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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]

Adaptive operator selection is an online method that automatically adjusts the application rate of different operators based on their actual performance. This paper proposes an adaptive operator selection paradigm based on dueling deep Q-network (DDQN), aiming to improve the training efficiency of the Q-network for solving multi-objective optimization problems. The Q-network is decomposed into state value and action advantage networks, allowing the agent to learn state values more frequently and accurately. A novel state space and reward mechanism are designed to adapt to the characteristics of evolutionary multi-objective optimization. Combining adaptive operator selection with a multi-objective evolutionary algorithm with adaptive weights (AdaW), an AdaW-DDQN algorithm with high adaptability is proposed. Experimental results on three complex benchmark suites demonstrate that the proposed adaptive operator selection paradigm significantly improves the performance of multi-objective optimization algorithms. The AdaW-DDQN algorithm provides an effective and efficient solution for solving multi-objective optimization problems. • An adaptive operator selection paradigm based on dueling deep Q-network is proposed. • Ten effective crossover operators are designed as a pool of candidate operators. • A new state space and reward mechanism are designed for the multi-objective optimization problem. • The proposed adaptive operator selection paradigm is embedded into MOEA/D with adaptive weights. • Experimental results show that AdaW-DDQN has strong generalization ability. [ABSTRACT FROM AUTHOR]

The weapon-target assignment problem is a challenging optimization issue, but reliability is seldom considered in the majority of existing literature. To address the high-reliability weapon-target assignment problem, this paper integrates weapon reliability and mission reliability into a multi-objective optimization model (MOD) and presents an improved algorithm termed MOEA/D-iAM2M to the problem. This algorithm effectively combines the strengths of adaptive search space decomposition-based MOEA (MOEA/D-AM2M) and two-stage hybrid learning-based MOEA (HLMEA), resulting in a faster convergence rate and a more extensive distribution of the Pareto solution set. Furthermore, a reference point is incorporated into MOEA/D-iAM2M to facilitate the adaptive weight adjustment. Numerical experiments are carried out to confirm the effectiveness of the proposed MOEA/D-iAM2M. This research is significant in the field of optimization and has practical value in the defense industry. [ABSTRACT FROM AUTHOR]