The Gaussian Process And Dynamic Hybrid Framework For Solving Expensive COPs

Evolutionary algorithms (EAs) are widely used to solve single/multi-objective optimizationproblems, due to EAs’ implicit parallelism, strong robustness and other characteristics.However, in the course of evolution, EAs require a large number of function evaluations andcomparisons for objective functions to the candidate solutions, in order to obtain acceptableoptimal solutions. But for complex optimization design problems, only one objective functionevaluation may need to consume lots of time or computing costs, called expensive problems.Therefore, it is costly by using EAs based on the original objective function value evaluationto search for the optimal solutions. At the same time, lots of optimization problems haveconstraint conditons, called constrained optimization problems (COPs). Although the existingconstrained optimization evolutionary algorithms (COEAs) have certain effect on COPs, theydonot involve COPs with expensive properties, which are called expensive COPs. Gaussianstochastic process model(GP) is a kind of surrogate model, which has characteristics such asless parameters, strong ability to overcome the over-fitting and so on. The prediction accuracyof GP can be improved by adding the sample points continually. COEAs consist of EAs andconstraint handling techniques. COPs are solved by EAs after transforming the constrainedproblems into the unconstrained problems by constraint handling techniques. A dynamichybrid framework (DyHF) is a COEA which using constraint handling techniques based onmulti-objective optimization and DE as the searching method. DyHF exhibits excellentperformance for COPs.This paper proposes a method named GP_DyHF for solving expensive COPs, whichcombine GP as a surrogate model with DyHF for its excellent searching ability. The researchcontents of this paper are as follows：(1) The processing method of sample set: GP_DyHF uses Latin hypercube samplingmethod(LHS) to get the initial sample set and uses fuzzy cluster to deal with big sample setfor reducing the computational cost of formation of surrogate model. Using the proposed twoupdating ways, the internal and external, to add and replace sample points for improving theprediction accuracy of surrogate models.(2) The enhanced algorithm: Enhancing the global search model and local search model inDyHF to improve the optimization ability of DyHF.(3) Ensemble algorithm: In the ensemble algorithm, combining GP with DyHF, the sampleset and the population are independent but can exchange information appropriately during theevolution. In order to use surrogate models and true functions reasonably, a dynamiccontrolling method, which can accelerate the convergence and reduce the number of fitnessevaluations, is proposed according to the feasible rate.GP_DyHF is tested by22benchmarks on CEC2006. The Experimental analysis show thatit can ensure a certain optimal solution accuracy while significantly reducing the number ofevaluations.