Research On Evolutionary Algorithms For Expensive Heterogeneous Many-objective Optimization Problems

Many engineering or scientific problems normally require optimizing multiple conflicting objective functions simultaneously.Many of these problems are not able to be shown in explicit mathematical models but require to be evaluated by physical experiments or high-precision simulations on the performance.However,the cost or time consumption is very high for a physical experiment or high-precision simulation,resulting in the impossible for evolutionary algorithms to solve these problems.A common way to assist evolutionary algorithms in solving this kind of problem is by using surrogate models.However,when the dimension of objective space increases,a more efficient search algorithm is required to find the set of optimal solutions on the one hand.On the other hand,an error approximation on an objective function may mislead the algorithms deviating from the correct search direction for expensive problems.Furthermore,the cost of each objective function evaluation is normally different for expensive high-dimensional multi-objective problems.Therefore,in this article,we give an intensive study on many-objective optimization algorithms and surrogate-assisted many-objective optimization algorithms for heterogeneous expensive many-objective optimization problems,which mainly include the following parts:1.A non-dominated sorting on performance indicator for evolutionary many-objective optimization(NSPI-EMO)and a decomposition-based many-objective evolutionary algorithm with optional performance indicators(MOEA/D-OPI)are proposed for many-objective optimization problems.In the NSPI-EMO approach,performance indicators for convergence and diversity are proposed,based on which the non-dominated sorting is conducted for selecting the next parent population.In the MOEA/D-OPI algorithm,a performance indicator is randomly chosen for each reference vector to select a solution to survive for the next generation.The experimental results on DTLZ and Ma F test problems with up to 30 show that the proposed two optimization algorithms are efficient for solving many-objective optimization problems.2.With the synchronous sampling mechanism,a performance approximation assisted expensive many-objective evolutionary algorithm(PA-EMa OEA)and sampling based on the mean value of ranking on approximation uncertainties for an expensive many-objective evolutionary algorithm(Sa MVRAU)are proposed for heterogeneous expensive manyobjective optimization problems.In PA-EMa OEA,the diversity and convergence performances are calculated for each historical data and used as samples for training surrogate models for diversity and convergence performance indicators,respectively.The expensive many-objective problem is solved by multi-objective searching and infill sampling based on surrogate models for diversity and convergence performance indicators.Experimental results show that the proposed method can reduce the computational complexity of the algorithm efficiently and can also reduce the probability of deviating from the correct search direction due to too many surrogate models.In Sa MVRAU,the approximation uncertainty of an individual is defined by the mean value of sorting on the approximation uncertainty for all objectives.The proposed approximation uncertainty is used for choosing solutions for real expensive objective evaluation.The experimental results on DTLZ and Ma F test problems and car side impacts indicate that the proposed method can solve expensive many-objective optimization problems within limited resources.3.A surrogate-assisted expensive many-objective optimization with asynchronous sampling(SEMa OA-AS)is proposed for heterogeneous expensive many-objective optimization problems.Whether the objective function is exactly evaluated is determined by the ratio between the cost of this objective function and the objective function with the cheapest cost among all objective functions.When the objective function is needed to be evaluated using the expensive objective function,the solution with the maximum approximation uncertainty or the solution with the minimum approximation uncertainty will be selected for expensive evaluation on this objective function.Experimental results show that the proposed method performs better for solving expensive many-objective problems than those with the synchronous sampling mechanism.