Research On Multi-Objective Artificial Physics Optimization Algorithm And Its Application

There are a lot of multi-objective optimization problems no matter in natural science area or in engineering applications. It is an important subject for researchers to find a multi-objective optimization algorithm with characteristics of efficient and robust. Aritificial Physics Optimization (APO) algorithm is a stochastic optimization algorithm proposed recently. It simulates social animals'forgaing from the viewpoint of artificial physics to solve global optimization problems with single objective, and it has a good performance in the aspects of convergence, diversity and robust. In this thesis, APO algorithm is applied into multi-objective optimization area and servel aspects of the algorithm, such as its framework establishment, its effectiveness, diversity of population, selection of fitness function, constraint handling, path planning of mobile robot, are studied to make it more effective. It mainly contains:1. Due to the similarities between APO algorithm and the classic population-based optimization algorithms, the feasibility of applying APO algorithm to solve multi-objective optimization problems is discussed detailedly. Synchronously, some key problems need to be solved when applying APO algorithm to multi-objective optimization area are analyzed. Then the framework of multi-objective artificial physics optimization algorithm is constructed. Based on it, a multi-objective artificial physics optimization algorithm is proposed by combinating with the idea of aggregating functions method. It is tested on a well-known benchmark suite and the experimental results show that the proposed approach is effective.2. The relationship between the diversity of population and virtual force exerted on an individual by the other individuals in population is analyzed based on the characteristics of APO algorithm. Then a multi-objective artificial physics optimization algorithm based on virtual force sorting is presented. At the same time, its convergence is analyzed theoretically. Simulation test shows that the proposed approach has a good performance especially with a perfect diversity comparing with those of the classic multi-objective evolutionary algorithms.3. The relationship between the mass of an individual in multi-objective artificial physics algorithm and the fitness value of the individual in multi-objective optimization problem is analyzed firstly. Then Pareto-based concept of rank and sharing techniques based on neighbourhood radius are used to construct mass function. Based on it, a multi-objective artificial physics based on rank is brought forward. The performance of the approach is tested on some well-known benchmarks and the results show that the proposed algorithm is competitive, effective and efficient comparing with some popular multi-objecitve optimization algorithms, such as the classic multi-objective evolutionary algorithm, multi-objective particle swarm optimization algorithm and standard multi-objective aritificial physics optimization algorithm.4. Constraint multi-objective artificial physics optimization algorithms are studied in this thesis. Firstly, feasibility-based method is adopted as constraint handling mechanism. Meanwhile, different mass functions and virtual force rules for feasible individuals and infeasible individuals are constructed, respectively. According to these rules, a constraint multi-objective artificial physics optimization algorithm based on virtual force decreasing is proposed, which deals the case of feasible individuals moving into infeasible area efficiently. As a result of that, the proposed approach can solve the problems with the solutions on the boundary of feasible area and infeasible area well. Synchronously, the convergence of the presented algorithm is analyzed with the basic technique of probability. Simulation test results prove it has a good performance. Then the constraint-preserving method is used as constraint handling mechanism. Combining with the idea of multi-objective artificial physics optimization algorithm based on rank, a constraint multi-objective artificial physics optimization algorithm based on rank is proposed and its performance is analyzed by simulation test.5. Using multi-objective artificial physics optimization algorithms to deal with mobile robot path planning problems with multiple optimization objectives are studied in this thesis. Firstly, the mobile robot's workspace is built up according to the information of obstacles. Therefor, the problem of mobile robot path planning is tuned into a constraint multi-objective optimization problem in continuous space. Then, the characteristics of mobile robot path planning problems are analyzed and the fitness function of mobile robot path planning is constructed, in which path length and path smoothness are optimization objectives. Thirdly, constraint multi-objective artificial physics optimization based on rank is used to plan mobile robot path. At the same time, the classic multi-objective evolutionary algorithm, NSGA-II, is adopted to plan mobile robot path in the same environment. The comparing results of simulation tests show that it is feasible and effective to use constraint multi-objective artificial physics optimization algorithm to solve the problems of mobile robot path planning. Finally, constraint multi-objective artificial physics optimization algorithm based on virtual force decreasing is used to plan the path of mobile robot. The feasible engineering domains for each constraint multi-objective artificial physics optimization algorithm are presented by analyzing the results of simulation tests.