nsga-ii algorithm

The design of facility layout and production planning accordingly is significantly important in the manufacturing industries. This type of design in traditional units is mainly based on the lowest cost of moving materials and effective environmental indicators, and social factors are ignored in the planning and design of facility layout; Therefore, usually, the arrangement does not match the human capacity, the intensity of the employees' work is not scientific and it causes a lot of damage to the physical and mental health of the employees for a long time. Considering the importance of the mentioned items, paying attention to biological issues such as energy, which is one of the main concerns of the country, and social issues, such as the safety of the operator's work environment, which is followed by governmental and non-governmental associations, can be considered a positive and new step in the layout design.

Design/methodology/approach: 

In this paper, a multi-objective mathematical programming model has been developed in a dynamic cellular manufacturing system, taking into account the minimization of the costs of moving and rearranging the facilities, the minimization of the risks of the work environment (the potential risk of placing machinery in a certain place), and the consumption of electrical energy in product production operations. To make the model closer to reality, other issues related to the production environment such as hiring and firing operators in each period, training, wages and their allocation are also included in the model. The proposed model is solved by designing samples in different dimensions, applying the epsilon constraint method and meta-heuristic algorithm NSGA-II and MOPSO, using performance indicators, and associated comparison and analysis by T-test.

Performance indices (spacing metric, diversification metric, mean ideal distance, CPU time) in solution methods were calculated and compared based on information inspired by the subject literature and the design of 15 problems with different dimensions. The results indicated that the quality of the solutions obtained from the NSGA-II algorithm was better than other methods and in terms of the solution time, the solution was reached at least two times earlier than the epsilon constraint method.

Research limitations/implications: 

For future studies, it is suggested to investigate the performance of other meta-heuristic algorithms to solve the proposed model; Also, the combination of other real-world industrial factors such as financial and energy resource limitations, facility idle time, and unequal facility dimensions can be considerably valuable for future research. In addition, the uncertainty of the parameters, which is one of the main and practical issues in the real world, can be added to the model in terms of demand or processing time.

Practical implications:

 The dynamic cellular manufacturing system is one of the well-known manufacturing systems that provides the possibility of increasing the level of reactivity, flexibility and agility in production to compete in the market, but with the growth of industrial development and the increasing attention of societies to the amount of energy consumption and the conditions of employees in production with a new challenge. It has been faced in such a way that it should include sustainability issues from the very beginning and in the design of the facility layout. The proposed model has provided a stable, dynamic and optimal layout by creating a balance between the dimensions of sustainability (cost, energy and layout safety) in manufacturing industries.

Social implications:

 Ignoring social issues and mismanagement of human resources has resulted in unforeseen costs for manufacturing companies. This study attempts to propose a model that is closer to reality and provides a more accurate and safe arrangement by considering various dimensions of human resource management in production, such as hiring, firing, training, wages, and allocation, which are effective tools for decision-making in organizations, alongside workplace safety.

Originality/value:

 In this paper, a nonlinear mixed integer programming model is proposed for the facility layout problem in a dynamic and sustainable cellular space. In this model, the amount of energy consumption, which is one of the main issues that manufacturing industries deal with, has been addressed and has helped industries in improving their performance. Two approaches have been proposed for this issue. The amount of energy used to move the machines and the amount of energy used in processing each part/product based on the selection of the best route. In this model, the best production route is selected in such a way that, in addition to reducing production costs, energy consumption in moving parts and processing each operation should be reduced.

We present a mathematical model for the problem of collaborative production system based on order with fairness to allocate production loads. The main objectives of the model are to minimize total production costs and maximize the use of resources in order to distribute production loads fairly in conditions of uncertainty. Fuzzy programming was used to control uncertain parameters. The results show that, with increasing the uncertainty rates, production system costs have increased. Since the capacity of factories is constant, with the increase in demand, the amount of production has increased and the maximum use of resources of each factory has also increased. Also, contrary to the trend of system cost changes, with the increase in the number of factories, the maximum use of available resources has decreased. To solve large sample problems, the NSGA II algorithm with a suitable chromosome is used to search the problem space. Numerical results of solving 15 sample problems show the high efficiency of NSGA II algorithm in solving the problem of cooperative production system in a very short time.

Finding a subset of features is an issue that has been widely used in a variety of fields such as machine learning and statistical pattern recognition. Since increasing the number of features increases the computational cost of a system, it seems necessary to develop and implement systems with minimum features and acceptable efficiency.

Considering objective, it's developmental research and in terms of two Meta-heuristic algorithms, namely genetic algorithm (GA) and multi-objective non-dominated sorting genetic algorithm (NSGA II). The multi-objective method compared to the single-objective method has reduced the number of features to 50% in all instances; it doesn't make much difference in classification accuracy. The proposed method is applied on six datasets of credit data, and the results were analyzed using two common classifiers namely, support vector machine (SVM) and K-nearest neighbors (KNN). Comparing two classifiers applied on datasets, K- nearest neighbors (KNN) compared to the support vector machine (SVM) has shown relatively better performance in increasing the classification accuracy and reducing the number of attributes.

