Phase Based Optimization And Its Application In High Dimensional Optimization Problems

The optimization problems in the real wor ld are often very complex.Especially,there are strong correlation among decision variables,large scale variables and strong conflicts among objective functions,all of which bring some severe challenges to the design of optimization algorithm.Under the requirement of big data environment,the research object generally has many properties,such as non-linear,non-convex,high-dimension,many multi-objectives and so on,or one of them.How to effectively solve the optimization problems with high or super-high dimensions has become a serious challenge in the field of computational intelligence.Inspired by the rich motion laws of matter in different phases,a computational model based on the motion characteristics of matter is proposed by exploring the potential optimization mechanism and search strategies.On this basis,a series of optimization algorithms are designed to elevate the shortcomings of traditional intelligent algorithms in solving different types of high-dimensional problems.The research on current intelligent optimization has shown that we should emphatically consider the interaction among system components,diversity and coordination of autonomous subjects,functional complementarity when designing a computational model or system with strong adaptive learning and effective optimization ability.This paper systematically analyses some key problems in the construction of computational model,the synergy of individual or subsystem behavior and the complementarity of functions in intelligent algo rithm design.Several kinds of optimization algorithms are designed to effectively solve common high-dimensional,variable-coupled high-dimensional and large scale multi-objective optimization problems,which effectively promote the theoretical research of intelligent optimization algorithms.These will provide the methods for the design of new intelligent system.The main contributions of which can be summarized as follows:(1)Inspired by the completely different motional characteristics of individuals under three different phases which are gas phase,liquid phase and solid phase in nature,a computational model based on the characteristics of state motion is constructed,and a new natural heuristic algorithm,Phase Based Optimization(PBO),is correspond ingly proposed to solve large-scale continuous optimization problems.From evolutionary points of view,in a search process of optimization,the varied kinds of motional characteristics of individuals in three different phases can be naturally utilized as three different search strategies.Firstly,by constantly observing and digging the motion law of substances in different phases,the motion characteristics of gas,liquid and solid phase are extracted,the corresponding search mechanism is analyzed,and the computational model of phase is established.Secondly,based on the search mechanism,the corresponding evolutionary operator is designed to construct the basic PBO algorithm.Thirdly,in order to verify the availability and advancement of the constructed model and proposed algorithm,six optimization problems in the C EC 2016 contest about big optimization are used to compare the performance with other advanced optimization algorithms.The experimental results show that the proposed PBO has better optimization performance and good potential for high dimensional problems.(2)To further reveal the essence of PBO algorithm,t he dynamic implementation process and search behavior of PBO algorithm are systematically analyzed.O n this basis,the phase transition process of population is analyzed by stochastic process and Markov theory.It is proved that PBO algorithm can converge to a satisfactory population with probability one when the population size is infinite.Those varied kinds of motional characteristics of individuals in different phases can be used as a heuristic search method for the optimal solution of an optimization problem.In addition,the time complexity of the algorithm is analyzed theoretically.Then,based on the 23 benchmark test functions summarized by Yao Xin,PBO is compared with the classical heuristic algorithms based on bio-evolution,swarm intelligence and other natural phenomena,the effectiveness and efficiency of PBO algorithm are verified.Besides,the effects of population size on PBO and the performance comparison of PBO under different problem dimensions are systematically investigated,respectively.Finally,PBO is applied to two application problems which are parameter estimation for frequency modulated sound waves synthesis and large scale transmission pricing problem,and the promising results indicate the applicability of PBO in both low and high dimensional real-world optimization problems.(3)Large scale optimization problems are more representative of real-world problems and remain one of the most challenging tasks for the design of new type of evolutionary algorithms.To improve the original PBO to solve large scale optimization problem,an effective search strategy combining complete stochastic search(the diffusion operator)and globally guided search(the improved perturbation operator)is utilized.The proposed strategy can give well-balanced compromise between the population diversity(diversification)and convergence speed(intensification)especially in solving high-dimensional optimization problems.We termed the improved algorithm as global-best guided PBO(GPBO)to avoid ambiguity.Seven well-known scalable benchmark functions and a real-world large scale transmission pricing problem are used to validate the performance of GPBO compared with some state-of-the-art algorithms.The experimental results demonstrate that GPBO can provide much better solution accuracy and convergence ability both on large scale benchmark functions and real-world optimization problem.(4)Cooperative Coevolution(CC)was introduced into evolutionary algorithms as a promising framework for tackling large scale optimization problems through a divide-and-conquer strategy.A number of decomposition methods to identify interacting variables have been proposed to construct subcomponents of a large scale problem,but if the variables are all non-separable,all the CC-based algorithms of decomposition will lose the functionality,therefore,classical CC-based algorithms are inefficient in processing non-separable problems that have many interacting variables.In this paper,a new CC framework which integrates global and local search algorithms is proposed for solving large scale optimization problems.In the stage of global cooperative coevolution,in addition to introducing the Hybrid Phase Based Optimization(HPBO)algorithm,we also introduce a new interacting variables grouping method named Sequential Sliding Window(SSW).When the performance of global search reaches a deviation tolerance or the variables are fully non-separable,we then use a more effective local search algorithm to subsequently search the solution space of the large scale optimization problem.The integration of global and local algorithms into CC framework can efficiently improve the capability in processing large scale non-separable problems.Experimental results on large scale optimization benchmarks show that the proposed framework is more effective than other existing CC frameworks.(5)Motivated by the ideas in the decompo sition based algorithms for solving MOPs and the effective search strategies with multi-population method for solving large scale single objective optimization problems,a novel multi-objective evolutionary algorithm based on decomposition is proposed,in which a multi-population meta-heuristic algorithm named as phase based optimization(PBO)is utilized as an effective search engine for enhancing the performance of the original MOEA/D,and is consequently termed MO EA/D-PBO.In order to generate the offspring using PBO to optimize the sub-problems decomposed by MOEA/D,the key step is to divide the whole population into three sub-populations.Three different sub-populations are divided by using the distance value between the individuals and the reference point in accordance with the principle from high to low.O n this basis,three different search strategies are executed to generate the better solutions according to the position characteristic of individuals with the reference point as the center.The empirical results demonstrate that MOEA/D-PBO can provide much better performance on large scale bi-objective and tri-objective optimization problems than MOEA/D-DE and IM-MOEA.Finally,the research works of this paper are summarized,and the prospectives of the further research is discussed.O ne prospective is how to automaticly choose optimization algorithms according to problem characteristics.Effectively extracting characteristic information from the large number of historical populations generated in the w hole process of search optimization is the second prospective.Certainly,it will be our eternal pursuit to seek more application areas of evolutionary algorithms.