Cumulative weighting optimization: The discrete case

Global optimization problems are relevant in many fields (e.g., control systems, operations research, economics). There are many approaches to solving these problems. One particular approach is model-based methods, which are a class of random search methods. A model-based method iteratively updates its probability density function. At each step, additional weight is given to solution subspaces that are more likely to yield an optimal objective value. Model-based methods can be analyzed by writing down a corresponding system of differential equations similar to the well known Fokker-Planck equation, which models the evolution of probability density functions for diffusions. We propose an innovative model-based method, Cumulative Weighting Optimization (CWO), which can be proven to converge to an optimal solution. Using this rigorous theoretical foundation, we design a CWO-based numerical algorithm for solving global optimization problems. Interestingly, the well-known cross-entropy (CE) method is a special case of this CWO-based algorithm.