Genetic algorithm and multi objective non-dominated sorting genetic algorithm have a good performance in increasing the accuracy of classification and reducing the number of attributes in feature selection problem of multi-class data. The results also indicate an increase in classification accuracy, simultaneously with a significant decrease in the number of features in both KNN and SVM methods.

According to the results, the proposed approach has a high efficiency in features selection problem.

Food supply chain management is very vital due to its high scale in industry, amount of wastage of food in theworld and relationship between wastage of food and under-nourishment. It consists of producing the food andmanufacturing companies, whole sale and distributors, brokers, food service places, restaurants and retail groceryfirms. Studying perishable goods in a supply chain can be helpful for industries that are related to these kinds ofgoods. Because of the important role of location and routing in a supply chain, unity of these elements leading toan efficient supply chain. Recently, multi-layer and multi-facility problems in a supply chain have been studiedin large scale. Connection between facilities (i.e., the best flow allocating between facilities and vehicle routingfor supplying the perishable foods) is one of the key subjects for this problem. This paper studies a perishable foodsupply chain network with disruption risk including the location of facilities, allocating flow between facilitiesand routing decisions. It also presents a multi-objective model to minimize the operational costs (e.g., openingcost, route repairing cost during the disruption and unsatisfied demands cost), minimize the response time, andmaximize the reliability of minimum routes. Validity of the model is investigated by the ε-constraint method inGams. Since this problem is an NP-hard one, the NSGA-II is used for solving this problem in large sizes. Finally,to show the efficiency of the proposed model, a real case study including 10 zone of district 1 of Tehran is applied.

Time, cost and quality are important goals of any project. Todays, the demand of project stakeholders to reduce total project costs has increased simultaneously time reduction and augment in quality of the project. This leads researchers to develop models that add quality factor to previous models of cost-time balance. In this paper, a time-cost-quality trade -off model with three objective functions includes minimizing project termination, minimizing total project cost and maximizing total quality of activities in a multi-modal PERT network was investigated. After presenting the appropriate mathematical model, a decision was made on the basis of a test plan of possible levels for each variable. Then, using the simulation process, random values of decision variables and response variables were implemented at each time, and we developed a neural network model using artificial neural networks. To solve this model, since the problem is in the NP-hard category, two multi-objective meta-heuristic algorithms NSGA-II and MOPSO were used. To determine the performance of the proposed model, the problem was tested on a small, medium and large-scale PERT network. The parameters of these two meta-heuristic algorithms were adjusted by Taguchi method and the results were based on the parameters set showed that the NSGA-II algorithm performs better than the MOPSO algorithm.

Portfolio is a collection or combination of investments in financial and non-financial assets that may be carried out by an individual or organization. How to select and optimize of portfolio is very important. One of the most important points that should be considered in the proposed approach for portfolio selection, is uncertainty. Because, one of the most important features of financial markets is their uncertainty. Thus, the purpose of this study is to present a bi-objective model for portfolio selection that is capable to be used under uncertainty of financial data and for this purpose, a robust optimization approach has been used. It should be noted that return and conditional value at risk (CVaR) are considered as model objectives, and the constraints of the number of shares and the purchasing volume of each share have been added to the model. Also, due to the complexity of the proposed model, a NSGA-II meta-heuristic algorithm has been used to solve the suggested model of research. Finally, the presented model was solved by using the actual data of 200 stocks of Tehran stock market for the period of 2017 and the results were analyzed. The results indicate the efficiency of the proposed approach portfolio selection according to the investor's preferences and constraints under uncertainty of financial data.

Data classification is one of the main issues in management science which took into account from different approaches. Artificial intelligence methods are among the most important classification methods, most of them consider total accuracy function in performance evaluation. Since in imbalanced data sets this function considers the cost of prediction errors as a fix amount, in this research a sensitivity function in used in addition to the accuracy function in order to increase the accuracy in all of the predefined classes. In addition, due to complexity in process of seeking information from decision maker, NSGA II algorithm is used to extract the parameters (Weight vector and cut levels between classes). In each iteration, based on the estimated weight vector and data sets, the algorithm calculate the score of each alternative using Sum Product function and then allocates the alternative to one of the classes, comparing to the estimated cut levels,. Then, using the fitness functions, the estimation class and the actual class will compare by two algorithms and this process will continue since optimizing the parameters. Comparison of the NSGA II and NRGA algorithms show the high efficiency of the proposed algorithm.

This research was carried out with the aim of simultaneously examining the two categories of the most commonly encountered issues in the field of production and operations including the redundancy allocation and the buffers allocation. The study sought to optimize goals such as accessibility, system costs, and buffer capacity and for this purpose, variables such as the optimum capacity of buffers between machines, the number of high-reliability machines and their allocation, and the appropriate time schedule for maintenance and repair were investigated.

