We consider an open shop scheduling problem with setup and processing times separately such that not only the setup times are dependent on the machines, but also they are dependent on the sequence of jobs that should be processed on a machine. A novel bi-objective mathematical programming is designed in order to minimize the total tardiness and the makespan. Among several multi-objective decision making (MODM) methods, an interactive one, called the TH method is applied for solving small-sized instances optimally and obtaining Pareto-optimal solutions by the Lingo software. To achieve Pareto-optimal sets for medium to large-sized problems, an improved non-dominated sorting genetic algorithm II (NSGA-II) is presented that consists of a heuristic method for obtaining a good initial population. In addition, by using the design of experiments (DOE), the efficiency of the proposed improved NSGA-II is compared with the efficiency of a well-known multi-objective genetic algorithm, namely SPEAII. Finally, the performance of the improved NSGA-II is examined in a comparison with the performance of the traditional NSGA-II.

Abstract Background and objectives As a crucial issue in aqua sciences, optimizing dam reservoirs exploitation has been studied with a variety of optimization techniques. In recent years, a large number of multi-objective Meta-Heuristic algorithms have been introduced. One of these algorithms is the second version of the multi-objective genetic algorithm with nun-dominated sorting, which was introduced in 2002 by Deb and et.al. In this research, the innovation and aim are to use the particle swarm algorithm with nun-dominated sorting approach and evaluate the efficiency of this algorithm in the optimization of operation of the reservoir performance. Finally, the results are compared with the NSGA-II algorithm, which ultimately leads to a sustainable management policy for water resource systems, and in particular the exploitation of the reservoir. Materials and methods In this research, the multi-objective version of the genetic algorithm and particle swarm optimization were investigated using concepts such as Non-dominated sorting and crowding distance and used to solve the optimization problem of the Mulla-Sadra reservoir in Fars province. The problem of optimization defined with two goals. One of them was minimizing difference between agriculture demand end releases. The second of objective function was maximizing flood storage volume. The two algorithms compared with criteria such as the run time, the number of solutions placed on the Pareto front, standard deviation and performance criteria (dispersion criteria). Results The results of the research indicated that both algorithms have the ability to solve this optimization problem. Also the results indicated that the algorithms has somewhat more performance than some other criteria. The results of the investigation of the runtime of each of the algorithms showed that the performance of the multi-objective particle swarm algorithm (NSPSO-II) is far more than the NSGA-II algorithm, so that the average runtime of the NSGA-II algorithm in the population of 50 The value of 21.3879 seconds is approximately three times the average runtime in the NSPSO-II algorithm with a value of 6.3169 seconds. Regarding the performance criterion, the NSPSO-II algorithm has a better performance than the NSGA-II algorithm. On the other hand, according to the number of solutions on the Pareto front, the NSGA-II algorithm found a lot more solutions on the Pareto front, which is why standard deviation in the NSGA-II algorithm was less than NSPSO-II. Conclusion The NSGA-II algorithm found a lot more solutions on the Pareto optimal front, and the solutions on the Pareto optimal fronted properly covered the Pareto front, unlike the NSPSO algorithm. Also, comparing the solutions in the Pareto optimal front showed that the NSPSO-II algorithm was stepped up to maximize the second target function, while the NSGA-II algorithm moved in the direction of minimizing the objective function. Keyword: Crowding Distance, Dominate, Flood, Malla-Sadra Dam, Performance Criteria.

This paper proposes a modified non-dominated sorting genetic algorithm (NSGA-II) for a bi-objective location-allocation model. The purpose is to define the best places and capacity of the distribution centers as well as to allocate consumers, in such a way that uncertain consumers demands are satisfied. The objectives of the mixed-integer non-linear programming (MINLP) model are to (1) minimize the total cost of the network and (2) maximize the utilization of distribution centers. To solve the problem, a fuzzy modified NSGA-II with local search is proposed. To illustrate the results, computational experiments are generated and solved. The experimental results demonstrate that the performance metrics of the fuzzy modified NSGA-II is better than the original NSGA-II.

Different inventory control systems try to determine how much and when to order at the least relevant cost while maintaining a desirable service level for customers. In this article, a continuous review stochastic inventory system, with three objectives, is optimized. In this model, contrary to the traditional inventory models, customer serviceis not considered a shortage cost in the objective function. But the frequency of stock out occasions and the number of items stocked out annually are to be minimized. For determining the Pareto optimal set, multi-objective evolutionary algorithms are used. First, NSGA-II, MOGA, VEGA, RWGA are developed. Then some improvements in NSGA-II mechanisms are made and R-NSGA-II is developed. Subsequently, these algorithms are examined for some criteria such as set coverage and spacing, and the best algorithms for each criteria are presented. The Result shows that R-NSGA-II has good scores formost criteria. Afterwards, Pareto optimal set is ranked using the method of global criteria.

One of the most important issues in finance is how to choose an investment portfolio. Activists in this field are seeking to select a portfolio that controls risk with high return. Due to the increasing limitations of the capital market, the efficiency of classical methods has been discussed. Hence, researchers have turned their attention to metaheuristic algorithms. The aim of this study is to determine the optimal portfolio of pharmaceutical companies accepted in the Tehran Stock Exchange by two methods of multi-objective genetic algorithm (NSGA-II) and maximum Sharp ratio. In this study, the multi-objective genetic algorithm (NSGA-II) is under Conditional Value at Risk criterion. Also, the data of 13 companies in the period of 90-97 were used to form the portfolio. The results show that in the multi-objective genetic algorithm (NSGA-II) method, the stock with the lowest Value at Risk gains the most weight in the optimal portfolio. Also, the optimized portfolio by multi-objective genetic algorithm is more return and at the same time less risky.

