Utilisation of pruned Pareto-optimal solutions in the multi objective optimisation: an application to system redundancy allocation problems

Multi-objective optimisation problems normally have not one but a set of solutions, which are called Pareto-optimal solutions or non-dominated solutions. Once a Pareto-optimal set has been obtained, the decision-maker faces the challenge of analysing a potentially large set of solutions. Selecting one solution over others can be quite a challenging task because the Pareto set can contain an unmanageable number of solutions. This process is called post-Pareto optimality analysis. To deal with this difficulty, this study proposes the approach that promisingly prunes the Pareto optimal set. In this study, the newly developed approach uses Monte-Carlo simulation taking into account the decision maker's prioritisation to prune the Pareto optimal set. Then, the central weight vector, the optimal frequently appearance index and upper and lower bands of weights are enclosed to each solution to facilitate selecting a final solution. The well-known redundancy allocation problem is used to show the performance of the proposed method.