Evolutionary Algorithm for Knee-Based Multiple Criteria Decision Making

Although numerous effective and efficient multiobjective evolutionary algorithms have been developed in recent years to search for a well-converged and well-diversified Pareto optimal front, most of these designs are computationally expensive and have to maintain a large population of individuals throughout the evolutionary process. Once the Pareto optimal front is found satisfactorily, the cognitive burden is then imposed upon decision makers to handpick one solution for implementation among a massive number of candidates even with powerful multicriteria decision-making tools. With the increase in the number of decision variables and objective functions in the face of real-world applications, these problems have become a daunting challenge. In this article, we propose a recursive evolutionary algorithm, called EvoKnee(R), to directly search for global knee solutions, but also multiple local knee solutions using the minimum Manhattan distance approach as opposed to an enormous number of Pareto optimal solutions. Compared with the traditional evolutionary approaches, the proposed design herein only preserves nondominated solutions in rank one in each generation. Boundary Individuals Selection is tailored to select only M-2 boundary individuals where M is the number of objectives. Relieving the burden of maintaining a large population size and its diversity throughout a lengthy evolutionary process, this design with a very low computational cost allows the evolutionary algorithm to converge to knee solutions quickly. To facilitate the experimental validations, a simulator with a graphical user interface is developed under the Delphi XE7 platform and made available for public use. In addition, the proposed algorithm is evaluated with the DO2DK, DEB2DK, DEB2DK2, and DEB3DK benchmark functions. The comparison results validate that the proposed EvoKnee(R) algorithm is computationally and efficiently finding all global and local knee solutions.

Automated summary

In this article, a recursive evolutionary algorithm EvoKnee(R) is proposed to directly search for global knee solutions and multiple local knee solutions using the minimum Manhattan distance approach, instead of a large number of Pareto optimal solutions. Unlike traditional approaches, only nondominated solutions in rank one are preserved in each generation, reducing computational cost and allowing quick convergence to knee solutions.