Research On Numerical Constraint Handling Techniques For Evolutionary Algorithms

A lot of problems we encountered in real world applications are constrained optl-mization problems. Evolutionary algorithms are widely used to deal with constrained optimization problems due to their powerful search ability and robustness. Differ-ent kinds of evolutionary algorithms are brought about by researchers to solve con-strained optimization problems. Based on recent studies, we propose two new algo-rithms to solve complicated constrained optimization problems and constrained opti-mization problems encountered in engineering design, respectively.1. There are many constraints in constrained optimization problems and these con-straints may be conditioned by each other. These constraints make it more diffi-cult for evolutionary algorithms to solve constrained optimization problems than to solve unconstrained optimization problems. The difficulty of using evolution-ary algorithms to deal with constrained optimization problems is how to select a more superior individual from two compared individuals. It is easy to decide which one is superior when both two individuals are feasible. However, it is difficult to decide which one is superior when there is at least one infeasible in-dividual between two individuals. In view of this situation, we propose a refer-ence point based constraint handling method for evolutionary algorithm, which is called RPCH. Firstly, a reference point is selected by a mechanism according to the composition of the population. When two adjacent individuals are com-pared, if they have the pareto dominance relationship, the point which dominates the other has a higher rank. Otherwise, the distances of objective values of these two individuals to the selected reference point are measured. The point that has a smaller distance ranks higher. In this way, all points in the population have a unique rank value. After all the individuals in the population are ranked, the best μ out of λ individuals are selected as parents to reproduce and continue to evolve. Extensive experiment results show that RPCH can solve 21 out of 24 constrained optimization problems efficiently. What’s more, RPCH has updated the optima solution of instance g22. Comparison with some state-of-the-art al-gorithms shows that RPCH is a competitive algorithm to solve constrained opti-mization problems.2. Sometimes, the cost of evaluating the constrained optimization problems in real world is expensive, therefore, people want to find the optima with the minimum cost. In other words, people want to find the optima as fast as possible. However, if the convergence speed is too high, it will decrease the diversity of the popula-tion, which can make the population trap into local optima. If we pay too much attention to population diversity, the convergence speed of the population will slow down. To improve the convergence speed while ensuring the solution qual-ity, we propose a fast differential evolution approach to solve several constrained engineering design optimization problems, which is called FDE. In this approach, a new mutation strategy "DE/current-to-ppbest" is proposed to get a balance be-tween exploration and exploitation of the population. What’s more, a ranking based selection mechanism rather than pairwise comparison based selection se-lects the promising individuals from the combination of parents and offspring to update the population. Experimental results on 5 instances extracted from engi-neering design shew that FDE can acquire quite competitive performance. FDE is comparable to other state-of-the-art approaches in terms of solution quality. As for convergence speed, FDE is more fast, or at least comparable to, other state-of-the-art approaches. When the number of function evaluation is limited or the cost of function evaluation is expensive, FDE is a good choice.