Near the most of real-world decision-making issues, especially in the water resource management area, are multi-objective issues that are taken based on different and conflicting goals. Due to the wide range of application of these issues, different models have been proposed to solve them, NSGA-II and MOPSO are the most important of these multi-objective optimization models. The purpose of this study is to compare the performance of NSGA-II and MOPSO algorithms in solving multi-objective optimal operation of a hydropower reservoir. Due to the fact that the hydropower reservoirs are involved in providing the peak load of the network electricity, a neural network to predict daily energy prices in peak hours was developed initially, then the results were used to optimize the multi-objective operation of Karun 5 Dam reservoir, includes two goals of maximizing annual income and maximizing minimum daily energy production. Although the run time of the NSGA-II method is about twice as high as the MOPSO, the precision of its results is 20% better for both purposes than MOPSO.

This paper presents a Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) for the optimal operation of a complex multipurpose and multi-reservoir system. Firstly, MOEA/D decomposes a multi-objective optimization problem into a number of scalar optimization sub-problems and optimizes them simultaneously. It uses information of its several neighboring sub-problems for optimizing each sub-problem. This simple procedure makes MOEA/D have lower computational complexity compared with non-dominated sorting genetic algorithm II (NSGA-II). The algorithm (MOEA/D) is compared with the Genetic Algorithm (NSGA-II) using a set of common test problems and the real-world Zohre reservoir system in southern Iran. The objectives of the case study include water supply of minimum flow and agriculture demands over a long-term simulation period. Experimental results have demonstrated that MOEA/D can improve system performance to reduce the effect of drought compared with NSGA-II superiority. Therefore, MOEA/D is highly competitive and recommended to solve multi-objective optimization problems for water resources planning and management.

This paper presents a multi-objective mathematical model for the reverse supply chain of hospital waste management in Iran during the COVID-19 pandemic, incorporating dimensions of sustainability. The objectives of the model are as follows: 1) Minimizing the costs associated with building facilities and waste treatment centers, vehicle fuel costs, and environmental costs due to pollutant emissions; 2) Maximizing the energy generated from the waste combustion process; 3) Minimizing the risk of virus transmission resulting from inadequate waste management; and 4) Maximizing the number of job opportunities in the established centers. It is important to note that existing uncertainties are addressed through the application of fuzzy set theory. Given the multi-objective nature of the model, two multi-objective algorithms, namely the Pareto archive-based Krill Herd Algorithm and Non-dominated Sorting Genetic Algorithm II (NSGA-II), are employed to solve the defined problem. The results indicate that the proposed Krill Herd Algorithm converges to a solution with higher quality and dispersion compared to NSGA-II. Additionally, through a comparison of the spacing index and running time of the two algorithms, it is observed that NSGA-II explores the solution space with higher uniformity and solves the model in less time.

Distribution centers (DCs) play important role in maintaining the uninterrupted flow of goods and materials between the manufacturers and their customers.This paper proposes a mathematical model as the bi-objective capacitated multi-vehicle allocation of customers to distribution centers. An evolutionary algorithm named non-dominated sorting ant colony optimization (NSACO) is used as the optimization tool for solving this problem. The proposed methodology is based on a new variant of ant colony optimization (ACO) specialized in multi-objective optimization problem. To aid the decision maker choosing the best compromise solution from the Pareto front, the fuzzy-based mechanism is employed for this purpose. For ensuring the robustness of the proposed method and giving a practical sense of this study, the computational results are compared with those obtained by NSGA-II algorithm. Results show that both NSACO and NSGA-II algorithms can yield an acceptable number of non-dominated solutions. In addition, the results show while the distribution of solutions in the trade-off surface of both NSACO and NSGA-II algorithms do not differ significantly, the computational CPU time of NSACO is considerably lower than that of NSGA-II. Moreover, it can be seen that the fast NSACO algorithm is more efficient than NSGA-II in the viewpoint of the optimality and convergence.

Traffic jam is a daily problem in nearly all major cities in the world and continues to increase with population and economic growth of urban areas. Traffic lights, as one of the key components at intersections, play an important role in control of traffic flow. Hence, study and research on phase synchronization and time optimization of the traffic lights could be an important step to avoid creating congestion and rejection queues in a urban network. Here, we describe the application of NSGA-II, a multi-objective evolutionary algorithm, to optimize both vehicle and pedestrian delays in an individual intersection. Results show that parameters found by improved NSGA-II can be superior to those defined by a traffic engineer with respect to several objectives, including total queue length of vehicles and pedestrians.
In this paper, we improve NSGA-II algorithm based to the regression line to find a Pareto-optimal solution or a restrictive set of Pareto-optimal solutions based on our solution approaches to the problem, named PDNSGA (Non-dominated Sorting Genetic Algorithm based on Perpendicular Distance). In this paper, our purpose is to present a solution methodology to obtain all Pareto-optimal solutions to optimize traffic signal timing and enable the decision-makers to evaluate a greater number of alternative solutions. The proposed algorithm has the capability of searching Pareto front of the multi-objective problem domain. Further jobs should be concerned on the signal timing optimization method for the oversaturated coordinated intersections or small-scale road network and real-field applications with the traffic signal controller. The high speed of the proposed algorithm and its quick convergence makes it desirable for large scheduling with a large number of phases. Furthermore, we have used the mean deviation from the ideal point (MDI) measure to compare the performance of the MOGA, PDNSGA, NSGA-II, and WBGA by the ANOVA method. It is demonstrated that the our proposed algorithm (PDNSGA) gives better outputs than those of MOGA, NSGA-II, and WBGA in traffic signal optimization problem, statistically .