Multi-objective Mixed-integer Programming Research Articles

Multi-objective branch-and-bound for the design-for-control of water distribution networks with global bounds

This study investigates a design-for-control (DfC) problem formulation for the joint minimization of pressure-induced leakage, maximization of resilience, and minimization of cost in water distribution networks (WDN). The DfC problem, which consists in simultaneously installing new valves and/or pipes and optimizing valve control settings, results in a challenging optimization problem belonging to the class of non-convex multi-objective mixed-integer non-linear programs (MOMINLP). Due to their complex mathematical structure, multi-objective WDN design-for-control problems have previously been solved using general-purpose evolutionary algorithms or local deterministic methods, which do not provide guarantees on the quality of the returned solutions. While branch-and-bound (BB) frameworks have been proposed to approximate the Pareto fronts of MOMINLPs with global bounds, they rely on the availability of attainable solutions which, for WDN design-for-control problems, can be hard to identify. Moreover, in the absence of general-purpose solvers, the performance of multi-objective BB implementations depends, for a given application, on the choice of adequate branching and lower bounding strategies. In this study, we investigate a multi-objective BB algorithm based on tailored branching, lower bounding and additional upper bounding strategies to efficiently approximate the Pareto front of WDN design-for-control problems with bounds of ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon$$\\end{document}-non-dominance. The proposed algorithm is applied to the optimal DfC of two case study networks and is shown to outperform alternative solution methods.

Fuzzy-random robust flexible programming on sustainable closed-loop renewable energy supply chain

Photovoltaic (PV) systems have become a widely accepted method of harnessing solar energy in recent decades. In addition to the growing use of renewable energies are being used due to the depletion of fossil fuel supplies and the corresponding pollution generated by these non-renewable fuels. Since PV systems possess a limited lifespan, and are predicted to eventually become outdated, sustainability and recycling that should be incorporated into the structure of the solar system supply chain. The management of high and low moisture waste (H&LMW) is crucial due to its harmful environmental impacts, including sludge waste, carbon dioxide (CO2), and acid compounds. This study explores the integration of research on H&LMW and PV systems, focusing on energy generation from biogas, incineration power plants, and PV systems. In this respect, we propose a multi-objective mixed-integer programming model to construct a sustainable closed-loop renewable energy supply chain by considering forward and reverse flow through solar, biogas, and incineration power plants. Reducing CO2 with power-to-gas technology is thought to be an environmentally friendly approach. A novel fuzzy-random robust flexible programming approach based on Me measure is proposed, which overcomes the limitations of addressing the uncertainty of the parameters. Next, in order to solve the suggested multi-objective model, a novel strategy known as utility function based multi-choice conic goal programming is presented. A case study explores the sustainable challenges of a closed-loop renewable energy supply network in India’s renewable energy sector. The experimental results indicate that 9 candidate locations are selected for solar wafer production facilities, while 10, 9, and 15 locations are chosen for solar cell production, module manufacturing, and solar power plants, respectively. A sensitivity analysis reveals that the proportion of air pollution limitations possessively rises from 100% to 80% corresponding to the aggregate cost increases from INR 8021452 to INR 8056542.

Multi-objective mixed integer programming modelling for closed-loop supply chain network design: an enhanced Benders decomposition algorithm

Considering a closed-loop supply chain (CLSC) network with uncertain demand and recycling rates, this article innovatively designs a multi-objective mixed-integer programming model that incorporates corporate social responsibility (CSR), a facility retrofit strategy (FRS), a flexible supply strategy (FSS) and a vehicle selection strategy (VSS). Then, robust optimization methods are applied to construct robust models under three situations of uncertainty. For the computational complexity of large-scale problems, an enhanced Benders decomposition algorithm (EBDA) is designed. A numerical case analysis is conducted using five different scale instances. First, compared to other algorithms, EBDA accelerates the solution efficiency while ensuring convergence. Secondly, the sensitivity of the objective weights and the trade-offs of multiple objectives are analysed. Finally, the impact is analysed of the uncertain environment, CSR, an FRS, an FSS and a VSS on the CLSC network. Decision makers need to balance three objectives to manage CLSC and use these strategies appropriately to address the negative impact of an uncertain environment.

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.

