Many-objective Evolutionary Optimization Algorithms And Applications

In the real world,we are often faced with problems with multiple objectives,which are called Multi-Objective Problems(MOPs).MOPs with at least four objectives are informally known as Many-Objective Problems(MaOPs).As an important class of MOPs,MaOPs appear widely in many real-world applications,such as engineering design,air traffic control,nurse rostering,car controller optimization,water supply portfolio planning,with up to hundreds of objectives.Evolutionary Algorithms(EAs)are population-based,black-box search/optimization methods and don't need particu-lar assumptions like continuity or differentiability.They are very suitable for deal-ing with MOPs.In the past few decades,researchers have proposed plenty of Multi-Objective Evolutionary Algorithms(MOEAs),It has been shown that the Pareto-based MOEAs may deteriorate their performance significantly oin MaOPs.This is mainly due to that the proportion of non-dominated solutions increase enormously.As a result,the dominance-based primary criterion fails to discriminate solutions,the density-based secondary criterion is activated to determine which solutions are able to survive the en-vironmental selection.Therefore,the final solution set might not even converge to PF but stagnate far away from it.In order to deal with many-Objective Problems(MaOPs),researchers have pro-posed a series of algorithms.Based on the key idea used,we categorize MaOEAs into seven classes:the relaxed dominance based,diversity-based,aggregation-based,indicator-based,reference set based,preference-based,and dimensionality reduction approaches.As a reference set based algorithm,The Two Archive Algorithm(TAA)uses two archives,namely Convergence Archive(CA)and Diversity Archive(DA)as non-dominated solution repositories,focusing on convergence and diversity respec-tively.However,as the objective dimension increases,the size of CA increases enor-mously,leaving little space for DA.Besides,the update rate of CA is quite low,which causes severe problems for TAA to drive forth.Moreover,since TAA prefers DA mem-bers that are far away from CA,DA might drag the population backwards.In order to deal with these weaknesses,this paper proposes an improved version of TAA,namely ITAA.Compared to TAA,ITAA incorporates a ranking mechanism for updating CA which enables truncating CA while CA overflows.Besides,a shifted density estima-tion technique is embedded to replace the old ranking method in DA.The efficiency of ITAA is demonstrated by the experimental studies on benchmark problems with up to 20 objectives.Traditional multi-objective evolutionary algorithms face great challenge when deal-ing with many objectives.This is due to a high proportion of non-dominated solutions in the population and low selection pressure towards the Pareto front.In order to tackle this issue,a series of indicator-based algorithms have been proposed to guide the search process towards the Pareto front.However,a single indicator might be biased and lead the population to converge to a sub-region of the Pareto front.In this paper,a multi-indicator based algorithm is proposed for many-objective optimization problems.The proposed algorithm,namely Stochastic Ranking based multi-indicator Algorithm(SRA),adopts the stochastic ranking technique to balance the search biases of differ-ent indicators.Empirical studies on a large number(39 in total)of problem instances from two well-defined benchmark sets with 5,10 and 15 objectives demonstrate that SRA performs well in terms of Inverted Generational Distance and hypervolume met-rics when compared with state-of-the-art algorithms.Empirical studies also reveal that,in case a problem requires the algorithm to have strong convergence ability,the perfor-mance of SRA can be further improved by incorporating a direction-based archive to store well-converged solutions and maintain diversity.With the explosively increase of information and products,recommender systems have played a more and more important role in the recent years.Various recommen-dation algorithms,such as content-based methods and collaborative filtering methods,have been proposed.There are a number of performance metrics for evaluating recom-mender systems,and considering only the precision or diversity might be inappropriate.However,to the best of our knowledge,no existing work has considered recommen-dation with many objectives.In this paper,we model a many-objective search-based recommender system and adopt a recently proposed many-objective evolutionary algo-rithm to optimize it.Experimental results on the Movielens data set demonstrate that our algorithm performs better in terms of Generational Distance(GD),Inverted Gener-ational Distance(IGD)and Hypervolume(HV)on most test cases.