Two methods for the maximization of homogeneous polynomials over the simplex

The paper deals with the numerical solution of the problem P to maximize a homogeneous polynomial over the unit simplex. We discuss the convergence properties of the so-called replicator dynamics for solving P. We further examine an ascent method, which also makes use of the replicator transformation. Numerical experiments with polynomials of different degrees illustrate the theoretical convergence results.

Enhancing Backtracking Search Algorithm using Reflection Mutation Strategy Based on Sine Cosine

Backtracking Search Algorithm (BSA) is a younger population-based evolutionary algorithm and widely researched. Due to the introduction of historical population and no guidance toward to the best individual, BSA does not adequately use the information in the current population, which leads to a slow convergence speed and poor exploitation ability of BSA. To address these drawbacks, a novel backtracking search algorithm with reflection mutation based on sine cosine is proposed, named RSCBSA. The best individual found so far is employed to improve convergence speed, while sine and cosine math models are introduced to enhance population diversity. To sufficiently use the information in the historical population and current population, four individuals are selected from the historical or current population randomly to construct an unit simplex, and the center of the unit simplex can enhance exploitation ability of RSCBSA. Comprehensive experimental results and analyses show that RSCBSA is competitive enough with other state-of-the-art meta-heuristic algorithms.