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Showing 3 results for Multi-Objective Optimization
Mr. Hassan Heidari-Fathian, Dr. Seyyed Hamid Reza Pasandideh,
Volume 8, Issue 1 (4-2017)
Abstract
A multi-periodic, multi-echelon green supply chain network consisting of manufacturing plants, potential distribution centers, and customers is developed. The manufacturing plants can provide the products in three modes including production in regular time, production in over time, or by subcontracting. The problem has three objectives including minimization of the total costs of the green supply chain network, maximization of the average safe inventory levels of the manufacturing plants and the distribution centers and minimization of the environmental impacts of the manufacturing plants in producing, holding and dispatching the products and also the environmental impacts of the distribution centers in holding and dispatching the products. The problem is first formulated as a mixed-integer mathematical model. Then, in order to solve the model, the augmented weighted Tchebycheff method is employed and its performance in producing the Pareto optimal solutions is compared with the goal attainment method.
Dr Mohammad Mohammadi, Dr Davood Darvishi,
Volume 16, Issue 1 (3-2025)
Abstract
Prostate cancer is the most common cancer in men and the second leading cause of cancer-related death worldwide. Over the years, researchers from various fields, beyond medicine, have sought to expand their understanding of the disease to develop more effective treatments. Treatment planning for high-dose-rate (HDR) brachytherapy involves designing the trajectory of the radiation source to deliver sufficient doses to the target area while minimizing exposure to surrounding organs at risk (OAR) within clinically safe limits. Since the exact tumor volume is not known, the model uses gray numbers instead of tumor volume, which provides more accurate results.
In this study, four powerful multi-objective evolutionary algorithms (MOEAs) NSGA1-II, PESA2-II, SPEA3-II, and MOPSO4 are employed. Instead of yielding a single best solution, these algorithms produce a set of Pareto-optimal solutions, each representing a trade-off where no one solution is definitively better than the rest. However, they demonstrate improved performance compared to other optimization methods. The results show that the MOPSO algorithm performs better than the other three powerful algorithms in terms of solution quality and maintaining diversity among solutions.
Mr. Sajjad Mohseni Andargoli, Dr. Abdollah Arasteh, Dr. Ali Divsalar,
Volume 16, Issue 2 (8-2025)
Abstract
The explosive growth of global e-commerce and the increasing complexity of last-mile logistics have made the strategic placement of smart lockers a critical concern in modern urban logistics systems. Conventional methods, which rely solely on Multi-Criteria Decision Making (MCDM) methods for obtaining solutions, suffer from several limitations when implemented in uncertain, significant, and multi-objective scenarios. This paper proposes a stochastic multi-objective optimisation model for the BWM, prioritising decision criteria, which is solved by combining a hybrid metaheuristic solution methodology. The proposed model optimizes both total cost and sustainability performance from economic, environmental, and social perspectives, as well as robustness to demand uncertainty. An empirical study using Babol City, Iran, is presented to test and demonstrate the proposed framework. Candidate locker location and demand areas were examined based on expert-elicited criteria weights, with the preparation of a multi-objective mixed-integer programming model. In order to alleviate the computation burden, a combined structure of NSGA-II and LNS (referred to as NSGA-II+LNS) was proposed, which outperforms classical evolutionary algorithms in terms of convergence into the Pareto frontier. Factual results indicate that factoring in economic affordability, accessibility, and environmental impact is key to optimal locker capacity design. Robust solutions under demand fluctuation can save up to 18% more on service reliability, providing strong deterministic answers. This article makes the following theoretical and practical contributions: (i) a novel sustainable-oriented, deterministic model for smart locker location is proposed; (ii) advanced metaheuristics are integrated with MCDM in urban logistics, whereas fewer studies have focused on integrating them; and (iii) policy implications are suggested not only to policymakers but also to logistics operators who want robust last-mile delivery strategies..
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