Study of the sequential constraint-handling technique for evolutionary optimization with application to structural problems

Engineering design problems are most frequently charac-terized by constraints that make them hard to solve and time-consuming. When evolutionary algorithms are used to solve these problems, constraints are often handled with the generic weighted sum method or with techniques specific to the prob-lem at hand. Most commonly, all constraints are evaluated at each generation, and it is also necessary to fine-tune different parameters in order to receive good results, which requires in-depth knowledge of the algorithm. The sequential constraint-handling techniques seem to be a promising alternative, be-cause they do not require all constraints to be evaluated at each iteration and they are easy to implement. They neverthe-less require the user to determine the ordering in which those constraints shall be evaluated. Therefore two heuristics that allow finding a satisfying constraint sequence have been developed. Two sequential constraint-handling techniques using the heuristics have been tested against the weighted sum technique with the ten-bar structure benchmark. They both performed better than the weighted sum technique and can therefore be easy to implement, and powerful alternatives for solving engineering design problems

Uncertainty and Constraint Handling in Evolutionary Algorithms

This paper proposes two evolutionary algorithms. Firstly, a dynamic evolutionary algorithm is proposed that uses variable relocation vectors to adapt the current population to the new environment. The relocation vectors introduce a certain radius of uncertainty to be applied specifically to each individual and in effect restoring diversity and accelerating exploration. Furthermore, the algorithm provides higher re-usage, faster convergence and better adaptation. As a technique to be used at transient periods, the proposed algorithm provides the next evolutionary cycle with better initial population than any other randomly generated population. The algorithm can be easily integrated into standard evolutionary algorithms and other uncertainty handling techniques. Secondly, this paper proposes a new constraint handling technique for multi-objective evolutionary algorithms based on adaptive penalty functions and distance measures. Through this design, the objective space is modified to account for the performance and constraint violation of each individual. The modified objective functions are used in the non-dominance sorting to facilitate in evolution of optimal solutions not only in the feasible space but also in the infeasible space. The number of feasible individuals in the population is used to guide the search process either toward finding more feasible solutions or toward locating optimal solutions. The proposed method is simple to implement and does not need any parameter tuning.School of Electrical & Computer Engineerin

Exploiting Linkage Information and Problem-Specific Knowledge in Evolutionary Distribution Network Expansion Planning

This paper tackles the Distribution Network Expansion Planning (DNEP) problem that has to be solved by distribution network operators to decide which, where, and/or when enhancements to electricity networks should be introduced to satisfy the future power demands. We compare two evolutionary algorithms (EAs) for optimizing expansion plans: the classic genetic algorithm (GA) with uniform crossover and the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) that learns and exploits linkage information between problem variables. We study the impact of incorporating different levels of problem-specific knowledge in the variation operators as well as two constraint-handling techniques: constraint domination and repair mechanisms. Experiments show that the use of problem-specific variation operators is far more important for the classic GA to find high-quality solutions to the DNEP problem. GOMEA is found to have far more robust performance even when an out-of-box variant is used that doesn't exploit problem-specific knowledge. Based on experiments, we suggest that when selecting optimization algorithms for real-world applications like DNEP, EAs that have the ability to model and exploit problem structures, such as GOMEAs and estimation-of-distribution algorithms, should be given priority, especially when problem-specific knowledge is not straightforward to exploit, e.g. in the case of black-box optimization

Adaptive Ranking Based Constraint Handling for Explicitly Constrained Black-Box Optimization

A novel explicit constraint handling technique for the covariance matrix adaptation evolution strategy (CMA-ES) is proposed. The proposed constraint handling exhibits two invariance properties. One is the invariance to arbitrary element-wise increasing transformation of the objective and constraint functions. The other is the invariance to arbitrary affine transformation of the search space. The proposed technique virtually transforms a constrained optimization problem into an unconstrained optimization problem by considering an adaptive weighted sum of the ranking of the objective function values and the ranking of the constraint violations that are measured by the Mahalanobis distance between each candidate solution to its projection onto the boundary of the constraints. Simulation results are presented and show that the CMA-ES with the proposed constraint handling exhibits the affine invariance and performs similarly to the CMA-ES on unconstrained counterparts.Comment: 9 page

A Feature-Based Comparison of Evolutionary Computing Techniques for Constrained Continuous Optimisation

Evolutionary algorithms have been frequently applied to constrained continuous optimisation problems. We carry out feature based comparisons of different types of evolutionary algorithms such as evolution strategies, differential evolution and particle swarm optimisation for constrained continuous optimisation. In our study, we examine how sets of constraints influence the difficulty of obtaining close to optimal solutions. Using a multi-objective approach, we evolve constrained continuous problems having a set of linear and/or quadratic constraints where the different evolutionary approaches show a significant difference in performance. Afterwards, we discuss the features of the constraints that exhibit a difference in performance of the different evolutionary approaches under consideration.Comment: 16 Pagesm 2 Figure