Research On Surrogate-assisted Evolutionary Algorithms For Expensive Optimization Problems

Some optimization problems in the real world involve time-consuming simulations or expensive experiments.These problems usually consume plenty of time or material resources to do one real evaluation,so they are also referred to as expensive optimization problems.It is unpractical to use evolutionary algorithms to solve these problems as evolutionary algorithms usually need many exact function evaluations to find acceptable solutions.To enhance optimization efficiency,many studies have incorporated surrogate models into evolutionary algorithms to solve these expensive optimization problems.Surrogate models can predict fitness values for expensive problems.In addition,surrogate models based on classification algorithms can be used to classify solutions into promising and unpromising solutions.Although this approach can effectively reduce the number of exact evaluations required to solve expensive problems,some shortcomings still exist.For example,algorithms which do not consider the uncertainty of the surrogate model are easy to be premature;the optimization efficiency of the surrogate-assisted evolutionary algorithms on high-dimensional problems needs to be improved;the current surrogateassisted local search methods have low search efficiency.In this paper,some strategies have been proposed to address the above defects.The main contents are as follows:(1)For expensive single-objective optimization problems with medium dimensions,algorithms which do not consider the uncertainty of the used surrogate model may fall into the local optimum.An ensemble of surrogates assisted particle swarm optimization algorithm is proposed to address this issue.The predicted fitness values and uncertainty of unknown points can be provided by using two different RBF models to build an ensemble model.According to the predicted information,an LCB(lower confidence bound)criterion with a variable weight coefficient is proposed to balance the exploration and exploitation of the swarm.For faster convergence and avoiding wrong attraction of models,optima of two surrogates(polynomial regression model and radial basis function model)are evaluated in the convergence state of particles.10-,20-,and 30-dimension test problems and an engineering case are used to test the performance of the proposed algorithm.Experimental results show the efficiency of the proposed algorithm.(2)Surrogate-assisted evolutionary algorithms which only use one swarm have low search efficiency in solving high-dimensional expensive single-objective optimization problems.A surrogate-assisted multi-swarm optimization algorithm is proposed to address this issue.The proposed algorithm includes two swarms: the first one uses the learner phase of teaching-learning-based optimization to enhance exploration,and the second one uses the particle swarm optimization for faster exploitation.These two swarms can learn from each other.A dynamic swarm size adjustment scheme is proposed to control the evolutionary progress.Two coordinate systems are used to generate promising positions for the particle swarm in order to further enhance its search efficiency on different fitness landscapes.Moreover,a pre-screening criterion based on self-improvement is proposed to select promising individuals for exact evaluations.Several commonly used benchmark functions with their dimensions varying from 30 to 200 and an engineering case are adopted to evaluate the proposed algorithm.Experimental results demonstrate the efficiency of the proposed algorithm.(3)In solving expensive multi-objective optimization problems,commonly used surrogate-assisted local search methods can only promote the exploitation of positions where the evolutionary population is located.To accelerate the search of the population in promising sparse areas and guarantee the diversity of the obtained non-dominated solutions,a predicted Pareto front model-based local search method is proposed.The sparse points in the predicted Pareto front model are used to guide search directions of the local search.It can promote the population to explore sparse areas in the current Pareto front.In addition,to enhance the efficiency of the local search,optima of the surrogate models are used to promote the predicted Pareto front model toward the real Pareto front.The proposed local search method is incorporated into a surrogate-assisted multi-objective evolutionary algorithm.To reduce expensive evaluations,a pre-screening criterion which uses nondominated ranks and distance information is proposed to select promising individuals for exact evaluations.The proposed algorithm is evaluated with ZDT and DTLZ instances with their dimensions varying from 8 to 30 and an engineering case.Experimental results demonstrate the efficiency of the proposed local search method and the superiority of the proposed algorithm.(4)In solving high-dimensional expensive multi-objective optimization problems,algorithms which only use the surrogate-assisted pre-screening criterion or surrogate-based infill points have low search efficiency and ability.To enhance search efficiency,a multioffspring method is proposed to accelerate the search.In addition,a hierarchical prescreening criterion is proposed to select the surviving offspring and exactly evaluated offspring.The pre-screening criterion can maintain the diversity and superiority of the offspring by using reference vectors and the non-dominated rank.Several offspring with good diversity and convergence are exactly evaluated to reduce the number of exact evaluations.Furthermore,two types of surrogate-based infill points are used to further improve the search efficiency.The Pareto front model-based infill points are used to enhance the exploration of sparse areas in the predicted Pareto front,while the infill points from the surrogate-assisted local search are used to accelerate the exploitation towards the real Pareto front.ZDT and DTLZ instances with their dimensions varying from 8 to 200 and a neural network training problem are used to test the performance of the proposed algorithm.Experimental results demonstrate the efficiency of the proposed algorithm.(5)In solving expensive many-objective optimization problems,current offspring generation methods used in surrogate-assisted many-objective evolutionary algorithms have low search ability.To enhance search efficiency of the population,a predicted Pareto front model-based multi-offspring method is proposed.A predicted Pareto front model is first built with current non-dominated solutions.Then,some sparse areas are found in the model.Solutions close to each sparse area are used to produce multi-offspring solutions to promote the search of the area.The proposed offspring generation method is incorporated into a surrogate-assisted many-objective evolutionary algorithm.A pre-screening criterion based on the clustering method and non-dominated rank is proposed to select promising solutions for exact evaluations.The clustering method and the non-dominated rank can ensure the diversity and convergence of the selected solutions,respectively.10-,20-,and 30-dimension DTLZ instances with 3,4,6,8 and 10 objectives and a car cab design problem are used to test the proposed algorithm.Experimental results have demonstrated the efficiency of the proposed offspring generation method and the superiority of the proposed algorithm.Finally,we conclude the paper and discusses some future work.