Considering the categorization of emergency and preventive failures for machinery, taking into account the cost of any failure for machinery, and considering the non-exponential and increasing distribution function for a variety of failures, it is very difficult to obtain and calculate mathematical functions related to the objectives of Availability and Cost explicitly. Therefore, a combination of simulation, experimental design, and neural network approach was used to estimate these two objective functions. In order to solve the proposed model, the NSGA-II algorithm was coded in MATLAB. Also, in order to analyze the efficiency of the suggested Algorithm, the MOPSO Algorithm was used and the Algorithms were compared with each other based on the performance measures of the algorithms.

After applying the numerical example with the approach used, the results of the research indicate the validity of the proposed methodology for the problem under study.

Based on the set of solutions obtained from the algorithms used, different combinations of variables (including the number of machines per station, buffer capacity and duration of repairs) can be used to achieve the appropriate level of objectives.

In petrochemical companies, the existence of various, long job shifts can endanger the physical and mental health of employees, while having a proper timetable, in accordance with labor laws and policies, can help reduce the consequences of the disruption of their work shifts. The purpose of this research is to develop a model for timing the manpower of petrochemical companies in such a way that, by meeting the requirements of the company and the optimal number of employees in each shift, it can minimize the company's payment costs, and maximize the performance and preferences of the employees. The researchers used integer programming model. Because of the complexity of the issue and the multi-objective nature of the model, to solve the mathematical model, NSGA-II algorithm has been used. In order to obtain a better performance of the algorithm, its parameters were tuned using the Taguchi calibration method. Based on the findings from various scenarios, the 21-day working model is better than the 16-day working model. Since the model is multi-objective and is solved using the Pareto's approach, the decision maker can, according to the circumstances, choose one of the optimal Pareto solutions. Petrochemicals can apply scientific and optimum operation research approaches and its applications, in order to set up employee work schedules, create work-life balance, reduce work-related fatigue, decrease job burnout and improve their performance and productivity. Although scheduling and selecting the appropriate working model is complicated for petrochemical companies, NSGA-II algorithm can be used as an apt and powerful tool in decision making over choosing best working model.

This research studies the multi-mode project scheduling problem aiming to planning of payments considering limited resources. This model tries to propose a schedule as much as possible close to reality with taking the realistic assumptions into account. In the proposed model, renewable resources (including manpower, machinery, and equipment) as well as non-renewable resources (including consumption and money) are simultaneously considered. Then, the issues of scheduling and planning the project payment with the objectives of increasing the NPV of the project and reducing the completion time of the project in are examined. In doing so, a nonlinear mathematical programming model is presented based on the assumptions made in the problem space, to formulate the problem. Then, to validate the model, several random instances are designed in different dimensions and solved by GAMS software and ε-constraint method. To tackle the problem in large dimensions, we also proposed the NSGA-II algorithm. Finally, efficiency of the developed methodology is measured by comparing the results with ε-constraint method.

Cellular manufacturing systems (CMSs) are as one of the most important manufacturing methods.In this paper, is presented a multiple objective model to constitute a CMS under dynamic conditions subject to flexibility of operation processing, assigning machine to each operation and defining cost parameters as fuzzy numbers. In the proposed model, are considered objectives such as minimization of manufacturing system costs and fuzzy costs variance. Also in this paper, in order to attainment of effective solutions, is proposed a hybrid algorithm by NSGA-II and progressive Simulated Annealing (SA) and is applied experimental design of Taguchi for tuning the parameters of this algorithm. For surveying efficiency of the proposed algorithm, results obtained from solving several different sample problems, based on criteria of CPU time, generational distance, spacing and quality metric, are compared and analyzed with results of NSGA-II original algorithm.

In today's competitive market, sourcing is one of the most important strategic decisions of organizations. This problem by considering such factors as transportation, quality and production capacity, selects suppliers for long-term cooperation. Inventory control tactical decisions and selection of optimal inventory policy have a great impact on the cost because many organizations have a tremendous amount of capital in the form of inventory. So far, little research has been done in the area of integrated sourcing and inventory policy and systematic approach to this issue has not yet been considered. In this study, we sought to fill this research gap. In real world problems, it is difficult to calculate the exact cost of inventory shortages. To resolve this problem, shortage number was considered as a separate goal. Also, due to the probabilistic nature of the demand of plants, the objective functions cannot be calculated with conventional methods, so simulation was used to estimate the fitness of objective functions. The issue raised in this study is NP-Hard, so multi-objective meta-heuristics were used for finding the optimum solutions. Then six test problems were developed from small to large. The quality of the Pareto approximation obtained from the NSGA-II and MOPSO algorithms were evaluated by six criteria. Results showed that the solutions generated by the NSGA-II algorithm, the higher the quality.