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Elevator systems in buildings face challenges due to unpredictable passenger flow, which can make scheduling elevators complicated to optimize their operation. Most of the existing algorithms are developed based on pattern recognition and may not be effective in scenarios where patterns are difficult to classify, especially when elevator operations involve uncertain human behaviors. To address this issue, this paper proposes a time-dependent optimization model that considers long-term and multi-floor peaks, with a focus on peak floors. The proposed model accounts for dynamic scheduling patterns of elevators and represents passenger flow direction as a relation matrix. The proposed direction optimization method contains several functions to guide iteration direction and improve the efficiency of an iteration process based on classical algorithms. This method also ensures the stability of Markov chains by adjusting an iteration process. The feasibility of the proposed method is supported by the relevant theory, and experimental results show that the direction-optimized algorithms outperform classical algorithms, resulting in the superb operating efficiency of elevators at a lower cost. This paper contributes to the development of efficient algorithms for scheduling elevators in complex traffic patterns, which can improve performance of elevator group systems in buildings. The proposed method is not only limited to elevators but can also be extended to other transportation systems with flow requirements. • Estimating the relation between peak floors without pattern recognition. • Four relations are defined to classify the passenger flow. • Dynamically modifying three metaheuristic algorithms' iteration law. • The application for transportation systems with unpredictable flow. [ABSTRACT FROM AUTHOR]

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]

Submodular maximization is one of the central topics in combinatorial optimization. It has found numerous applications in the real world. In the past decades, a series of algorithms have been proposed for this problem. However, most of the state-of-the-art algorithms are randomized. There remain non-negligible gaps with respect to approximation ratios between deterministic and randomized algorithms in submodular maximization. In this paper, we propose deterministic algorithms with improved approximation ratios for non-monotone submodular maximization. Specifically, for the matroid constraint, we provide a deterministic 0.283 − o (1) approximation algorithm, while the previous best deterministic algorithm only achieves a 1/4 approximation ratio. For the knapsack constraint, we provide a deterministic 1/4 approximation algorithm, while the previous best deterministic algorithm only achieves a 1/6 approximation ratio. For the linear packing constraints with large widths, we provide a deterministic 1 / 6 − ϵ approximation algorithm. To the best of our knowledge, there is currently no deterministic approximation algorithm for the constraints. [ABSTRACT FROM AUTHOR]