Multi-objective optimization methods can be criticized for lacking a statistically valid measure of the quality and representativeness of a solution. This stance is especially relevant to metaheuristic optimization approaches but can also apply to other methods that typically might only report a small representative subset of a Pareto frontier. Here we present a method to address this deficiency based on random sampling of a solution space to determine, with a specified level of confidence, the fraction of the solution space that is surpassed by an optimization. The Superiority of Multi-Objective Optimization to Random Sampling, or SMORS method, can evaluate quality and representativeness using dominance or other measures, e.g., a spacing measure for high-dimensional spaces. SMORS has been tested in a combinatorial optimization context using a genetic algorithm but could be useful for other optimization methods.
Schedule Management Optimization (SMO) is a tool for automatically generating a schedule of project tasks. Project scheduling is traditionally achieved with the use of commercial project management software or case-specific optimization formulations. Commercial software packages are useful tools for managing and visualizing copious amounts of project task data. However, their ability to automatically generate optimized schedules is limited. Furthermore, there are many real-world constraints and decision variables that commercial packages ignore. Case-specific optimization formulations effectively identify schedules that optimize one or more objectives for a specific problem, but they are unable to handle a diverse selection of scheduling problems. SMO enables practitioners to generate optimal project schedules automatically while considering a broad range of real-world problem characteristics. SMO has been designed to handle some of the most difficult scheduling problems -- those with resource constraints, multiple objectives, multiple inventories, and diverse ways of performing tasks. This report contains descriptions of the SMO modeling concepts and explains how they map to real-world scheduling considerations.