multi objective particle swarm optimization

In this research, a tri-objective mathematical model is proposed for the Transportation-Location-Routing problem. The model considers a three-echelon supply chain and aims to minimize total costs, maximize the minimum reliability of the traveled routes and establish a well-balanced set of routes. In order to solve the proposed model, four metaheuristic algorithms, including Multi-Objective Grey Wolf Optimizer (MOGWO), Multi-Objective Water Cycle Algorithm (MOWCA), Multi-objective Particle Swarm Optimization (MOPSO) and Non-Dominated Sorting Genetic Algorithm- II (NSGA-II) are developed. The performance of the algorithms is evaluated by solving various test problems in small, medium, and large scale. Four performance measures, including Diversity, Hypervolume, Number of Non-dominated Solutions, and CPU-Time, are considered to evaluate the effectiveness of the algorithms. In the end, the superior algorithm is determined by Technique for Order of Preference by Similarity to Ideal Solution method.

Maintenance costs are one of the major costs in plants and companies. The observation in many cases illustrates the lack of plans or mistakes in maintenance activities that incurred great costs. In this study, the number of equipment failures have been determined. Then the failure rate and reliability of each equipment are calculated. The third step calculates total system reliability so the initial plan is presented. After that, by using the obtained information, the sustainability aspects of the program will generate and the maintenance costs and sustainability functions will assess. At the end, this multi-objective optimization problem is solved by MOPSO algorithm and the results are compared with a simulation method. As a result, with this reliability centered maintenance program, the reliability of each equipment, as well as the whole system are improved; economic aspect of sustainability and customer satisfaction are increased; environmental pollutions and maintenance costs are decreased by offering more reliability based program; a scheduling plan for each maintenance procedures is provided and also more stable internet connection is established by reducing the system failures.

In this article, a multi objective model is presented to select and allocate the order to suppliers in uncertainty condition and in a multi source, multi customer and multiproduct case in a multi period state at two levels of supply chain. Objective functions considered in this study as the measures to evaluate suppliers are cost including purchase, transportation and ordering costs, timely delivering, shipment quality or wastages which are amongst major quality aspects, partial and general coverage of suppliers in respect of distance and finally suppliers weights making the products orders amount more realistic. The major limitations are price discount for products by suppliers which are calculated using signal function. In addition, suppliers weights in the fifth objective function is calculated using fuzzy Topsis technique. Lateness and wastes parameters in this model are considered as uncertain and random triangular fuzzy number. Finally the multi objective model is solved using two multi objective algorithms of Non-dominated Sorting Genetic Algorithm (NSGA-II) and Particle Swarm Optimization (PSO) and the results are analyzed using quantitative criteria Taguchi technique was used to regulate the parameters of two algorithms.

Many researches in inventory control area of knowledge have been focused on single objective and multi-objective problem of determining the economic quantity of order. In single objective problems, costs were considered as the objective. However, multi-objective problems have not been well investigated. For instance, there are no hint to transportation cost, budget, or holding costs, or only capacity and demand constraints have been considered in these researches. This study focuses on developing a model accompanied by costs, quality and the time of delivery.The economic order quantity of multi-product from multi-supplier in multi-period under uncertainty in demand and discounted prices are considered in this paper. In first step, a mathematical model is developed for this problem. This mathematical model is solved by using multi-objective optimization method i.e. goal programming. Then, a meta-heuristic method based on multi-objective particle swarm optimization is proposed. Results of the small size numerical examples show that solutions found by using the proposed meta-heuristic method are in average, 5% worse than solutions found by using the mathematical methods; however, it needs much lower computational time.