Adaptive Decomposition Based Evolutionary Multi-objective Optimization Algorithm And Its Application

Decomposition based evolutionary multi-objective optimization algorithms can effectively converge and have good diversity on the multi-dimensional optimization problems.However,the choice of its scalarizing method depends on the problem itself,namely the Pareto front(PF)shape.Given a problem,a special method need choosing based on prior knowledge to achieve great results.The penalty-based boundary intersection(PBI)method is frequently used one.It works well in convex problems with a small penalty value but is better at non-convex problems with a larger value.Based on the above analysis,a simple yet effective strategy called Pareto adaptive PBI(PaP)is proposed by which a suitable penalty value can be adaptively identified,maintaining fast convergence speed,meanwhile,leading to a good approximation of the PF even without prior knowledge.The PaP strategy integrated into the state-of-the-art decomposition algorithm,MOEA/D,denoted as MOEA/AD,is examined on a set of multi-objective benchmarks with different PF shapes.Experimental results show that the PaP strategy is more effective than the weighted sum,the weighted Tchebycheff and the PBI method with(representative)fixed penalty values in general.As the performance of MOEA/AD can be degraded by the points far from the search direction,thus a larger adapted penalty value is obtained in some cases.Furthermore,this paper proposes a localized adaptive strategy,which assigns a hypercone to each subproblem according to its weight vector,and then the range of optimization and adaptive search in each subproblem is constrained by the hypercone.Therefore the subproblems can find the most appropriate penalty value corresponding to the PF subdomain.The strategy is combined with the MOEA/D framework,forming the constrained adaptive MOEA/D algorithm,denoted as MOEA/LAD.The results obtained on the test problems show that the effectiveness of the MOEA/LAD is further improved in terms of convergence and diversity,compared with the original algorithm.In addition,MOEA/AD and MOEA/LAD are applied to a real-world problem – multi-objective optimization of a hybrid renewable energy system(HRES)whose PF is unknown.The optimal design aims to find suitable configurations of photovoltaic(PV)panels,wind turbines,batteries and diesel generators in HRES such that the system cost and the fuel emission are minimized,and the system reliability is maximized.The proposed algorithm effectively obtains the optimal configuration,and the obtained solution is more close to PF than that of the competitors.The experimental results further confirm the feasibility and superiority of the algorithm.