Evolutionary Algorithms For Complex Mixed-Variable Optimization Problems And Their Applications

Evolutionary algorithm is a kind of population-based metaheuristic algorithm.They are widely used on solving different kinds of optimization problems.Current researches about the evolutionary algorithm mainly focus on solving optimization problems with only continuous variables or discrete variables.However,many optimization problems in the real world contain more than one kind of decision variables.These kind of optimization problems are called as mixed-variable optimization problems.In the region of evolutionary algorithms,the researches about how to solve mixed-variable optimization problems are not too much.Therefore,this paper mainly discusses how to solve mixed-variable optimization problems by using evolutionary algorithms.According to whether the optimization problem contains constraints,the numbers of the objective functions,and the kinds of variables included in the optimization problem,mixedvariable optimization problems can be classified into different types.This paper mainly focuses on three types of mixed-variable optimization problems: mixed-integer programming(MIP)problems,expensive optimization problems with continuous and categorical variables(EOPCCV),and expensive constrained optimization problems with continuous and categorical variables(ECOPCCV).The main contributions of this dissertation are listed as follows:When using methods such as rounding and truncation to deal with integer restrictions,the population tends to converge to an solution which is located in a feasible part with a big size,thus ignoring the optimal solution in a small feasible part.To overcome this issue,a biobjective optimizationbased two-phase method(BOTo P)is proposed.In the first phase,a measure function is designed to compute the degree that a solution violates integer restrictions.By employing this measure function as the second objective function and removing integer restrictions,a MIP problem is transformed into a constrained biobjective optimization problem.By solving this transformed constrained biobjective optimization problem,the population is able to approach the optimal solution.A new comparison rule is designed to solve this transformed optimization problem.Then,the second phase is implemented based on the population obtained in the first phase.It aims to enhance the convergence precision and obtain the optimal solution.This phase is implemented by combining different evolutionary with rounding and feasibility rule to solve the original MIP problem.We employ 16 test problems to investigate the performance of BOTo P.The experimental results show that the designed method is able to solve MIP problems with good performance.Moreover,we also employ BOTo P to solve the pressure vessel design problem.According to the results,BOTo P achieves competitive performance.To cope with the MIP problems with a large number of feasible parts,a cutting and repulsion-based evolutionary framework(Ca R)is proposed.Ca R includes two main strategies: the cutting strategy and the repulsion strategy.In the cutting strategy,an additional constraint is constructed based on the objective function value of the best solution found so far,the aim of which is to continuously cut unpromising discontinuous feasible parts.In the repulsion strategy,once it has been detected that the population has converged to a discontinuous feasible part,the population will be reinitialized.Moreover,a repulsion function is designed to repulse the previous explored discontinuous feasible parts.As a result,the population is able to explore other promising feasible parts.To investigate the performance of Ca R,we employ Ca R to solve 16 test problems.From the experimental results,compared with other three evolutionary algorithms,Ca R shows competitive results on solving MIP problems.Moreover,we also use Ca R to solve two optimization problems in the real world(i.e.,the deployment optimization problem in the multi-unmanned aerial vehicle assisted Internet of things data collection system,and the path planning problem of the curvature constrained unmanned aerial vehicle).The results show that Ca R is able to solve these two real-world problems with good performance.A multi-surrogate-assisted ant colony optimization algorithm(Mi SACO)is proposed to solve EOPCCVs.Mi SACO contains two main strategies: multi-surrogate-assisted selection and surrogate-assisted local search.In the former,the radial basis function(RBF)and least-squares boosting tree(LSBT)are employed as the surrogate models.Afterward,three selection operators(i.e.,RBF-based selection,LSBT-based selection,and random selection)are devised to select three solutions from the offspring generated by ACO.In the latter,sequence quadratic optimization coupled with RBF is utilized to refine the continuous variables of the best solution found so far.We employ 30 test problems to investigate the performance of Mi SACO.According to the experimental results,compared with other four surrogate-assisted optimization algorithms,Mi SACO achieves excellent performance.For ECOPCCVs,a two-phase surrogate-assisted evolutionary algorithm(To PSAEA)is proposed to further discuss how to incorporate the constraint-handling techniques into the algorithms effectively.In the first phase,a Gaussian processes(GP)model is constructed for each of the objective function and constraints of the solving ECOPCCV.Then,the constructed GP model is combined with evolutionary algorithms and two different kinds of constraint-handling techniques(i.e.,constrained expected improvement and cutting-based feasibility rule)to guide the population to approach the optimal solution.In the second phase,three different kinds of surrogate models(i.e.,RBF,LSBT,and GP)are combined with the constrained expected improvement and cutting-based feasibility rule to guide the evolution of the population.We employ 21 test problems to investigate the performance of To PSAEA.The experimental results show that the proposed method can solve ECOPCCVs with good performance.Moreover,To PSAEA is used to deal with the crashworthiness design of the side body of an automobile.The results show that the proposed method is able to deal with such an optimization problem in the real world.