A Multiscale Approach for Free-Float Bike-Sharing Electronic Fence Location Planning: A Case Study of Shenzhen City

As an emerging technological means for managing free-float bike-sharing parking, electronic fences have attracted increasing attention in major cities as a solution to the challenges posed by disorderly parking of free-float bikes. Existing research has predominantly focused on employing clustering methods from the perspectives of free-float bike-sharing companies and users to plan and deploy electronic fences. However, the results often deviate significantly from the actual phenomenon. Therefore, scientific location selection is particularly important to fully harness the effectiveness of electronic fences. This paper proposes a multiscale clustering method based on free-float bike-sharing parking features to determine the optimal locations for electronic fences. A multiobjective mixed-integer programming model is established to address the location planning problem of electronic fences, determining the planning positions, quantities, and areas of electronic fences. A case study is conducted using a local area free-float bike-sharing dataset from Shenzhen city to validate the effectiveness of the proposed method. Comparative results with traditional approaches solely relying on K-means or DBSCAN methods demonstrate that the proposed approach achieves efficient location selection, through multiscale fusion site selection in the study area of 1.5∗1 km, and only 25 electronic fences need to be planned and deployed, covering a total area of 1691.88 square meters, which can provide rational placement solutions and better utilize the effectiveness of electronic fences. This method can thus offer decision-making support for the planning and location selection of electronic fences in free-float bike-sharing systems.

A General Framework for Providing Interval Representations of Pareto Optimal Outcomes for Large-Scale Bi- and Tri-Criteria MIP Problems

The Multi-Objective Mixed-Integer Programming (MOMIP) problem is one of the most challenging. To derive its Pareto optimal solutions one can use the well-known Chebyshev scalarization and Mixed-Integer Programming (MIP) solvers. However, for a large-scale instance of the MOMIP problem, its scalarization may not be solved to optimality, even by state-of-the-art optimization packages, within the time limit imposed on optimization. If a MIP solver cannot derive the optimal solution within the assumed time limit, it provides the optimality gap, which gauges the quality of the approximate solution. However, for the MOMIP case, no information is provided on the lower and upper bounds of the components of the Pareto optimal outcome. For the MOMIP problem with two and three objective functions, an algorithm is proposed to provide the so-called interval representation of the Pareto optimal outcome designated by the weighting vector when there is a time limit on solving the Chebyshev scalarization. Such interval representations can be used to navigate on the Pareto front. The results of several numerical experiments on selected large-scale instances of the multi-objective multidimensional 0–1 knapsack problem illustrate the proposed approach. The limitations and possible enhancements of the proposed method are also discussed.

Reliable scheduling and routing in robust multiple cross-docking networks design

This study introduces a novel framework called Reliable Pollution Scheduling and Routing with Multi-Cross-Docking. The core idea behind this framework is to optimize the processing and transportation of products through each vehicle, ensuring that each vehicle serves its specified destinations only once before returning to the cross-dock. The objective of this research is to develop a multi-objective mixed integer programming model that efficiently manages scheduling and routing complexities in a multi-cross-docking system, taking into account uncertainties in demand. The primary goals of the model are to minimize the overall costs associated with pollution, loading/unloading, and transportation, while simultaneously reducing distribution and shipping durations. Additionally, the model aims to maximize the reliability of the supply chain for perishable products, contributing to sustainable development in the supply chain domain. To address the inherent complexity of the model, especially in dealing with demand uncertainties, we employ a robust optimization method. The multi-objective challenge is tackled using an innovative hybrid approach that combines goal programming and genetic algorithms. The effectiveness of our proposed solution strategies is rigorously assessed using a variety of metrics and subjected to comprehensive statistical testing. Furthermore, we validate the competence of our methodology by conducting a real-world case study, which includes sensitivity analysis of demand parameters and robustness analysis. Our findings confirm that our solution technique produces high-quality solutions. Notably, our approach optimizes route planning for delivery and pick-up phases, resulting in a significant 36.5% reduction in transportation time and a noteworthy 17.27% decrease in the overall system costs compared to existing conditions. Additionally, we observe a substantial 23.15% reduction in vehicle arrival times at cross-docks, contributing significantly to reduced product expenses.

Two-stage electricity production scheduling with energy storage and dynamic emission modelling

With increasing environmental concerns and energy crisis, a variety of renewable energy sources (RES) are being increasingly utilised worldwide. However, the integration of RES such as wind power and photovoltaics in large-scale can lead to increased load fluctuations, which can undermine the overall environmental benefits and pose risks to the secure and stable operation of the power system. To mitigate this challenge, a two-stage electricity production scheduling is developed incorporating energy storage system (ESS) and dynamic emission modelling (DEM). In the first stage, a multi-objective mixed integer programming model schedules the production of RES, increasing penetration rate and system stability. In the second stage, a data-driven dynamic emission model is developed to optimise the load allocation of thermal power unit to reduce the carbon emissions. Furthermore, a flexible operating reserve strategy is proposed to handle the uncertainty resulting from the intermittent character of RES. Experimental results demonstrate that the proposed method effectively schedules the production of RES thereby alleviating the contradiction between high RES utilisation and stable system operation. Compared to the benchmark model, the proposed method can reduce the carbon emissions and total cost of the system by 20.34% and 10.65%, respectively.

