Interactive fuzzy multiobjective reliability optimization using NSGA-II

Abstract

In many practical situations where reliability enhancement is involved, the decision making is complicated because of the presence of several mutually conflicting objectives. Presence of multiple objectives in a problem, in principle, gives rise to a set of optimal solutions (largely known as Pareto-optimal solutions), instead of a single optimal solution. This type of problem is known as multiobjective optimization problem (MOOP). In general, a MOOP can be solved using weighted sums or decision-making schemes. An alternative way is to look for the Pareto-optimal front. Many evolutionary algorithms (EAs) like genetic algorithm (GA) have been suggested to solve MOOP, hence termed as multiobjective evolutionary algorithms (MOEAs). Nondominated sorting genetic algorithm (NSGA-II) is one such MOEA which demonstrates the ability to identify a Pareto-optimal front efficiently. Thus, it provides the decision maker (DM) a complete picture of the optimal solution space. This paper presents the reliability optimization of a life-support system in a space capsule where reliability of the system is maximized while minimizing the cost. An interactive fuzzy satisficing method for deriving a Pareto-optimal solution preferred by the DM is presented here. Prior preference of the DM has been taken into account here. Using the concept of fuzzy sets and convex fuzzy decision making a multiobjective fuzzy optimization problem is formulated from the original crisp optimization problem. Different nonlinear membership functions based on the DM’s preference have been employed for the fuzzification. Then, NSGA-II is applied to solve the resulting fuzzified MOOP. Resulting Pareto-optimal solution gives the DM variety of alternatives to seek an appropriate solution by modifying parameters interactively according to his/her preference again. Various Pareto-optimal fronts under different preferences of DM have been reported.