Epsilon-constraint Method Research Articles

A Stochastic Sustainable Closed-Loop Supply Chain Networks for Used Solar Photovoltaic Systems: Meta-Heuristic Comparison and Real Case Study

This research presents a novel approach to setting up a sustainable Closed-Loop Supply Chain (CLSC) network for used solar photovoltaic (PV) systems, addressing end-of-life product waste from solar panel installations and manufacturing centers. The model accounts for uncertainties in PV systems and aims to efficiently collect, refurbish, and recycle used solar PV systems, promoting a circular and environmentally responsible waste management strategy. The supply chain network comprises vendors, collection centers, hybrid centers, distribution centers, and manufacturing centers, with objectives to maximize total profit, minimize environmental risk, and maximize service levels by demonstrating the profitable reuse of used solar photovoltaic systems by manufacturers. The epsilon-constraint method is utilized to handle the model's multi-objectiveness and identify Pareto optimal solutions. A case study in Iran is conducted to validate the methodology's performance, comparing results obtained from three meta-heuristic methods: Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), Multi-Objective Particle Swarm Optimization (MOPSO), and Multi-Objective Gray Wolf Optimization (MOGWO). The average error rates are 0.0358 for MOGWO, 0.1248 for MOPSO, and 0.2066 for NSGA-II. Sensitivity analysis highlights the significant impact of demand variations on all objective functions. Lastly, the numerical results are discussed to provide managerial insights for informed decision-making.

Optimization of carbon emission in an integrated machine-piece scheduling and vehicle routing problem and its solution using MOPSO and NSGAII metaheuristic algorithms

The growth of the global economy is accompanied by significant energy consumption, and greenhouse gas emissions create various problems such as global warming and environmental degradation. To protect the environment, governments are seeking to reduce carbon emissions. Production systems that operate solely based on economic factors in the workshop only consider problems such as production speed, cost, and processing time. Two aspects can be effective in saving energy and reducing emissions at the production planning level: using routing to find the shortest path for collecting workpieces to the workshop, and turning off machines with long idle times and restarting them at the appropriate time. If the workshop production problem is combined with vehicle routing, a new problem arises. According to the research conducted so far, an integrated mathematical model for production routing has not been designed in a situation where the routing is before the production workshop. In this research, this bi-objective model is introduced, and it is solved using the augmented epsilon-constraint (AEC) method. The proposed mixed-integer linear programming model of this research includes three dimensions: environmental, social (customer satisfaction), and economic simultaneously. Given the high complexity of the mathematical model, MATLAB software and MOPSO and NSGA-II algorithms were used to solve it at higher dimensions. Seven evaluation criteria were used to compare the two proposed algorithms, and the results show that the MOPSO algorithm performs better. The findings suggest that minimizing pollution may involve sacrificing on-time delivery to customers. Consequently, decision-makers must carefully weigh the trade-off between reducing environmental impact and maintaining satisfactory delivery performance, ultimately deciding on an acceptable pollution level.

Strategical and tactical supply chain optimisation for smart production planning and control 4.0

Industry 4.0 (I4.0) technologies generate new opportunities for developing smart models, algorithms and tools to support supply chain (SC) production planning and control (PPC), or smart PPC (SPPC 4.0). Paired with opportunities, challenges arise in integrating sustainability and resilience in SC network design (SCND) according under I4.0. The main novelty of this paper is to propose two multi-objective models that integrate strategical and tactical PPC decisions into a sustainable-resilient SC under I4.0 towards SPPC 4.0. Sustainability is incorporated in terms of reducing costs and CO2 emissions, and a job creation factor. Resilience is incorporated in terms of contracting support suppliers. To solve the multi-objective models, the augmented epsilon constraint method (AUGMECON) was used. This algorithm minimises a target objective function while it treats the others as constraints. Our experiments indicate that AUGMECON is sensitive to the choice of epsilon values. Furthermore, a synthetic data generation tool called SR1-SR2_SynthDataGenerator was developed. This tool generates input datasets to validate and evaluate our models against benchmarks. A stochastic model (SR2) is also proposed that, with small datasets, takes 8.39 seconds to solve. The proposed models can be useful for industries that seek sustainable and resilient SCs to adapt to changing environments.

