Novel Multi-agents Dynamic Evolutionary Algorithms For Complex Optimization

Nowadays there is a socio-economic environment with increasingly competitive global economy, exhausting energy resources, growing intense awareness of saving and environmental protection. The numerous industries such as industrial manufacturing, agriculture, national defense, transportation, and financing are under the pursuit of high output, high yield, high efficiency, low emission and safety. Facing up with the situation, the complex optimization problems focusing on multi peak distribution, non-convex constraints and local extrema need to be solved. This paper starts with the limitation of the heuristic optimization algorithms for solving complex optimization problems. Firstly, an important hidden factor which causes trapping into local optimum is discovered, and a rainforest algorithm (RFA) is proposed in order to avoid the problem. Secondly, a novel multi-agents system is designed to improve the scalability of the original rainforest algorithm, which is constructed to realize a dynamic diversified evolutionary algorithm (DDEA) that has better portability and is easier to be programed. Finally, the evolutionary algorithms basing on the heuristic multi-layer agents are studied on different types of optimization problems. Furthermore, two kinds of newly dynamic evolutionary algorithms are put forward to solve complex convex constrained optimization problems and singular non-convex constraint optimization problems in actual applications. The main contents and contribution of the paper are as follows:(1) The paper is based on the background of the widely used heuristic optimization algorithms in complex multimodal optimization problems. By thorough mechanism analysis of swarm intelligence optimization algorithms with the goal of avoiding premature convergence towards local extrema, pseudo-collision is found as a recessive premature convergence phenomenon which directly affects the speed and accuracy of the optimization algorithms. Further investigate on the sampling of agents indicates that unconstrained motion sampling and the lack of information on samples distribution are the basic reasons for pseudo-collision. In order to deal with this problem, rain forest algorithm (RFA) specifically aiming at complex nonconvex optimization is developed by imitating the growth pattern of plants in nature. Variable population is advised to substitute for fixed population to carry out optimization sampling in dynamic partitions and classifications, which will effectively reduce pseudo-collision. The principles of uniform and non-uniform sampling are suggested to facilitate the trade-off between exploration and exploitation. By performance test on six complex benchmark functions and comparing with particle swarm optimization (PSO) and genetic algorithm (GA), it has been proved that RFA can always be the first to obtain the global optimal result in several experiments. The sampling figures describing cumulative distribution also show that RFA has high flexibility of controlling sample density. It demonstrates that the proposed algorithm can effectively reduce the "virtual" collisions and has high precision and stability of the global optimal solution when improving the efficiency of optimization.(2) In order to further improve the generality and portability of rain forest algorithm and simplify the algorithm procedure to expand its applications, the paper proposes a new multi-agent system with a more flexible structure and designs a dynamic diversified evolutionary algorithm (DDEA) that will alleviates the principal contradiction of exploration and exploitation in sampling distribution. A three layers proxy model(TLPM) which includes the characteristic attribute of each agent, organization mode of multi-agents and information sharing between different agents, is abstracted from RFA and is used to construct a novel multi-agents evolutionary pattern. The multi-agents system with flexible and self-organization characteristics is combined into the dynamic diversity evolutionary algorithm(DDEA), which not only has advantages of easy program implementation, extension and transplantation, but also can realize the fast switching of exploration and exploration to effectively solve the principal contradiction in the sampling distribution strategy. The paper also presents the performance test on speed and accuracy of the proposed DDEA algorithm implementing on six different types of benchmark functions, comparing with the current commonly used algorithms such as PSO and GA. The experimental results show that DDEA can manage individual agent with different density distribution reasonably according to the fitness and lock global optimal region more quickly with less samples while obtaining relatively accurate and stable optimums, which implies that the multi-agents system has more prominent adaptive ability and evolutionary efficiency.(3) Bi-directional dynamic diversity evolutionary algorithm(BDDEA) and iterative dynamic diversity evolutionary algorithm(IDDEA) are put forward respectively for solving usual complex constraint non-convex optimization problems and singular constraint non-convex optimization problems. Firstly, since the optimums in most of the complex non-convex constrained optimization problems locate at the boundary of feasible region, sampling in the feasible region will take a lot of time to find considerable optimal results. Furthermore, the optimization results are often uncertain due to the fact that the method of adding penalty function not only induces new selection problems, but also makes the objective function more complex. Secondly, singular non-convex constraint optimization problems can not be solved effectively in actual engineering because the unique environment near the global optimal point often leads to ill-convergence in the exploitation process of optimization. Thus, two kinds of algorithms developed from DDEA, diversity of bidirectional dynamic evolutionary algorithm (BDDEA) and the diversity of iterative dynamic evolutionary algorithm (IDDEA), are suggested to deal with complex constraints and singular constraints problem near to local optimums, respectively. In BDDEA, relative dominant areas inside and outside the feasible region are respectively estimated by object fitness and penalty function, which avoids the difficulty in choosing penalty coefficient and distortion of objective function caused by penalty function. Meanwhile, both the optimization speed and accuracy are greatly improved by the proposed bi-directional evolution method. As to IDDEA, it makes full use of the great exploration ability of DDEA and constructs a subregion partition strategy, where the optimization subregions are gradually narrowed and the proportion of subregion near to the local optimum and the global optimal subregion are amplified relatively to prevent mistake convergence in local optima. To verify the effectiveness of the proposed methods, a performance comparison with common algorithms on various benchmark functions is carried out. Complex structure optimization design in practical engineering problems are also used to test IDDEA by comparing with previous optimization results. The experimental results show that BDDEA can distribute more samples on the constrained boundary, especially near the optimum, which will improve the character emergence of objective function effectively and accelerate the speed of finding the global optimum. The successful applications of IDDEA in various actual engineering problems also demonstrate that this method can solve the problem on singular non-convex constraint and finally get better design parameters to satisfy the requirement of high performance design.