Dynamic Multitasking Modeling And Optimization For Expensive Problems

Expensive optimization problems(EOP)exist widely in various important practical applications.The goal of EOPs is to find the global optimal value of a given problem in a very limited computation costs,it presents a great challenge to the solving ability of EOP optimization methods.Among various optimization methods,surrogate-assisted evolutionary algorithm(SAEA)has become a popular method to solve complex and computationally expensive optimization problems efficiently.The search performance of SAEA depends on the modeling method and evolutionary algorithm it uses.Multiple functions reflecting different characteristics of the problem can be obtained by modeling EOP with different surrogate models,so as to comprehensively describe the characteristics of EOP.In evolutionary multitasking(EMT),simultaneous optimization of multiple tasks through knowledge transfer between tasks can significantly improve the efficiency of optimization.Using EMT to optimize these surrogate models simultaneously and effectively combining the prediction results of multiple surrogate models can improve the probability of finding the real optimal solution.Inspired by this idea,this paper designs a multi-surrogate multi-tasking evolutionary algorithm based on the multi-tasking optimization framework to solve EOPs.The main research work is as follows:1.Designing a multifactorial differential evolution algorithm with optima-based transformation(MFDE-OBT).In MFDE-OBT,an improved assortative mating operation is designed based on the DE/rand/2 mutation operator.This operation generates offspring by perturbing the current optimal individual.The object of the assortative mating is a vector added for the perturbation,which is the sum of two difference vectors generated by a random sample with a certain probability from an individual set that can be same as or different from the one of the task involving the optimal individual.In addition,an opposition-based search strategy is designed to balance the exploitation and exploration of the search space.MFDE-OBT is compared with six published evolutionary multitasking algorithms on a set of single-object multitasking functions.The experimental results show that MFDE-OBT is significantly superior to the other six competitors in solving highly similar tasks.2.Designing a multi-surrogate multi-tasking genetic algorithm with adaptive local modeling strategy(MS-MTGA).First,MS-MTGA transforms expensive optimization problems into multi-tasking optimization problems by integrating global and local surrogate models.Secondly,the optimization information learned by historical local surrogate models into a new local model to accelerate the local exploitation.The training samples of the local model updated at each iteration are adopted from the optimal points of historical local models.Meanwhile,in order to make the optimization of the model more oriented,the globally optimal individual of the objective function is also selected to guide the construction of the local surrogate model.MS-MTGA is tested on a set of benchmark functions and two engineering design optimization problems.Experimental results demonstrate the superiority of MS-MTGA algorithm in solving complex and composite expensive problems.Compared with other existing SAEAs,MS-MTGA proposed based on EMT has obvious advantages.To be specific,the algorithm proposed in this paper can obtain feasible and high-precision optimal solutions for both high-dimensional and low-dimensional problems,and also shows strong advantages in solving practical engineering design optimization problems.MS-MTGA effectively saves computational cost when solving EOPs,and has guiding significance for solving EOPs in algorithm design.