Multi-objective Problem Solving Based On Decomposition Strategy And Its Application

There are various kinds of multi-objective optimization problems in real life,and evolutionary algorithms are widely used in solving multi-objective optimization problems because of their rapid calculation speed and high solution precision.Usually,evolutionary algorithms can find a set of optimal solution sets by converging to the Pareto front with a population of particles.However,for complex Pareto front,heuristic evolutionary algorithms cannot converge the particles to the optimal solution quickly.To solve this problem,the decomposition strategy-based evolutionary algorithm MOEA/D(A Multi-objective Evolutionary Algorithm Based on Decomposition,MOEA/D)improves the search efficiency by divide-and-conquer and ensures that the particles located at the Pareto front are both convergent and multiple.However,MOEA/D with Weighted Sum Approach(WS)decomposition strategy is not suitable for solving nonconvex problems and the solution set is not enough with real-time.In addition,MOEA/D using Chebyshev decomposition strategy often does not pay enough attention to the constraints,which can cause inaccuracy of the solution set.The shortcomings of the existing decomposition strategies are combined,and further research on them is necessary.In this paper,two algorithms of hybrid decomposition strategies are designed to address the problems in dynamic updating of the solution set and balancing constraints,and verified on the problem of microgrid economics.The main research of this paper is as follows:(1)The decomposition framework of helper and equivalent objective is applied to decompose the constrained optimization problem.Among them,the equivalent objective serves to control the main direction of the search,and its optimal solution set needs to be consistent with the optimal solution set of the constrained problem.This is not the case for the helper objective,which is derived from the original objective and is responsible for providing diverse evolutionary directions.After the objective is decomposed,the weights of the decomposed subproblems are dynamically updated,and then the evolutionary direction and pressure are adjusted so that the solution set is optimized in real time.(2)To address the shortcomings of particle swarm algorithm which is easy to fall into local optimum and the diversity overflow problem of sine cosine algorithm,the heuristic algorithm is mixed with decomposition strategy and two methods are proposed: 1)Hybrid particle swarm gray wolf algorithm: based on the respective advantages of particle swarm optimization algorithm and gray wolf optimization algorithm,the method of parameter adaption is combined to reduce the possibility of particles falling into local optimum.The experimental results show that the number of optimal values of the function obtained is more than that of classical algorithms such as crow search,constrained simulated annealing,and water circulation with constraints under suitable tuning parameters;2)Sine cosine improvement algorithm for reverse population: the difficulty of solving high-dimensional functions is reduced by decomposition strategy,and the preprocessing of reverse population is used to reduce the inferiority of random population,which can effectively solve the diversity overflow problem and balance algorithm convergence and diversity.Through the CEC2017 dataset test,the experimental results show that the designed sine cosine improvement algorithm has the best performance in 27 out of 28 test functions in the 10 D case,24 in the 30 D case,and 26 in the 50 D case.(3)Microgrid is a system composed of distributed power sources and energy storage devices,which can communicate closely with the distribution network to ensure the reliability of power supply.Economy is one of the important indicators for microgrid operation evaluation.The problem of optimizing the economy of microgrid involves various factors,such as the operating cost of battery,interaction cost with distribution network,environmental cost and other constraints and objectives,which is a multi-objective constraint problem.The traditional multi-objective optimization approach suffers from premature convergence and insufficient diversity in the search process when solving the microgrid economy optimization,while the decomposition strategy can effectively solve the above problems.In this paper,we start from the aspect of the economics of grid connection in microgrid,take the minimum cost of battery operation and the minimum cost of power withdrawal from the distribution network as the objectives,establish the microgrid model with battery capacity and balance power as the constraints,and apply the two algorithms mentioned in point(2)to the microgrid cost optimization problem,and the simulation results prove that the method in this paper can effectively optimize the economics of microgrid.