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Combinatorial optimization problems (COPs) play an important role in both industrial production and theoretical research. As a classical class of optimization algorithms, evolutionary algorithms have shown good performance in COPs. However, as the size of the problem increases, it becomes difficult for evolutionary algorithms to produce satisfactory solutions within the specified time. In recent years, neural network algorithms have been applied to solve COPs and have shown superior effects. Inspired by this, this paper proposes a new algorithm based on graph structure for solving COPs. Through relaxation, COPs are transformed into their corresponding continuous optimization problems. The output state of our algorithm is converted to a discrete solution by approximation method. Compared with previous algorithms, our algorithm can not only solve COPs with general form such as binary quadratic programming (BQP), but also solve COPs with special form, which greatly expands the application scope of neural network algorithms. In addition, our algorithm can be embedded into other problem frameworks such as solving multi-objective combinatorial optimization problem (MOCOP) through scalarization method. A new penalty function is added to the objective function, which enables our algorithm to overcome the inconsistency between the optimal solution of the original problem and the corresponding continuous problem, so that our algorithm can perform well on various problems. Several numerical simulations are used to illustrate the effectiveness of our algorithm in solving COPs. Experimental results show that our algorithm can effectively solve COPs with general form and has a shorter solving time compared to traditional evolutionary algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a novel population robustness-based switching response framework (PR-SRF) is proposed to develop effective dynamic multi-objective optimization algorithm (DMOA), which integrates different response strategies to comprehensively cope with the dynamic behaviors. In particular, the population robustness is described by the quantification of how severely the environmental changes affect current population, which is timely graded as three levels of weak, strong, and normal to enable the adaptive switch of three different responses of diversity-enhancement, diversity-maintenance, and the knowledge-transfer, respectively. In this way, associations between the adopted responses and the changing environments are successfully established, thereby facilitating more intelligent decision when handling the dynamic behaviors. According to the benchmark evaluation results, the proposed PR-SRF-DMOA yields better comprehensive performance than several other DMOAs with popular response strategies, and it also outperforms another three DMOAs with hybrid responses, which demonstrates the great competitiveness of our algorithm. In addition, ablation study proves that the proposed PR-SRF can sufficiently exploit the merits of different responses, which effectively alleviates the negative knowledge transfer in extremely fluctuating environments, thereby providing valuable references for the development of evolutionary transfer optimization (ETO) algorithms. [ABSTRACT FROM AUTHOR]

• Teaching-learning-based optimization (TLBO) is one of population-based heuristic stochastic swarm intelligent algorithm. • In this paper, a comprehensive survey on the recent advances in TLBO is presented. • Literature survey reveals some interesting challenges and future research directions. Teaching-learning-based optimization (TLBO) algorithm which imitates the teaching–learning process in a classroom, is one of population-based heuristic stochastic swarm intelligent algorithms. TLBO executes through similar iterative evolution processes as utilized by a standard evolutionary algorithm. Unlike traditional evolutionary algorithms and swarm intelligent algorithms, the iterative computation process of teaching–learning-based optimization is divided into two phases and each phase executes iterative learning operation. In this paper, we present a comprehensive survey on the recent advances in TLBO. A review of the current literature reveals intriguing challenges and suggests potential future research directions. [ABSTRACT FROM AUTHOR]

For optimization algorithms of fully complex-valued neural networks, complex-valued stepsize is helpful to make the training escape from saddle points. In this paper, an adaptive orthogonal gradient descent algorithm with complex-valued stepsize is proposed for the efficient training of fully complex-valued neural networks. The basic idea is that, at each iteration, the search direction is constructed as a combination of two orthogonal gradient directions by using the algebraic representation of complex-valued stepsize. It is then shown that the determination of suitable complex-valued stepsize is facilitated by a decoupling method such that the computational complexity involved in the training process is greatly reduced. The experiments are finally conducted on pattern classification, nonlinear channel equalization and signal prediction to confirm the advantages of the proposed algorithm. [ABSTRACT FROM AUTHOR]