Research And Implementation Of Multimodal Optimization Methods Based On Population

Multimodal optimization is widely used in the fields of mechanical or electrical system design, electric power system planning, protein structure prediction and so on. The paper mainly concentrates on the problem of niching in multimodal optimization, prematurity in evolutionary computation. Abstract convexity is also introduced for these issues. Within the framework of evolutionary computation, the hybrid methods benefits for keeping the multimodal properties, and improving the results’ reliability at the same time. Finally, we applys multimodal optimization to the protein structure prediction issues. The detail works and research research achivements are listed as fowllows:1. The paper takes a brief overview for the development of multimodal optimization in the last decades, and against the commonly used strategies, we analyse its merits and demerits.2. A new multimodal optimization based on dynamic radius is proposed in this paper. In this algorithm, we design a two stage annealing schedule. The radius of species sets large enough initially, in favor of exploring all the possible species in the whole feasible space. With proceeding of the algorithm, it narrows to a very small space, where exploitation takes over to improve the quality of each seed in each species. In order to generate some high quality individuals, the crossover and mutation operators in Differential Evolution(DE) are integrated into species perturbing procedure, creating m perturbing trial individuals, expecting to detect some promising regions and strengthen the search within detecting niches. Subsequently, we use these trial individuals to update the current population. With the guidance of the annealing schedule, the proposed algorithm achieves well balance between exploration and exploitation.3. Within the framework of basic evolutionary algorithms, a new multimodal optimization algorithm based on local abstract convexity support hyperplanes is proposed in this paper by combining the abstract convexity theory. Firstly, the original bound constrained optimization problem is converted to an increasing convex along rays (ICAR) relaxed problem over unit simplex by using the projection transformation method. Secondly, we construct the underestimate support hypeplanes with the information of trial individual’s neighbourhood, which also contributes to identifying the potential niches dynamically, thus lowering the replacement error, and avoiding premature. Finally, with the aid of descendent direction of support hypeplanes, the detected niches would get enhanced at the same time.4. For the high-dimensional conformational space sampling bottleneck, the ECEPP/3force field model is converted to an increasing convex along rays(ICAR) function subjected to unit simplex firstly by projection transformation. Based on abstract convex theory, the support hyperplanes of the increasing convex along rays function is also proved and presented explicitly. Within the framework of Conformational Space Annealing(CSA) algorithm, the underestimate supporting hyperplanes of original potential function model is established using the subdifferentials of local minimized energy landscape of individuals in iterative procedure. Furthermore, the proposed algorithm can gradually reduce the conformational sample space using the local minima, which can be explicitly enumerated by a very efficient combinatorial method. At the same time, we can effectively reduce the function evaluations of original force field model, whose computation can be quite expensive, by using the lower estimation. Experiment results demonstrate that proposed algorithm can find the lowest energy configuration of Met-enkephalin (TYR1-GLY2-GLY3-PHE4-MET5), and it is more fast and reliable than other optimization methods given in paper.5. Finally, the works and contribution in this paper are summarized, it present the results of the scientific research works as well as the shortcomings in the process and outlook the prospect for multimodal optimization areas and the further research plans.