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
This implementation is 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.