Optimisation of multi-level logistics network for agricultural products under community group buying model

This paper introduces a rapidly developing new online retail model, community group buying, and proposes a three-level agricultural logistics network optimisation model. Under the community group buysing model, it is necessary to use different types of vehicles for transportation of agricultural products with different temperature control requirements. The study establishes a multi-objective mixed integer programming model with the objectives of shortest transportation time and minimum total cost, taking into account the freshness penalty cost incurred during transport. The multi-objective problem is transformed into a single objective by normalisation and weighting methods. According to the calculation for the actual case, this paper solves the problems of community group buying grid warehouse location, multiple vehicles use strategy, loading capacity, transportation path optimisation and self-pickup station demand allocation. In addition, through sensitivity analysis, the management insights of community group buying enterprises are obtained: (1) The community group buying enterprises should use brokers of the community group buying model to enhance customer stickiness; (2) The enterprises should focus on developing business in less developed regions; (3) The enterprises need to adjust the proportion of time efficiency and logistics costs according to the real situation.

A Scenario-based Interval Multi-objective Mixed-integer Programming Model for a Water Supply Problem: An Integrated AHP Technique

A Scenario-based Interval Multi-objective Mixed-integer Programming Model for a Water Supply Problem: An Integrated AHP Technique

A humanitarian vehicle routing problem synchronized with drones in time-varying weather conditions

This paper applies the cooperative delivery mode of trucks synchronized with drones to humanitarian logistics (HVRP-SD), considers the impact of time-varying weather conditions on the synchronous delivery from two dimensions (HVRP-SD-TVW): drone safety and drone delivery efficiency, and investigate a multi-objective optimization problem. This issue concerns not only the delivery timeliness of relief supplies, but also the fairness of supplies allocation. First, we establish a basic multi-objective mixed integer programming model for HVRP-SD, and then establish an extended mathematical model for HVRP-SD-TVW. To solve the multi-objective optimization problem, we develop a hybrid multi-objective evolutionary algorithm (HMOEA). According to the characteristics of HVRP-SD-TVW, HMOEA designs a variable-length two-dimensional array encoding method, fitness evaluation rules, multimodal mutation, and specialized local search operators. A set of numerical experiments prove that HMOEAS is highly competitive, and both the multimodal mutation and local search have significant effects on improving the quality of solutions. Further, taking the emergency supplies distribution in flood-stricken areas of Gongyi City, China in 2021 as a sample case, we prove that weather conditions play an important role in the truck-drone synchronized delivery decision by comparing the results of the basic model and extended model. In addition, we respectively analyze the variation in solutions under different weather scenarios, departure times, and drone risk resilience to guide decision-making.

Multi-objective multi-fidelity optimisation for position-constrained human-robot collaborative disassembly planning

ABSTRACT Human-robot collaborative disassembly lines are widely used by remanufacturing companies to disassemble end-of-life (EOL) products. When disassembling large-sized EOL products, each workstation on a disassembly line is generally divided into multiple operating positions, so that different operators can disassemble the same product at their respective positions at the same time, thereby greatly improving efficiency. This paper focuses on a position-constrained human-robot collaborative disassembly planning (PC-HRCDP) problem for the above-mentioned lines, including three subproblems of disassembly sequence planning, disassembly line balancing and robot path planning. A multi-objective mixed integer programming model for PC-HRCDP is developed to solve small-scale instances. Furthermore, a multi-objective multi-fidelity optimisation (MO-MFO) algorithm is proposed to solve large-scale instances. Comprehensive experiments are conducted based on 10 problem instances generated in this study. Experimental results show that the proposed MO-MFO is better than a high-fidelity optimisation algorithm in terms of running time. In addition, benefiting from the strategy of MO-MFO to allocate the limited high-fidelity computational budget to solutions in the two stages of multi-objective optimisation and optimal sampling, MO-MFO is significantly better than the existing representative multi-fidelity optimisation algorithms in terms of the hyper-volume and the inverted generational distance.

