Monotonicity Analysis, Evolutionary Multi-Objective Optimization, and Discovery of Design Principles

Optimization algorithms are routinely used to find the minimum or maximum solution corresponding to one or more objective functions, subject to satisfying certain constraints. However, monotonicity analysis is a process which, in certain problems, can instantly bring out important properties among decision variables corresponding to optimal solutions. As the name suggests, the objective functions and constraints need be monotonic to the decision variables or the objective function must be free from one or more decision variables. Such limitations in their scope is probably the reason for their unpopularity among optimization researchers. In this paper, we suggest a generic two-step evolutionary multi-objective optimization procedure which can bring out important relationships among optimal decision variables and objectives to linear or non-linear optimization problems. Although this “innovization” (innovation through optimization) idea is already put forward by the authors elsewhere [6], this paper brings out the similarities of the outcome of the proposed innovization task with that of the monotonicity analysis and clearly demonstrates the advantages of the former method in handling generic optimization problems. The results of both methods are contrasted by applying them on a specific engineering design problem, for which the computation of exact optimal solutions can be achieved. Besides showing the niche of the proposed multi-objective optimization based procedure in such important design tasks, this paper also demonstrates the ability of evolutionary optimization algorithms in finding the exact optimal solutions.