In this reSearch, a job shop scheduling problem with an assembly stage is studied. The objective function is to find a schedule that minimizes the completion time of all products. At first, a linear model is introduced to express the problem. Then, in order to confirm the accuracy of the model and to explore the efficiency of the algorithms, the model is solved by GAMS. Since the job shop scheduling problem with an assembly stage is considered as an NP-hard problem, a hybrid algorithm is used to solve the problem in medium to large sizes in a reasonable amount of time. This algorithm is based on genetic algorithm and Parallel Variable Neighborhood Search. The results of the proposed algorithms are compared with those of genetic algorithm. Computational results showed that, for small problems, both HGAPVNS and GA have approximately the same performance. In addition, in medium to large problems, HGAPVNS outperforms GA.

In this paper, a numerical method for solving bounded continuous-time nonlinear optimal control problems (NOCPs) that based on Variable neigh-borhood descent (VND) algorithm is proposed. First, the genetic algorithm (GA) is combined with an improved VND that uses efficient Neighborhood interchange. Then, to improve the efficiency of the algorithm for practical and large-scale problems, the Parallel processing approach is implemented for discrete form of NOCP. It performs the required complex computations in Parallel. The resulting Parallel algorithm is applied to a benchmark of nine practical problems such as Van Der Pol problem and chemical reactor problem. For large-scale problems, the Parallel hybrid Variable neighbor-hood descent algorithm (PHVND) is capable of obtaining optimal control values effectively. Our experimentation shows that PHVND outperforms the best-known heuristics in terms of both solution quality and computa-tional efficiency. In addition, computational results indicate that PHVND produces superior results compared to sequential quadratic programming or GA.

Project portfolio selection is a critical challenge for many organizations as they often face budget constraints that limit their ability to support all available projects‎. ‎To address this issue‎, ‎organizations seek to select a feasible subset of projects that maximizes utility‎. ‎While several models for project portfolio selection based on multiple criteria have been proposed‎, ‎they are typically NP-hard problems‎. ‎In this study‎, ‎we propose an efficient Variable Neighborhood Search (VNS) algorithm to solve these problems‎. ‎Our algorithm includes a formula for computing the difference value of the objective function‎, ‎which enhances its accuracy and ensures that selected projects meet desired criteria‎. ‎We demonstrate the effectiveness of our algorithm through rigorous testing and comparison with a genetic algorithm (GA) and CPLEX‎. ‎The results of the Wilcoxon non-parametric test confirm that our algorithm outperforms both GA and CPLEX in terms of speed and accuracy‎. ‎Moreover‎, ‎the variance of the relative error of our algorithm is less than that of GA‎.

A social network consists of individuals and the relationships between them, which often influence each other. This influence can propagate behaviors or ideas through the network, a phenomenon known as influence propagation. This concept is crucial in applications like advertising, marketing, and public health. The influence maximization (IM) problem aims to identify key individuals in a social network who, when influenced, can maximize the spread of a behavior or idea. Given the NP-hard nature of IM, non-exact algorithms, especially metaheuristics, are commonly used. However, traditional metaheuristics like the Variable Neighborhood Search (VNS) struggle with large networks due to vast solution spaces. This paper introduces DQVNS (Deep Q-learning Variable Neighborhood Search), which integrates VNS with deep reinforcement learning (DRL) to enhance Neighborhood structure determination in VNS. By using DQVNS, we aim to achieve performance similar to population-based algorithms and utilize the information created step by step during the algorithm's execution. This adaptive approach helps the VNS algorithm choose the most suitable Neighborhood structure for each situation and find better solutions for the IM problem. Our method significantly outperforms existing metaheuristics and IM-specific algorithms. DQVNS achieves a 63% improvement over population-based algorithms on various datasets. The results of implementation on different real-world social networks of varying sizes demonstrate the superiority of this algorithm compared to existing metaheuristic, IM-specific algorithms, and network-specific measures.