Multi-objective green scheduling of integrated flexible job shop and automated guided vehicles

The traditional flexible job shop scheduling problem (FJSP) ignores transportation issues or merely introduces a time lag for transportation tasks while assuming an infinite number of transportation resources. With the development of intelligent manufacturing, automated guided vehicles (AGVs), which are the key transportation equipment for manufacturing enterprises, have been widely used for their high flexibility and stability. In addition, the increase in energy consumption and the trend of green manufacturing make it critical to take into account energy-related objectives in the decision-making of scheduling. Therefore, the multi-objective green scheduling problem of integrated flexible job shop and AGVs (MOGSP-IFJS&AGVs) is addressed in this paper. To solve this problem effectively, the multi-objective mixed-integer programming (MMIP) model is formulated to minimize total energy consumption and makespan simultaneously. An efficient heuristic algorithm (EHA) is designed to solve the MMIP model. In the EHA, one solution encoding scheme and corresponding greedy insertion decoding method considering the selection of AGVs are presented. To acquire a high-quality initial population, the population initialization method balancing the processing time and energy consumption is designed. Further, a local search strategy is presented to enhance the quality of solutions and accelerate the convergence speed of the EHA. Experiment results of 45 test instances indicate that the EHA can obtain better solutions than that of comparison algorithms, which confirms the effectiveness of the EHA for solving the MOGSP-IFJS&AGVs.

Bi-Objective Integrated Scheduling of Quay Cranes and Automated Guided Vehicles

Operational efficiency is one of the key performance indicators of a port’s service level. In the process of making scheduling plans for container terminals, different types of equipment are usually scheduled separately. The interaction between quay cranes (QCs) and automated guided vehicles (AGVs) is neglected, which results in low operational efficiency. This research explores the integrated scheduling problem of QCs and AGVs. Firstly, a multi-objective mixed integer programming model (MOMIP) is conducted, with the aim of minimizing the makespan of vessels and the unladen time of AGVs. Then, embedded with a new heuristic method, the non-dominated sorting genetic algorithm-II (NSGA-II) is designed for the scheduling problem. The heuristic method includes two parts: a bay-based QC allocation strategy and a container-based QC-AGV scheduling strategy. Finally, in order to test the performance of the proposed algorithm, differently sized benchmark tests are performed, and the results are compared to the multi-objective particle swarm optimization algorithm (MOPSO) and the weighted-sum method. The computational results indicate that the proposed algorithm can effectively solve the multi-objective integrated scheduling problem of QCs and AGVs. For large-scale problems, the NSGA-II algorithm has better performance and more obvious advantages compared to others. The proposed method has the capability of providing a theoretical reference for the QC and AGV scheduling of container terminals.

Designing a vaccine supply chain network considering environmental aspects

In the fight against SARS-COV-2, the vaccine has become a ubiquitous preventive measure. Vaccination programs for COVID-19 are inadvertently creating large amounts of bio-medical and plastic waste, negatively impacting the environment. This perspective takes a critical stance regarding the waste generated by vaccines and the subsequent knock-on effects. Vaccine production and storage have contributed to global warming due to their environmental impacts. The vaccine supply chain (VSC), essential in global health due to its high relevance to humans, must be optimally designed and implemented to ensure high service levels at minimal cost and environmental concerns. This investigation aims to demonstrate a pattern of the green vaccine supply chain network (GVSCN) when the coronavirus was circulating. The presented model can illustrate a balance between environmental protection and economic growth during the epidemic. This model is sensitive to the economic and environmental impact structures. The cost includes the standard and hygiene costs. This study provides a multi-objective mixed-integer programming (MOMIP) problem. The multi-objective gray wolf optimizer (MOGWO) algorithm is utilized to address the developed model. The novelty and our contributions to the investigation on this topic are i) Suggesting a green vaccine supply chain network application model to demonstrate useful the trade-offs between two green supply chain aspects, ii) Designing the hygienic and safe network for the vaccine supply chain, iii) Developing economic indicators in the pandemic conditions, iv) Analyzing the impacts of vaccine supply chain activities on economy and environment. An actual case in Iran is also studied to probe the effectiveness of the proposed model.

Fuzzy robust flexible programming with [formula omitted] measure for electric sustainable supply chain

Electricity as a source of energy, is one of the most essential part in our life. In recent time, it is noted that the temperature of earth increases in compare to the previous years. It is caused due to burning of the conventional energy sources such as gas, oil, and coal from thermal power plant and other sources, which brings about global warming. Bases on this fact, we propose a multi-objective mixed-integer programming model to design an electric sustainable supply chain network by considering resiliency and responsiveness. In order to formulate the environmental issues, a power-to-gas (P2G) technology is considered as an environment-friendly system. The presence of P2G can reduce the carbon level and it has some major advantages, i.e., it collects carbon dioxide (CO2) from thermal power plant and then converts CO2 to hydrogen (H2) with the help of water (H2O) and methane (CH4) gas. The drawbacks in addressing the uncertainty of the parameters are overcome by proposing a novel fuzzy robust flexible programming approach based on Me measure. Thereafter, a new approach namely, multi-choice conic goal programming with utility function is introduced to solve the proposed multi-objective model. Damodar Valley Corporation (DVC) in India is considered as a case study about electric network that envisages the sustainable issues of an electric supply chain. Finally, experimental results show that one bio-fuel plant, one photovoltaic plant, one air turbine plant, and two mixed-cycle power plants are build at the end of the scheduled period.

