Improved Evolutionary Algorithms To Solve Constrained Optimization Problems

Constrained optimization problems (COPs) belong to a kind of mathematical programming problem, which is frequently encountered in the disciplines of science and engineering application. A considerable number of constrained optimization evolutionary algorithms have been proposed due to increasing interest in solving constrained optimization problems by evolutionary algorithms.The crossover operator is redesigned by using the principle of good points set in number theory in this dissertation, so that the new crossover operator can produce a small but representative set of points as the potential offspring. Novel constrained optimization evolutionary algorithm based on good point set, namely COAGPN, is proposed to tackle constrained optimization problems in this dissertation. Firstly, COP is transformed into a bi-objective optimization problem; secondly, the new crossover operator produces offspring. After that the BGA mutation operator is applied to offspring for enhancing the diversity of the offspring population. Finally, according to the evolutionary information of the current offspring population, a tournament selection operator or Pareto dominance is used to choose the best individuals for the next population.The proposed COAGPN is tested on 12 complex benchmark test functions. The computational experiments show that COAGPN can converge to optimal or close-to-optimal solutions efficiently; what's more, it has high rate and rapid speed to achieve optimal or close-to-optimal solutions. The empirical evidence suggests that it is robust, efficient, and generic when handling linear/nonlinear equality/inequality constraints. Compared with two other state-of-the-art algorithms referred in this dissertation, COAGPN outperforms or performs similarly to them in terms of the best, mean, and worst objective function values and the standard deviations. More importantly, this approach is easy to implement and its computational cost is relatively low.Constrained optimization evolutionary algorithm based on memory, which integrates particle swarm optimization (PSO) with differential evolution (DE), named MCOEA, is proposed. A population and a memory unit are evolved in the evolution progress. PSO focuses on evolving half individuals of the population with the higher degree of constraint violations while DE focues on evolving the individuals of the memory unit. The population and unit interact with each other through Acquire() and Guide(). Traditionally, PSO is easy to fall in stagnation when no particle discovers a position that is better than its previous best position for several generations. Since DE has strong search capability, it is incorporated to update the previous best positions of particles to help PSO jump out of stagnation. Thus, the algorithm quickens the speed of convergence and improves the algorithm's performance.The presented method is tested on 12 well-known benchmark functions and 5 engineering optimization functions. The empirical evidence suggests that MCOEA is robust, efficient, and generic when handling linear/nonlinear equality/inequality constraints. From the comparison study, MCOEA outperforms or performs similarly to seven state-of-the-art approaches in terms of the quality of the resulting solutions.