Cooperative Immune Clone Co-evolutionary And Quantum Particle Swarm For Solving Constrained Multi-objective Optimization

In recent years, it is wildly accepted that multi-objective optimization problem has became a research focus. And in practical applications, we find that the problem we need to deal with has some constraints more or less, especially the real-life problem. Thus phenomenon emerged a new research direction-constrained multi-objective optimization problem. We hope that we can design an algorithm that is able to output a set of solutions uniformly distributed on the Pareto front of the test problem. Because this problem is closer to real life, this issue has high research value. And based on that, new algorithms are constantly being proposed.Traditional non-evolutionary algorithm can’t found the Pareto front of test problem well. Most algorithms output only one value in one run, undoubtedly this is very difficult to express the entire Pareto front of the test problem. While the evolutionary algorithm(EA) dealing with the constrained multi-objective optimization problem achieved great success. Evolutionary algorithm can output several values, this means we just need one-time evolutionary calculation, the output can express the Pareto front of test problem well. So it has become a main research directions that how to make better use evolutionary algorithm to solve this problem. The main contents include:1. The proposed algorithm introduces a constraint handling strategy and the strategy is modified to use it better. Specific process is as follows, constraints deviation value is added to objective function value to form a new objective function value. The next step is selection process. The proposed algorithm does not only retain the feasible non-dominated solutions, but also utilizes the non-feasible solutions which have small constraint deviation value and objective function value. Then, a quantum rotating gate is designed to accelerate the computational speed.2. Based on the immune clone algorithm and co-evolutionary algorithm, the cooperative immune clone co-evolutionary algorithm is designed combining the theoretical model of co-evolution algorithm to deal with constrained multi-objective optimization problem. The first step of the algorithm is to produce several different populations through the initialization process, and the evolution of each population isindependent, the next population is generated by the immune cloning operation in the population during each iteration. After the iteration process of each population, different populations communicate and cooperate through the mechanism of shared neighborhood. This algorithm designs a multi-level elite population policy which can be efficiently used to save the outstanding individuals found by the algorithm. In addition, this method also utilizes a sort crowding strategy, which can improve the algorithm computational efficiency under the premise to ensure the performance of diversity.3. Particle swarm’s search ability is good,Quantum Particle Swarm based on Particle swarm operator also has a good performance of global exploration and local search ability. However, when a problem has several non-contiguous optimal regions, the algorithm can’t find all optimal regions. So on the basis of quantum particle swarm this paper has added a mutation operator, help the individuals jump out the local optimum solutions.This research is supported by the National Natural Science Foundation of China(No. 61371201)...