Light beam search based multi-objective optimization using evolutionary algorithms

For the past decade or so, evolutionary multi-objective optimization (EMO) methodologies have earned wide popularity for solving complex practical optimization problems, simply due to their ability to find a representative set of Pareto-optimal solutions for mostly two, three, and some extent to four and five-objective optimization problems. Recently, emphasis has been made in addressing the decision-making activities in arriving at a single preferred solution. The multiple criteria decision making (MCDM) literature offers a number of possibilities for such a task involving user preferences which can be supplied in different forms. This paper presents an interactive methodology for finding a preferred set of solutions, instead of the complete Pareto-optimal frontier, by incorporating preference information of the decision maker. Particularly, we borrow the concept of light beam search and combine it with the NSGA-II procedure. The working of this procedure has been demonstrated on a set of test problems and on engineering design problems having two to ten objectives, where the obtained solutions are found to match with the true Pareto-optimal solutions. The results highlight the utility of this approach towards eventually facilitating a better and more reliable optimization-cum-decision-making task.