A closed-loop dual-channel supply chain network for leather products: An integrated simulation optimization clustering approach

The leather industry is pivotal to the economic development of certain countries; however, it also poses significant environmental challenges. Thus, this study aims to design a closed-loop leather supply chain network that incorporates waste recycling and product regeneration processes. In light of the growing prevalence of both in-store and online shopping, the concept of a dual-channel supply chain is examined. Furthermore, as advertising through traditional and social media continues to expand, this research uniquely investigates the impact of two advertising modalities—SMS and social networks—alongside the design and layout of retail environments, considering their effects on product sales within the supply chain context. Additionally, outlet stores are integrated into the model to facilitate the sale of products that may become outdated over time, thereby enhancing the model's real-world applicability. To achieve this, a multi-product, multi-period mathematical model is developed to minimize costs and maximize customer responsiveness in both forward and reverse supply chain flows. The K-means clustering method is employed to categorize customers based on recency, frequency, and monetary (RFM) features. Through simulation, demand parameters are derived for each customer cluster across various scenarios. Moreover, the Aghezzaf approach is utilized to address scenario-based uncertainties within the model, and the proposed multi-objective model is solved using the Augmented Epsilon constraint method. A real-world case study is conducted to apply the proposed model, and critical parameters are examined through sensitivity analysis to validate its effectiveness. The findings suggest that incorporating return flows into the supply chain can significantly enhance both producer profitability and customer responsiveness regarding leather products.

Providing a framework to optimize the sustainable construction material supply chain with the possibility of horizontal transfers

The application of Supply Chain Management (SCM) principles has gained considerable attention across various industries to enhance operational efficiency and business performance. In the construction sector, SCM can guide managers in strategic planning and foster collaboration with suppliers, leading to more effective project execution. Despite its importance, limited research has focused on designing sustainable supply chains for construction materials under uncertain conditions. This study aims to bridge this gap by introducing a robust optimization framework that incorporates sustainable development criteria, specifically the minimization of harmful environmental effects and the reduction of worker unemployment. Additionally, the research introduces an innovative concept of horizontal transfers between downstream members, which not only reduces supply deficiencies but also indirectly increases profitability for these members. This article is a part of a Doctoral dissertation. It follows a two-step approach. First, suppliers of construction materials are ranked based on sustainable development criteria using a multi-criteria decision-making method. The best-ranked supplier is then integrated into a mathematical model for optimizing the supply chain design. Given the NP-hard nature of the problem, the CPLEX 12.1 solver with the epsilon constraint method is used to solve small-scale models. For larger-scale problems, three meta-heuristic algorithms are developed: multi-objective ant-lion, multi-objective gray wolf, and multi-objective dragonfly. The results show that while both the ant-lion and gray wolf algorithms deliver comparable average performance, the gray wolf algorithm excels in terms of solution time, making it more effective for real-time problem-solving. This makes the gray wolf algorithm the most efficient choice for addressing large-scale, multi-objective supply chain challenges. This research introduces a novel framework for designing sustainable construction supply chains under uncertain conditions. By focusing on criteria such as minimizing harmful environmental effects and reducing worker unemployment, this study addresses key aspects of sustainable development. Additionally, the innovative horizontal transfer mechanism and the insights into algorithmic performance provide valuable contributions to the field, especially for real-world applications in the construction industry.

Multi-objective modeling of price and pollution in large-scale energy hubs with load management

This study introduces a novel multi-objective model that addresses emission costs, large-scale user operational expenses, and the efficiency of the electric storage system within an integrated energy hub encompassing heating, water, power, and gas sources. A key objective of this model is to maximize the performance of the electrical storage system. The study employs the epsilon-constraint method to construct the Pareto front, aiming to balance profitability and emission reduction from virtual power plant units. The final decision-making process utilizes a fuzzy decision-making technique. Additionally, demand response program (DRP) is incorporated to optimize peak-hour demand and align the load profile with defined objectives. The proposed approach is evaluated across various operational scenarios within a sample system, demonstrating its effectiveness and potential benefits in terms of cost reduction and environmental impact mitigation. Focusing on environmental impact, the carbon dioxide (CO2) emissions are also lower under the DRP scenario, amounting to 10253.92 kg without DRP versus 10127.74 kg with DRP. This reduction in emissions aligns with sustainable energy management goals, showcasing DRP's capability to mitigate environmental impacts associated with energy generation and consumption. The percentage improvements in total costs and emissions further highlight the advantages of employing DRP. The reductions in total costs range from approximately 1.2%–1.4%, demonstrating cost savings across different cost categories. Similarly, the decrease in CO2 emissions by approximately 1.2% underscores DRP's role in promoting environmentally friendly energy practices.

