Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.

Leveraging proficiency and preference for online Karaoke recommendation

Recently,many online Karaoke(KTV)platforms have been released,where music lovers sing songs on these platforms.In the meantime,the system automatically evaluates user proficiency according to their singing behavior.Recommending approximate songs to users can initialize singers5 participation and improve users,loyalty to these platforms.However,this is not an easy task due to the unique characteristics of these platforms.First,since users may be not achieving high scores evaluated by the system on their favorite songs,how to balance user preferences with user proficiency on singing for song recommendation is still open.Second,the sparsity of the user-song interaction behavior may greatly impact the recommendation task.To solve the above two challenges,in this paper,we propose an informationfused song recommendation model by considering the unique characteristics of the singing data.Specifically,we first devise a pseudo-rating matrix by combing users’singing behavior and the system evaluations,thus users'preferences and proficiency are leveraged.Then we mitigate the data sparsity problem by fusing users*and songs'rich information in the matrix factorization process of the pseudo-rating matrix.Finally,extensive experimental results on a real-world dataset show the effectiveness of our proposed model.