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.

In this paper, a two-phase algorithm, namely IVNS, is proposed for solvingnonlinear optimal control problems. In each phase of the algorithm, we use aVARIABLE NEIGHBORHOOD SEARCH (VNS), which performs a uniform distributionin the shaking step and the successive quadratic programming, as the localSEARCH step. In the  rst phase, VNS starts with a completely random initialsolution of control input values. To increase the accuracy of the solutionobtained from the phase 1, some new time nodes are added and the valuesof the new control inputs are estimated by spline interpolation. Next, inthe second phase, VNS restarts by the solution constructed by the phase1. The proposed algorithm is implemented on more than 20 well-knownbenchmarks and real world problems, then the results are compared withsome recently proposed algorithms. The numerical results show that IVNScan  nd the best solution on 84% of test problems. Also, to compare theIVNS with a common VNS (when the number of time nodes is same in bothphases), a computational study is done. This study shows that IVNS needsless computational time with respect to common VNS, when the quality ofsolutions are not di erent signi cantly.

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.

The purpose of solving the problem of vehicle routing is to find a suitable route taking into account the existing conditions in the transportation problem. In this case, considering the routing conditions with several depots along with imposing traffic restrictions on some vehicles on some routes, will create quite real and complex conditions. Furthermore, in some cases, it is necessary to deliver the customer demand by visiting several times. For this purpose, in this reSEARCH, by simultaneous considering of multiple depots, split delivery and traffic restrictions, it has been tried to bring the conditions of the routing problem very close to real-world problems. In this paper, after presenting a mathematical model, the problem is solved in small-size instances using CPLEX solver. Then, due to NP-Hardness of considered problem, to solve it on a larger size instance, a VARIABLE NEIGHBORHOOD SEARCH algorithm is proposed. Finally, the simulated annealing algorithm is used to validate and evaluate the quality of the proposed algorithm. The computational results show that the proposed algorithm has good performance in terms of runtime and solution quality.

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.

The location-routing problem is one of the combined problems in the area of supply chain management that simultaneously make decisions related to location of depots and routing of the vehicles. In this paper, the single-depot capacitated location-routing problem under uncertainty is presented. The problem aims to fi nd the optimal location of a single depot and the routing of vehicles to serve the customers when the parameters may change under different circumstances. To get closer to real-world situations, travel time of vehicles, the fi xed cost of using vehicles and customers’ demand are considered as a source of uncertainty. A combined approach including robust optimization and stochastic programming was presented to deal with the uncertainty in the problem at hand. For this purpose, a mixed integer programming model is developed and a numerical example is provided to illustrate the solution procedure on the related network. To solve the problem, VARIABLE NEIGHBORHOOD SEARCH is also proposed. The results obtained from solving sample problems using an exact and heuristic algorithm represent the acceptable performance of the proposed algorithm.