Grouping and scheduling multiple sports leagues: an integrated approach

This paper introduces the multi-league grouping and scheduling problem, which integrates the grouping of teams into leagues and the scheduling of each league. This involves two possibly conflicting objectives: minimizing travel distance and minimizing capacity violations of venues shared by teams. We formulate this problem as a bi-objective mixed-integer programming model. Given the NP-hardness of the grouping problem, the integrated problem is particularly challenging. Hence, we design a two-layer constructive heuristic to efficiently approximate the Pareto set, using simulated annealing on the outer layer and an integer programming model on the inner layer. We further develop a speed-up version where the inner layer is solved heuristically. We develop a series of large-scale problem instances, including one based on data from the Royal Belgian Football Association. In a computational study, we compare our algorithms with an epsilon-constraint method and evaluate their results using various multi-objective solution quality metrics.

Dual resource constrained flexible job shop scheduling with sequence‐dependent setup time

AbstractThis study addresses the imperative need for efficient solutions in the context of the dual resource constrained flexible job shop scheduling problem with sequence‐dependent setup times (DRCFJS‐SDSTs). We introduce a pioneering tri‐objective mixed‐integer linear mathematical model tailored to this complex challenge. Our model is designed to optimize the assignment of operations to candidate multi‐skilled machines and operators, with the primary goals of minimizing operators' idleness cost and sequence‐dependent setup time‐related expenses. Additionally, it aims to mitigate total tardiness and earliness penalties while regulating maximum machine workload. Given the NP‐hard nature of the proposed DRCFJS‐SDST, we employ the epsilon constraint method to derive exact optimal solutions for small‐scale problems. For larger instances, we develop a modified variant of the multi‐objective invasive weed optimization (MOIWO) algorithm, enhanced by a fuzzy sorting algorithm for competitive exclusion. In the absence of established benchmarks in the literature, we validate our solutions against those generated by multi‐objective particle swarm optimization (MOPSO) and non‐dominated sorted genetic algorithm (NSGA‐II). Through comparative analysis, we demonstrate the superior performance of MOIWO. Specifically, when compared with NSGA‐II, MOIWO achieves success rates of 90.83% and shows similar performance in 4.17% of cases. Moreover, compared with MOPSO, MOIWO achieves success rates of 84.17% and exhibits similar performance in 9.17% of cases. These findings contribute significantly to the advancement of scheduling optimization methodologies.

Balancing Possibilist-probabilistic risk assessment for smart energy hubs: Enabling secure peer-to-peer energy sharing with CCUS technology and cyber-security

This paper introduces the Possibilistic-Probabilistic Risk-based Smart Energy Hub (PPR-SEH) scheduling model, addressing cybersecurity challenges in the transition to advanced energy systems characterized by decarbonization, decentralization, and digitalization. The model integrates cutting-edge technologies like Carbon Capture Utilization and Storage (CCUS) and demand response programs. It addresses uncertainties from renewable energy sources, demand variability, fuel supply, and energy price fluctuations using a Z-number-based approach. Covering various energy types—electricity, heat, cooling, gas, and water—the PPR-SEH model offers a comprehensive energy management solution. Employing a mixed-integer linear programming (MILP) framework optimized with the CPLEX solver in GAMS software, it uses an epsilon constraint method and a fuzzy satisfying approach for solution selection. The model also evaluates the economic and environmental impacts of peer-to-peer energy-sharing markets linked with carbon emission trading, enhancing the efficiency and sustainability of energy distribution. The findings reveal that incorporating robust cybersecurity measures and integrating demand response and CCUS significantly influence operational efficiency and sustainability, evidenced by an increase in costs and pollution by approximately 11.43 % and 1.8 %, respectively, compared to deterministic approaches. This study underscores the importance of robust planning and the beneficial impact of a carbon system on load curve management and economic returns in smart energy systems.

