existing experimental results. An improved multi-objective particle swarm optimization (MOPSO) algorithm named TOPSIS Fuzzy MOPSO (TFMOPSO) is proposed to solve the LW optimization problem. This algorithm utilizes the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to rank the solutions, while a fuzzy inference system is developed to select the algorithm strategy for finding two leaders among the non-dominated solutions. The performance of the proposed TFMOPSO has been tested on the optimization problem of the LW of the Ute dam. The results of TFMOPSO, along with three other state-of-the-art multi-objective algorithms, are explored in terms of hypervolume, coverage, and spacing metrics. It is demonstrated that the TFMOPSO outperforms other algorithms and studies for solving the LW multi-objective optimization problem for the case of Ute dam. Also, RBFNN is found to be one of the most appropriate approaches among studied algorithms in estimating the discharge coefficient of LW, while Pareto optimal solutions from TFMOPSO exhibit a significant improvement compared to the original design of Ute dam LW.