The concept of Pareto optimality is the default method for pruning a large set of candidate solutions in a multi-objective problem to a manageable, balanced, and rational set of solutions. While the Pareto optimality approach is simple and sound, it may select too many or too few solutions for the decision-maker’s needs or the needs of optimization process (e.g. the number of survivors selected in a population-based optimization). This inability to achieve a target number of solutions to keep has caused a number of researchers to devise methods to either remove some of the non-dominated solutions via Pareto filtering or to retain some dominated solutions via Pareto relaxation. The Skewboid method contains only a single parameter for relaxing the Pareto optimality condition (values between -1 and 0) and filtering more solutions from the Pareto optimal set (values between 0 and 1). This parameter can be correlated with a desired number of solutions so that this number of solutions is input instead of an unintuitive adjustment parameter.
This implementation is Visual Studio code that can be used with existing Visual Basic, C# code or as a macro for excel and corresponds to the experiments in the paper: M.I.Campbell, 2012, "The Skewboid Method: A Simple and Effective Approach to Pareto Relaxation and Filtering", ASME International Design Engineering Technical Conferences, Aug.12-15, Chicago, IL, DETC2012-70323.