Multicriteria optimization techniques for understanding the case mix landscape of a hospital

Various medical and surgical units operate in a typical hospital and to treat their patients these units compete for infrastructure like operating rooms (OR) and ward beds. How that competition is regulated affects the capacity and output of a hospital. This article considers the impact of treating different patient case mix (PCM). As each case mix has an economic consequence and a unique profile of hospital resource usage, this consideration is important. To better understand the case mix landscape and to identify those which are optimal from a capacity utilisation perspective, an improved multicriteria optimization (MCO) approach is proposed. As there are many patient types in a typical hospital, the task of generating an archive of non-dominated (i.e., Pareto optimal) case mix is computationally challenging. To generate a better archive, an improved parallelised epsilon constraint method (ECM) is introduced. Our parallel random corrective approach is significantly faster than prior methods and is not restricted to evaluating points on a structured uniform mesh. As such we can generate more solutions. The application of KD-Trees is another new contribution. We use them to perform proximity testing and to store the high dimensional Pareto frontier (PF). For generating, viewing, navigating, and querying an archive, the development of a suitable decision support tool (DST) is proposed and demonstrated.

A multi-objective planning and scheduling model for elective and emergency cases in the operating room under uncertainty

Hospitals are paramount hubs for delivering healthcare services, with their Operating Rooms (ORs) as a pivotal and financially substantial component. Efficient surgery ward planning is crucial in healthcare institutions, aiming to improve medical service quality while reducing costs. This research delves into the intricacies of integrated OR planning and scheduling, focusing on elective and emergency patients in an uncertain environment. To address these challenges, a mixed integer programming (MIP) framework is developed to minimize inactivity and patient wait times while optimizing high-priority resource allocation. Both upstream and downstream units of the ward, the Pre-operative Holding Unit (PHU), Post Anesthesia Care Unit (PACU), and Intensive Care Unit (ICU) are included. The inherently uncertain aspects of surgery, including surgical duration, Length of Stay (LOS), and the influx of emergency patients, demand an intelligent optimization approach. Consequently, a robust optimization strategy is harnessed to effectively grapple with this pervasive uncertainty. A deterministic model is introduced and improved using an enhanced epsilon constraint method. The culmination of this analytical journey yields a collection of Pareto-optimal solutions. Empirical results, supported by managerial insights, highlight the superiority of the proposed method over the traditional weighting approach.

Stochastic portfolio optimization: A regret-based approach on volatility risk measures: An empirical evidence from The New York stock market.

Portfolio optimization involves finding the ideal combination of securities and shares to reduce risk and increase profit in an investment. To assess the impact of risk in portfolio optimization, we utilize a significant volatility risk measure series. Behavioral finance biases play a critical role in portfolio optimization and the efficient allocation of stocks. Regret, within the realm of behavioral finance, is the feeling of remorse that causes hesitation in making significant decisions and avoiding actions that could lead to poor investment choices. This behavior often leads investors to hold onto losing investments for extended periods, refusing to acknowledge mistakes and accept losses. Ironically, by evading regret, investors may miss out on potential opportunities. in this paper, our purpose is to compare investment scenarios in the decision-making process and calculate the amount of regret obtained in each scenario. To accomplish this, we consider volatility risk metrics and utilize stochastic optimization to identify the most suitable scenario that not only maximizes yield in the investment portfolio and minimizes risk, but also minimizes resulting regret. To convert each multi-objective model into a single objective, we employ the augmented epsilon constraint (AEC) method to establish the Pareto efficiency frontier. As a means of validating the solution of this method, we analyze data spanning 20, 50, and 100 weeks from 150 selected stocks in the New York market based on fundamental analysis. The results show that the selection of the mad risk measure in the time horizon of 100 weeks with a regret rate of 0.104 is the most appropriate research scenario. this article recommended that investors diversify their portfolios by investing in a variety of assets. This can help reduce risk and increase overall returns and improve financial literacy among investors.

A Weighted and Epsilon-Constraint Biased-Randomized Algorithm for the Biobjective TOP with Prioritized Nodes

This paper addresses a multiobjective version of the Team Orienteering Problem (TOP). The TOP focuses on selecting a subset of customers for maximum rewards while considering time and fleet size constraints. This study extends the TOP by considering two objectives: maximizing total rewards from customer visits and maximizing visits to prioritized nodes. The MultiObjective TOP (MO-TOP) is formulated mathematically to concurrently tackle these objectives. A multistart biased-randomized algorithm is proposed to solve MO-TOP, integrating exploration and exploitation techniques. The algorithm employs a constructive heuristic defining biefficiency to select edges for routing plans. Through iterative exploration from various starting points, the algorithm converges to high-quality solutions. The Pareto frontier for the MO-TOP is generated using the weighted method, epsilon-constraint method, and Epsilon-Modified Method. Computational experiments validate the proposed approach’s effectiveness, illustrating its ability to generate diverse and high-quality solutions on the Pareto frontier. The algorithms demonstrate the ability to optimize rewards and prioritize node visits, offering valuable insights for real-world decision making in team orienteering applications.

