A new feasibility quality measure for optimization under uncertainty

This research introduces a new metric that measures the quality of solutions arising from uncertain optimization problems called hardness. The measure considers the intensity with which a specific solution of an optimization problem under uncertainty can violate the set of constraints. This is done in a comparative way, which is not found in other quality measures present in the literature. Another attractive feature is the possibility of the decision maker establish the importance of each constraint during the metric evaluation process, which gives more flexibility to a posterior analysis. The hardness measure presented better performance than the other metric presented in the literature, being able to describe the difference between solutions with intermediate uncertainty protection in a detailed way. It is concluded that the hardness quality measure, when carrying out a relative feasibility comparison weighted by the decision maker's preferences, is the best choice to identify the most protected solution.