Design And Application Of Many-objective Evolutionary Algorithms Based On Cone Decomposition

Multi-objective optimization problems are broadly applied in the field of engineering.With the improvement of project complexity,the number of objectives to be optimized in engineering problems become more and more,and optimization problems which have greater than or equal to 4 optimization objectives,are also called as many-objective optimization problems.Due to the increasing number of optimization objectives,the existing multi-objective evolutionary algorithms encounter some challenging issues in handling with these many-objective optimization problems,which affect the convergence speed and the maintenance of population diversity,as well as make the computational complexity dramatically increase.These also have led to many-objective evolutionary algorithms became a hot research topic in the field of evolutionary computation.In recent years,the decomposition based multi-objective evolutionary algorithm received widespread attention because of its superior performance,and numerous new many-objective evolutionary algorithms proposed in recent years maintain population diversity by generally introducing the idea of decomposition.However,pure classical decomposition based multi-objective evolutionary algorithm,such as MOEA/D,has potential deficiency which seriously affects the algorithm's performance in terms of convergence and population diversity when solving complex many-objective optimization problems.In order to efficiently solve many-objective optimization problems from the perspective of pure decomposition based multi-objective evolutionary algorithm as well as handling with the shortage of the classic decomposition based multi-objective evolutionary algorithm MOEA/D,a many-objective evolutionary algorithm based on cone decomposition is proposed in this thesis.The main contributions of this thesis are summarized as follows:1)A universal cone decomposition strategy is proposed according to the conception of individual's direction vector introduced firstly.This strategy not only decomposes the manyobjective optimization problem into a series of scalar subproblems,but also assigns a unique cone sub-region to each subproblem.In addition,the K-D tree is adopted to quickly locate the corresponding cone sub-region in high-dimensional objective space for each given individual.2)Based on the cone decomposition strategy,a cone update mechanism for individual update is further designed to allow the offspring individual only need to update the best individual currently associated with its corresponding cone sub-region.The mechanism can accurately locate the appreciate individual for updating in the similar search direction,as well as successfully limits the number of updated individuals.3)A many-objective evolutionary algorithm based on cone decomposition is proposed.Firstly,the cone update mechanism is adopted in this algorithm to solve the potential problems of the classical decomposition based multi-objective evolutionary algorithm.Further more,the penalized direction distance is further designed based on the direction vector as cone subproblem's new scalar objective function in this algorithm to better drive the individual to gradually approach the Pareto front along the search direction of the subproblem in highdimentional objective space.4)Moreover,in order to extend the capability of handling with some special cases in manyobjective optimization problems including ones with scale difference among objectives,ones with constraints and ones with irregular Pareto front,a scalar handling mechanism,a constraint handling mechanism based on threshold comparison and a direction vector adaptive adjustment mechanism are designed for the proposed cone decomposition based manyobjective evolutionary algorithm.5)Finally,experiments on DTLZ benchmark test instances and its variants,MOP benchmark test instances,as well as five engineering problems,like Car Cab Design Problem and Planing Machining Problem,are conducted to make comparing tests and performance assessment in terms of the quality of solution set and computation efficiency among the proposed algorithms including its extending versions and six other state-of-art multi-objective evolutionary algorithms.Experimental results on benchmark test instances and engineering problems indicate that the proposed many-objective evolutionary algorithm based on cone decomposition in this thesis has an advantage of high computational efficiency,as well as obtains the solution set with the best overall quality when handling with many-objective optimization problems and complex optimization problems.In all,the many-objective evolutionary algorithm based on cone decomposition can be seen as the best optimizer for many-objective optimization among all comparing algorithms in this thesis.