Evolutionary Multi-objective Optimization Procedure Research Articles

A Computationally Fast Convergence Measure and Implementation for Single-, Multiple-, and Many-Objective Optimization

A previous study suggested a Karush–Kuhn–Tucker proximity measure (KKTPM) that is able to identify relative closeness of any point from the theoretical optimum point without actually knowing the exact location of the optimum point. However, the drawback of the KKTPM metric is that it requires a new optimization problem to be solved for each solution to find its convergence measure. In this paper, we propose a number of approximate formulations of the KKTPM measure by studying its calculation procedure so that the KKTPM measure can be computed in a computationally fast manner and without solving the inherent optimization problem. The approximate KKTPM values are evaluated in comparison with the original exact optimization-based KKTPM value on standard single-objective, multiobjective, and many-objective optimization problems. In all cases, our proposed “estimated” approximate method is found to achieve a strong correlation of KKTPM values with the exact values, and achieve such results in two or three orders of magnitude smaller computational time. We also present a parser-based KKTPM computational procedure, which can be used independently or in conjunction with an evolutionary multiobjective optimization procedure.

Modelling the Pareto-optimal set using B-spline basis functions for continuous multi-objective optimization problems

In the past few years, multi-objective optimization algorithms have been extensively applied in several fields including engineering design problems. A major reason is the advancement of evolutionary multi-objective optimization (EMO) algorithms that are able to find a set of non-dominated points spread on the respective Pareto-optimal front in a single simulation. Besides just finding a set of Pareto-optimal solutions, one is often interested in capturing knowledge about the variation of variable values over the Pareto-optimal front. Recent innovization approaches for knowledge discovery from Pareto-optimal solutions remain as a major activity in this direction. In this article, a different data-fitting approach for continuous parameterization of the Pareto-optimal front is presented. Cubic B-spline basis functions are used for fitting the data returned by an EMO procedure in a continuous variable space. No prior knowledge about the order in the data is assumed. An automatic procedure for detecting gaps in the Pareto-optimal front is also implemented. The algorithm takes points returned by the EMO as input and returns the control points of the B-spline manifold representing the Pareto-optimal set. Results for several standard and engineering, bi-objective and tri-objective optimization problems demonstrate the usefulness of the proposed procedure.

Hybrid evolutionary multi-objective optimization and analysis of machining operations

Evolutionary multi-objective optimization (EMO) has received significant attention in recent studies in engineering design and analysis due to its flexibility, wide-spread applicability and ability to find multiple trade-off solutions. Optimal machining parameter determination is an important matter for ensuring an efficient working of a machining process. In this article, the use of an EMO algorithm and a suitable local search procedure to optimize the machining parameters (cutting speed, feed and depth of cut) in turning operations is described. Thereafter, the efficiency of the proposed methodology is demonstrated through two case studies – one having two objectives and the other having three objectives. Then, EMO solutions are modified using a local search procedure to achieve a better convergence property. It has been demonstrated here that a proposed heuristics-based local search procedure in which the problem-specific heuristics are derived from an innovization study performed on the EMO solutions is a computationally faster approach than the original EMO procedure. The methodology adopted in this article can be used in other machining tasks or in other engineering design activities.