Designing a sustainable-resilient humanitarian supply chain for post-disaster relief process, an earthquake case study in Haiti

Purpose Throughout human history, the occurrence of disasters has been inevitable, leading to significant human, financial and emotional consequences. Therefore, it is crucial to establish a well-designed plan to efficiently manage such situations when disaster strikes. The purpose of this study is to develop a comprehensive program that encompasses multiple aspects of postdisaster relief. Design/methodology/approach A multiobjective model has been developed for postdisaster relief, with the aim of minimizing social dissatisfaction, economic costs and environmental damage. The model has been solved using exact methods for different scenarios. The objective is to achieve the most optimal outcomes in the context of postdisaster relief operations. Findings A real case study of an earthquake in Haiti has been conducted. The acquired results and subsequent management analysis have effectively assessed the logic of the model. As a result, the model’s performance has been validated and deemed reliable based on the findings and insights obtained. Originality/value Ultimately, the model provides the optimal quantities of each product to be shipped and determines the appropriate mode of transportation. Additionally, the application of the epsilon constraint method results in a set of Pareto optimal solutions. Through a comprehensive examination of the presented solutions, valuable insights and analyses can be obtained, contributing to a better understanding of the model’s effectiveness.

A Multi-Objective Model for Designing a Sustainable Closed-Loop Supply Chain Logistics Network

Background: The growing concern for environmental and social issues has led to a focus on designing sustainable supply chains and increasing industrial responsibility towards society. In this paper, a multi-objective mixed-integer programming model is presented for designing a sustainable closed-loop supply chain. The model is aimed at the minimization of the total cost with the total used facilities, the negative environmental impacts, and the maximization of the positive social impacts. Methods: The epsilon-constraint method is utilized for solving the model and further extracting the Pareto solutions. Results: The result of the research clearly shows an optimal trade-off between the conflicting objectives, where, by paying more attention to the social and environmental aspects of sustainability, the total costs are increased or by optimizing the number of facilities, a better balance between the dynamics associated with the short-term and long-term goals is reached. The results of the sensitivity analysis also show that increasing the demand of the supply chain has the greatest impact on the supply chain costs compared to other objectives. Conclusions: Consequently, investigating such comprehensive sustainable objectives provides better insights into the impact of design variables on the expectations of stakeholders.

Bi-objective optimization modeling for biomass supply chain planning

Biomass energy plays an essential role in renewable energy for many reasons, such as reducing the dependence on fossil fuels and lowering greenhouse gas emissions, providing heat, electricity, and biofuels for various applications, and utilizing waste materials for helpful energy products. Besides, it can create employment opportunities and promote rural development, especially in developing countries where biomass resources are abundant and accessible. In the context of renewable energy research and application, this paper aims to develop a multi-objective mixed integer linear programming for designing multiple echelon biomass supply chain networks. The model is formulated to consider the economic costs and environmental impact of biomass distribution from the suppliers to the biomass plants. In this research, the Epsilon constraint method is adopted to generate Pareto fonts, which provides the trade-offs between two objectives. Moreover, sensitivity analysis is implemented to provide decision-makers with information about a network with changed parameters such as demand. Our model allows the decision maker to determine the capacity of warehouses and biomass power plants, inventory levels, type of trucks, etc. The proposed model is verified and evaluated using a practical dataset from Can Tho province, Central Mekong River Delta in Vietnam, generating several benefits for energy security and sustainability. Such a network includes 3 types of power plants, 3 scales of warehouses, 13 potential locations, and 41 suppliers. From the generated solutions, with the proportion of biomass electricity satisfaction varying from 5% to 30%, Hung Phu, O Mon, and Cai Rang industrial parks are the most suitable for power plants.

Role of combinatorial optimization problems for the efficient decision making of a company- Case study-

All company seeks to improve their performance through achieving several objectives to stay in the labor market and increase competitiveness. The problem lies in the fact that it often relies on traditional methods for efficient decision-making, causing a waste of time and effort. The paper aims to find the best car service stations among several proposed stations by the Naftal Company, which seeks to achieve the two most important objectives; maximizing lubricants and tires revenues, and maximizing fuel and LPG revenues for the year 2019. The new applied case study was done with the help of the binary multi-objective knapsack problem, which is considered one of the most important problems in multi-objective combinatorial optimization problems. The problem was solved by the epsilon constraint method using MATLAB and CPLEX software. The study results confirmed that the proposed efficient solution set (Pareto optimal solutions) provides the decision maker with a comprehensive view of how to make their decision in a scientific, thoughtful, logical, and convincing manner that suits his situation and puts him at ease, away from trial and error or relying on self-experience.