A class of nonlinear multi-objective mixed integer programming model for oil and gas portfolio and algorithm solution

This paper is concerned with the oil & gas assets portfolio. A multi-objective portfolio model of oil & gas assets is studied from two perspectives—scale and revenue. Considering the nonlinear and integer constraints in the model, a class of oil & gas assets portfolio model of nonlinear multi-objective mixed integer programming is established. The weight of the multi-objective is solved by the support vector machine model. A hybrid genetic algorithm, which uses the position displacement strategy of the particle swarm optimizer as a mutation operation, is applied to the optimization model. Finally, two examples are applied to verify the effectiveness of the model and algorithm.

Operating room scheduling by emphasising human factors and dynamic decision-making styles: a constraint programming method

ABSTRACT As the most crucial component of a hospital, the operating room (OR) is the primary source of revenue generation and expenditures. The hospital’s overall performance will be enhanced if this ward’s scheduling is accurate. This study investigates a multi-objective mixed-integer programming model for daily OR scheduling of inpatient surgeries. A major consideration is the setup time (e.g. cleaning, sterilising, and preparing the necessary OR equipment) for the OR when commencing additional surgeries in the same OR. The surgical staff’s performance, interaction quality, and compatibility level play a significant role in the surgery’s quality, success, and safety. As individuals’ decision-making styles vary depending on the situation, one of the objectives increases the compatibility of surgical team members by considering their primary and backup decision-making styles. Another objective is to maximise the efficiency of the surgical team. To this end, this paper employs the TOPSIS method to calculate each person’s efficiency level. The final objective is to minimise OR costs (including the opening and overtime cost of OR and wait time cost for each person). To address problem’s computational complexity, this paper develops a constraint programming (CP) method, and also a novel hybrid mixed-integer linear programming-CP method to solve the real-world instances.

Fuzzy multi-objective truck scheduling in multi-modal rail–road Physical Internet hubs

The Physical Internet (PI) is an innovative concept that has the potential to significantly improve the efficiency, cost-effectiveness, and sustainability of the global supply chain industry, particularly in cross-docking operations. This paper addresses the truck-scheduling problem in rail–road PI-Hubs, taking into account simultaneously both uncertainty and multi-objective decision-making, which has not been fully explored in the literature, particularly for PI-structures. Our proposed approach defines a Multi-Objective Mixed-Integer Programming model (FMO-MIP) that incorporates fuzzy chance-constrained programming and ϵ-constraint to minimize both the total delay and the sum of PI-containers traveled distances, while considering the uncertainty on truck arrival times. This work takes into account the particularities of the Physical Internet and presents a novel decision-making solution to generate a robust Pareto front that aligns with decision-makers’ attitudes towards risk (optimistic/pessimistic) while balancing trade-offs between conflicting objectives.

An integrated sustainable bio-fuel and bio-energy supply chain: A novel approach based on DEMATEL and fuzzy-random robust flexible programming with [formula omitted] measure

The viability of the Indian government’s green initiative to blend 20% fuel grade ethanol with gasoline is investigated by modelling a sustainable integrated bio-fuel and bio-energy supply chain with multiple echelons in order to address the dual crisis of fossil fuels, i.e., environmental as well as gradually diminishing reserves. In order to find the best strategic and planning decisions, a multi-objective mixed integer programming model is developed that analyses the supply chain from a technological, economic, environmental, and social standpoints while handling various feedstocks, supply zones, products, and multiple periods. The drawbacks in addressing the uncertainty in the parameter as well as risk in decision making are overcome by introducing a novel fuzzy-random robust flexible programming approach based on Me measure and probabilistic programming. The presented model incorporates hybrid uncertainty, flexible constraints and a convex mixture of optimistic-pessimistic perspective of decision maker. A hybrid strategy combining the fuzzy Decision Making Trial and Evaluation Laboratory (DEMATEL) method and the multi-choice reference point goal programming with S-shaped utility function is presented to solve the generated multi-objective model. A case study in West Bengal, India is then performed that envisages the economic, environmental and social aspects of a bio-fuel and bio-energy supply chain.