Research Of Interval Many-objective Evolutionary Algorithms

Many-objective optimization is a common problem in practical applications.It has more than three conflicting objective functions.Due to the inherent uncertainty of the system,data measurement deviation and approximate modeling of the problem,there are often some uncertain parameters or variables in optimization problems,the problem of uncertain many-objective optimization has received extensive attention.In practical problems,it is much easier to obtain the variation range of uncertainty parameters than probability distribution function and membership function,so interval evolution becomes an effective approach to deal with uncertain many-objective optimization problems.Although evolutionary algorithms are widely used to directly solve interval many-objective optimization problems,the research of interval many-objective evolutionary algorithm is still in its infancy,and there are a series of problems and difficulties in effectively comparing the pros and cons of interval objectives and obtaining the Pareto front with excellent convergence,diversity and uncertainty.Therefore,this paper will carry out systematic research on the interval many-objective optimization algorithm.The main research work is as follows:（1）Aiming at the problem that interval Pareto domination faces insufficient selection pressure,an interval many-objective evolutionary algorithm based on flexible Pareto domination was proposed.Firstly,the possible optimal value and uncertainty of the individual are defined in the objective space,and the flexibility coefficientsγ₁ andγ₂ are introduced to design the flexible interval Pareto domination.Secondly,the individual relaxation degree is proposed to measure the crowding degree of individuals and further distinguish the advantages and disadvantages of individuals in the same Pareto domination layer.In order to verify the effectiveness of the proposed algorithm,it is compared with other three excellent interval multi-objective optimization algorithms for InDTLZ and InWFG testing suites.Experimental results show that the IIGD index values and IX index values obtained by the proposed algorithm are better than other algorithms,which verifies that the algorithm can expand the dominant region of candidate solutions,relieve the selection pressure,and also plays an important role in improving the diversity of the optimal solution set.（2）In order to solve Pareto domination failure caused by the exponential expansion of the proportion of non-domination solutions to candidate solutions,and rely too much on diversity maintenance mechanism easy to cause the Pareto optimal front convergence difficulties,an interval many-objective evolutionary algorithm guided by ideal hyperplane is proposed.Firstly,the objective space is divided into many regions,and an ideal hyperplane is constructed to guide the algorithm to search the region with strong convergence.Secondly,the interval objective functions are sampled by Latin hypercube,and the average distance between the sample point and the ideal hyperplane is used to measure the individual.Finally,three optimal solution selection mechanisms,namely random probability selection,global solution selection and average solution selection,were designed to enhance population diversity.Compared with other advanced algorithms,whether in InDTLZ or InMaOP testing problems,the proposed algorithm has more than half of the total optimal results on the IIGD index,and shows strong competitiveness on the IX index,which effectively proves the superiority of the algorithm in convergence and uncertainty.（3）Aiming at the problem that the algorithm focuses on maintaining certain properties and follows the "neighborhood hypothesis",resulting in a waste of search resources,local optimization,and difficulty in effectively balancing convergence,diversity,and uncertainty,an interval many-objective evolutionary algorithm for comprehensive evaluation index was proposed.In this algorithm,the virtual optimal solution is defined in the objective space,and convergence measure,spatial density measure and uncertainty measure criteria are proposed.Then,the algorithm introduces the weight factor,and designs four kinds of performance balance functions to select the optimal solution set through static parameters,random parameters,dynamic parameters and adaptive parameters.The experimental simulation results show that the optimal strategies for InMaOP and InWFG are adaptive performance balance function strategy and static performance balance function strategy respectively.In addition,compared with the other three excellent algorithms,The proposed algorithm can provide a solution with better convergence,diversity and less uncertainty,thus verifying the effectiveness of the proposed performance balance function.（4）For optimization problems with multiple features,it is almost impossible for one algorithm to get better results than all algorithms.An interval many-objective evolutionary algorithm for two-stage game integration is proposed.Firstly,the mating selection strategy pool and the environment selection strategy pool are constructed from the perspective of selection integration.Then,the evolutionary population is regarded as the game player,and the mating selection based on the population game is designed.Finally,the environment selection based on the radar count is designed,and the optimal solution set is selected in the way of individual cooperative game.Comparing the proposed algorithm with other six algorithms on InDTLZ,InWFG and InMaOP test problems,the experimental results show that the proposed algorithm has the most optimal IIGD results in three test problems.It is verified that the algorithm can make reasonable use of the strategy and mechanism of the existing algorithm,and further improve the overall performance of the algorithm through the coordination and joint action of multiple operators.（5）For the uncertainty problem of edge mobile computing offloading,with time delay,computational cost,energy consumption and the node load as the optimization objective,an interval many-objective joint optimization model of the power allocation and task offloading was was constructed.Compared with other excellent algorithms,the four algorithms proposed in this paper have better performance in solving this model,especially in terms of time delay and energy consumption.More importantly,they can provide auxiliary decision for obtaining more efficient resource allocation schemes in computational offloading problems.