A timely efficient and emissions-aware multiobjective truck-sharing integrated scheduling model in container terminals

In line with the development of green port terminals and the necessity of environmentally friendly efficient use of handling and transportation equipment, criteria such as emission reduction, energy minimization, and efficiency in a container terminal are prominent issues, which in recent years, have been the main concern of container terminal managers in developing terminal operating systems. Therefore, in this study, a bi-objective mixed integer mathematical programing model of integrated scheduling for ships’ loading and unloading operation sequencing in container terminals is proposed, which considers the minimization of containers’ flow time, trucks’ emission, and energy consumption as well as sharing trucks among quay cranes and decreasing their empty trips. In this model trucks’ technical specifications and polluting levels are input parameters for estimating emission and energy consumption of operation, which consequently leads to two uniform parallel machine scheduling models. To derive the exact solution of the model, the epsilon-constraint method is applied. Nevertheless, due to the problem’s NP-hardness attribute, two variants of non-dominated sorting genetic algorithm and multiobjective particle swarm optimization metaheuristic algorithms are proposed to identify the approximate Pareto front of solutions. In large-size problems, these algorithms outperform the epsilon-constraint method by finding acceptable results in a reasonable time. This model, which could be embedded in terminal operating software, not only yields a practical optimum operational sequence but also measures the amount of energy and emission from trucks during loading and unloading operations. The results, which utilized the data collected from Shahid Rajaee port in southern Iran, indicate that this practical model as compared to the current procedure in the terminal, results in a significant improvement in energy and emission reduction and terminal flow time.

Integrated location and routing for cold chain logistics networks with heterogeneous customer demand

The critical interdependence between facility location and vehicle routing is a fundamental component of cold chain logistics management (CCLM). Furthermore, integrating information within CCLM has the potential to enhance operational efficiency, reduce costs, improve risk management, and elevate product quality, ultimately ensuring that temperature-sensitive goods are delivered in best condition. This paper introduces a novel non-linear multi-objective model designed to concurrently optimize warehouse facility location and vehicle routing, addressing the challenges inherent in cold chain logistics processes. The model seeks to minimize the aggregate costs related to transportation, facility location, and delivery tardiness. The study accounts for several pragmatic assumptions to address real-world scenarios: multiple delivery requests per customer, handling mixed commodities, and distributing mixed commodities using a single vehicle. This paper firstly studies simultaneous pickup and delivery with multiple requests and heterogeneous customer demands, each of which should be preserved in a different range of temperatures and needs different vehicle types. The epsilon-constraint method is employed to validate the proposed model, and a set of advanced, hybrid multi-objective evolutionary algorithms (MOEA) are presented to tackle the problem in a real-world context. A comprehensive set of performance metrics is utilized supported by rigorous statistical testing.

Providing a New Multiobjective Two-Layer Approach for Developing Service Restoration of a Smart Distribution System by Islanding of Faulty Area

One of the essential capabilities of a smart distribution network is to improve network restoration performance using the postfault islanding method. Islanding of the faulty area can be done offline and online. Online islanding will decrease load shedding and operation cost. In this study, a novel two-step mathematical method for system restoration after the fault is presented. A new mathematical model for the optimal arrangement of the system for the faulty area in the first layer is proposed. In this layer, the main objective is to decrease the distribution system’s load shedding and operational costs. In this regard, after the fault event, the boundary of the islanded MGs is determined. Then, in the second layer, the problem of unit commitment in the smart distribution network is addressed. In addition to the load shedding, optimal planning of energy storage systems (ESSs) and nondispatchable distributed generation (DG) resource rescheduling are also determined in this layer. The important advantages of the proposed approach are low execution time and operational costs. A demand response (DR) program has also been used for optimal system restoration. Solving the problem using the multiobjective method with the epsilon-constraint method is another goal of the paper, which simultaneously minimizes the cost and the emissions of the smart distribution network. The proposed model has been tested on an IEEE 33-bus system. Better performance of the proposed model compared to the techniques in the literature has been proven.