For the past decade or so, evolutionary algorithms (EAs) emerged as a revolutionary approach (compared to classical approaches) for solving search and optimization problems involving multiple conflicting objectives. Such problems are common in engineering, science, and commerce. This paper suggests a base-line efficient algorithm (NSGA-II) for the purpose. Because of its simplicity, availability of a freely downloadable computer code, and demonstrated superiority over other existing methods, NSGA-II has been extensively used in many studies. The evolutionary multi-objective optimization (EMO) is a new, emerging and fast-growing field of research and application within engineering, operations research and computer science communities. Because of its broad-based applicability in academia and practice, NSGA-II has been, since its publication, either used as a baseline algorithm to compare with other methods or has been applied to new problems.

The paper suggests a multi-objective optimization algorithm which is capable of finding a well-distributed set of trade-off optimal solutions for two or more conflicting objectives of design. The methodology is new and pragmatic compared with classical methods, which usually convert multiple objectives into a single objective by using some subjective preference information. NSGA-II is useful for two reasons: (i) the knowledge of multiple trade-off solutions helps a decision-maker to make a better and more confident choice of a solution and (ii) multiple optimal solutions may provide useful design principles which may not be possible to obtain by any other means.

I was introduced to the techniques of solving optimization problems using evolutionary algorithms (EAs) by my mentor Prof. David E. Goldberg (currently at the University of Illinois) in 1987. Returning to IIT Kanpur in 1992 and interacting with local industries, I realized that most engineering design optimization problems involve conflicting objectives, for which there was no efficient method for finding multiple trade-off optimal solutions. It was apparent that the multi-member approach followed in EAs makes them ideal candidates to be used for solving multi-objective optimization problems. Taking a clue from Goldberg's seminal book on genetic algorithms (Reading: Addison-Wesley, 1989), I developed one of the earliest EMO algorithms—the non-dominated sorting GA (NSGA)—for the purpose in 1994. The current paper suggested NSGA-II, which is a mature, logical, and more efficient extension of NSGA, mostly resulted from our experience in working with multi-objective algorithms since 1993 at IIT Kanpur in India.