Intelligent Optimization Algorithm For Solving Multimodal Problem

Multimodal problems widely exist in fields,such as healthcare,agriculture,aerospace,national defense,and contain multiple optimal solutions.It includes multimodal single-objective optimization problem and multimodal multiobjective optimization problem.Finding an optimal solution cannot meet practical applications.It is important for decision-maker to locate all optimal solutions,which is beneficial for them making a swift decision.With the rapid development of computer technology,it has become the new normal to employ intelligent optimization algorithms to solve optimization problems.The advantages of intelligent optimization algorithms are easy operation and simple structure.In addition,intelligent optimization algorithm does not require gradient information and can find multiple optimal solutions in a single run.However,it is still in primitive phase that employ them to solve multimodal problems.There are many problems to be handled and studied,for example,the existing algorithms are easily trapped in local optimal regions,sensitive to some parameter,have poor population diversity,and so on.To deal with these concerning issues,the research is conducted along the route of “problem challenge–algorithm research–application verification–summary&outlook” in this dissertation,which analyzes the problem characteristics and challenges faced by the existing algorithms,proposes four intelligent optimization algorithms for multimodal problems,and applies the proposed algorithms to solve the practical problems.The main research contents are as follows:1.A penalty-based multimodal single-objective optimization algorithm is proposed.The current multimodal single-objective optimization algorithms often waste the computational resource in the region where the optimal solution has been located.In addition,these algorithms are easy to fall into local optimal regions and sensitive to niching parameter.When the penalty techniques is used to solve nonlinear equation systems,the performance is improved.Inspired by it,a penalty-based multimodal single-objective optimization algorithm is proposed.The proposed algorithm employs the penalty technique to reduce the fitness of individuals in the region where the local and global optimal solutions have been discovered.In this way,the computational resource can be saved to locate the other optima.There is still a key issue: how to determine whether a solution is local or global optimal solution when the optimal function value of black-box problem is unknown.Therefore,an elite selection mechanism is proposed,and the experimental results verify that this mechanism can quickly and effectively detect the optimal solutions discovered during the optimization process.The experimental results of 20 test functions in IEEE CEC2003 show that the proposed algorithm outperforms 11 competitive algorithms and three winning algorithms in competition.This research opens up a new idea to study multimodal single-objective optimization algorithms.2.An expensive multimodal-single objective optimization algorithm based on decomposition is designed.A large amount of computational resource is required during the evolution in the existing algorithms but the simulation experiment is expensive in the real application,which causes the relevant algorithms cannot effectively handle these problems.An expensive multimodal single-objective optimization algorithm based on decomposition is designed to address the above issue.It is important to reduce expensive simulations during optimization process.Therefore,the local surrogate model is designed to replace expensive simulations during optimization process.The experimental results show that the required computational resource is significantly reduced.How to locate all global optima is also a key issue.The decomposition idea has been used to solve expensive multiobjective optimization problems.The existing studies show that the decomposition idea is feasible.We first use the decomposition idea to solve expensive multimodal single-objective optimization problems.The problem is decomposed by the promising regions detection phase,and the subproblems are solved separately during the local search phase.The effectiveness of algorithm is verified by solving 20 test functions.This research supports the required multimodal single-objective optimization algorithms for the practical applications.3.A biobjective evolutionary algorithm is developed.A biobjective evolutionary algorithm is proposed to cope with the imbalance between diversity and convergence in both the decision and objective spaces caused by the convergence-first imbalance in existing multimodal multiobjective optimization algorithms.We first attempt to define the convergence and the diversity as two objectives to be optimized.In this way,a multimodal multiobjective optimization problem is transformed into a biobjective optimization problem,and the conflict between two objectives is verified.It can be found that the proposed algorithm performs the best in both decision and objective spaces by comparing the experimental results of seven representative algorithms on 22 test functions in CEC 2019.Especially,the proposed algorithm is superior to all competitors in the objective space.This research supports the required algorithms for multimodal multiobjective optimization.4.A multimodal multi-objective optimization framework is constructed.Multiobjective optimization algorithms lack the diversity preservation strategy in the decision space.When they are directly employed to solve multimodal multiobjective optimization problems,their performance is poor.Therefore,a multimodal multiobjective optimization framework is proposed by employ the biobjective transformation mechanism in aforementioned research.First,three balances is defined.Their importance and difference are analyzed.Two diversity selected strategies are designed by biobjective transformation mechanism to maintain the first two balances.In addition,an adaptive selection mechanism is developed to achieve the third balance.This framework can be integrated with any multiobjective optimization methods based on decomposition and indicator.Based on this framework,four algorithms are proposed.Their effectiveness are verified by the experimental results on 22 test functions.5.Multimodal multiobjective optimization algorithm is utilized to tackle real-world problems.We take feature selection and location selection optimization problems as examples to test the effectiveness of the above proposed algorithms.The multimodal property of these two problems is analyzed and the mathematical optimization model is built.Then,the above proposed algorithm is applied to deal with these two real-world problems.The experimental results prove their feasibility and application prospects.