The Hypervolume Indicator

The hypervolume indicator is one of the most used set-quality indicators for the assessment of stochastic multiobjective optimizers, as well as for selection in evolutionary multiobjective optimization algorithms. Its theoretical properties justify its wide acceptance, particularly the strict monotonicity with respect to set dominance, which is still unique of hypervolume-based indicators. This article discusses the computation of hypervolume-related problems, highlighting the relations between them, providing an overview of the paradigms and techniques used, a description of the main algorithms for each problem, and a rundown of the fastest algorithms regarding asymptotic complexity and runtime. By providing a complete overview of the computational problems associated to the hypervolume indicator, this article serves as the starting point for the development of new algorithms and supports users in the identification of the most appropriate implementations available for each problem.

Hybrid Modified Whale Optimisation Algorithm Simulated Annealing Technique for Control of SRM

The evolutionary multiobjective optimization is an identified field for researchers. The goal of evolutionary multiobjective optimization is to optimize several objectives simultaneously. The problem of multiobjective optimisation is more important when the objective function exhibits conflicting characteristics. In this work, metaheuristic techniques such as modified hybrid whale optimization algorithm with simulated annealing (hybrid mWOASA) is proposed for speed control along with minimization of ripple in torque of a 75 KW, 4-phase, 8/6 switched reluctance motor. The proposed method is used for the combined objective of control of speed with minimization of ripple in the output torque of switched reluctance motor (SRM) considering the armature current as constraint. It is noticed that torque ripple coefficient, integral square error of speed (ISE(speed)), and integral square error of current (ISE(current)) reduced significantly by proposed mWOASA technique as compared to hybrid WOASA, WOA.