Mixed Integer Linear Programming Research Articles

A novel integrated optimization method of micrositing and cable routing for offshore wind farms

In traditional wind farm planning, the design of wind turbine locations and cable layouts is usually undertaken sequentially. However, this approach may potentially result in suboptimal solutions. While the increased spacing between wind turbines enhances power output by reducing wake losses, it also imposes a negative impact by raising cable costs. Addressing this challenge, we propose a novel multi-objective optimization model that simultaneously considers the micrositing of wind turbines and cable routing. A joint framework of the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and the Mixed-Integer Linear Programming (MILP) is established to optimize the layout of wind turbine locations, points of connection, and cable paths. The results indicate that, compared to the traditional sequential optimization, our integrated optimization exhibits significant economic advantages since improved the balance between micro siting and cable routing. By strategically sacrificing a portion of power generation to reduce cable costs, the overall investment profitability can be remarkably improved, with a maximum gain equivalent to 10.02 % of the cable costs.

Energy optimization algorithms for multi-residential buildings: A model predictive control application

This study presents an optimization algorithm for Model Predictive Control (MPC) of the HVAC systems in multi-family residential buildings assessing the performance of four objective functions. Implemented in C++, using the free OR-Tools optimization library, the model is formulated a Mixed Integer-Linear Programming (MILP) problem. The study analyses the results of tests conducted on a 20-dwelling block in Switzerland across various weather and occupancy conditions, resulting in a parametric study of 64 cases.The models developed for the MPC are Grey-box type for the interconnected energy systems: the building, thermal storage tanks, a heat pump, the ventilation system and PV collectors, highlighting a radiant wall heating system integrated into the building facade. The tanks and the heat pump models were informed with manufacturer data, while for the building a R3C3 thermal-electrical equivalent model was developed, calibrated using TRNSYS simulations with a root mean square error of 1.7%.Findings demonstrate how the algorithm optimizes the operation according to the desired criteria, while ensuring indoor comfort with a 15-minute time resolution. The time execution of the majority of cases is under 3 min in a low-specs computer, affirming its practical viability for real-world implementation.

On a fair and risk‐averse urban air mobility resource allocation problem under demand and capacity uncertainties

AbstractUrban air mobility (UAM) is an emerging air transportation mode to alleviate the ground traffic burden and achieve zero direct aviation emissions. Due to the potential economic scaling effects, the UAM traffic flow is expected to increase dramatically once implemented, and its market can be substantially large. To be prepared for the era of UAM, we study the fair and risk‐averse urban air mobility resource allocation model (FairUAM) under passenger demand and airspace capacity uncertainties for fair, safe, and efficient aircraft operations. FairUAM is a two‐stage model, where the first stage is the aircraft resource allocation, and the second stage is to fairly and efficiently assign the ground and airspace delays to each aircraft provided the realization of random airspace capacities and passenger demand. We show that FairUAM is NP‐hard even when there is no delay assignment decision or no aircraft allocation decision. Thus, we recast FairUAM as a mixed‐integer linear program (MILP) and explore model properties and strengthen the model formulation by developing multiple families of valid inequalities. The stronger formulation allows us to develop a customized exact decomposition algorithm with both benders and L‐shaped cuts, which significantly outperforms the off‐the‐shelf solvers. Finally, we numerically demonstrate the effectiveness of the proposed method and draw managerial insights when applying FairUAM to a real‐world network.

Multi-objective optimal sizing and design of renewable and diesel-based autonomous microgrids with hydrogen storage considering economic, environmental, and social uncertainties

The multifaceted nature of human society necessitates the consideration of various indicators when planning and designing energy systems. The success of energy systems is contingent on their ability to reliably meet demands while satisfying different objectives that align with societal needs. This paper presents the multi-objective optimal design and configuration of hydrogen-storage-based microgrids to reliably meet electric load demands in remote regions while considering economic, environmental and social uncertainties. A comprehensive Mixed Integer Linear Programming (MILP) was adopted to model the microgrid consisting of renewable energy systems (RES), hydrogen energy storage system (HESS), battery energy storage system (BESS), and diesel generator (DG). Advanced Interactive Multidimensional Modelling System (AIMMS) was used to perform the deterministic and robust optimisation with special consideration on cost-greenhouse emissions minisation and employment generation maximisation. This study further performs a comparative analysis between hydrogen-based microgrids and lithium-ion battery-based microgrids in terms of the key objectives. In overall performance, the configuration consisting of photovoltaic (PV), wind turbine (WT), fuel cell (FC), electrolyser (EL) and low-pressure tank (LPT) outplays the other configurations considered in terms of total job factor, levelised cost of electricity, renewable energy penetration factor, carbon emission reduction capability. Considering both deterministic and robust solutions of the configuration, the levelised cost of electricity ranges between 0.131 and 0.169 $/kWh, the total lifetime cost varies from $2,002,100 to $6,784,740, and the job provision factor ranges between 0.339 and 0.447. Nevertheless, there is a need for further reduction of the investment cost for its continued technological and market penetration. This is a good basis for the adoption of hydrogen-based storage systems with renewable energy systems.

A multi-agent learning framework for mixed-integer linear programming

Mixed integer linear programming (MILP) is an important problem in the combinatorial optimization domain, which has wide applications in practical optimization scenarios. Given that most MILP problems fall into the NP-hard category, which the traditional methods may fail to solve, recent research has tried to derive MILP solutions using machine learning techniques. The whole MILP-solving procedure involves lots of modules, such as pre-solving, cut selection, node section, etc., and these modules are closely related and influence each other. However, the previous machine learning-based approaches neglect the connections between these modules, and focus on single-module learning techniques. To address this, we propose an initial step towards a more comprehensive multi-agent learning framework that allows different modules to interact and collaborate. Specifically, our current implementation involves two key modules: HEM for cut selection applied at the root node and GCNN for variable selection. By employing HEM to influence the training of GCNN, these two agents thus work in unison. Through extensive experiments on four MILP datasets in diverse scenarios, we observe significant improvements in solving time and PD integral metrics compared with the state-of-the-art learning-based MILP solving methods. This work lays the groundwork for future development of a fully integrated multi-agent framework.

Mixed-integer programming models for a multi-period integrated reverse logistics network with multiple recovery options and different quality levels of returns

This paper addresses an integrated reverse logistics (RL) model with a production route and multiple recovery options, including repair, refurbishing, remanufacturing, recycling, and selling spare components. We aim to use the quality grading system method to analyse returns comprehensively. In this regard, quality levels are used to classify returns and quality thresholds are utilised to categorise them into certain quality groups. The proposed model deals with different activities such as locating, purchasing, transporting, processing, inventory holding, recovering, and production in a planning horizon with multiple periods. A two-stage optimisation model is proposed to facilitate the decision-making process. In Stage 1, a mixed integer linear programming (MILP) model is proposed to minimise the costs and determine the number of returned products directed into different recovery routes. In Stage 2, another MILP is proposed to maximise the network’s profit. Furthermore, 350 scenarios are defined to examine the network’s performance and decide the optimal quality thresholds. Finally, the proposed models are applied to a real dataset and solved by the CPLEX solver through Pyhton. According to the results, scenarios that use multiple recovery options earn higher profits and lower costs as most demands are satisfied and the stock level of inventories decreases.

Integrated model to optimize supplier selection and investments for cyber resilience in digital supply chains

Digitalization has revolutionized the supply chain networks but also introduces vulnerabilities to the cyber threats. Notably, in past two years, the cyber-attacks on different organizations worldwide have increased at an alarming rate resulting in significant financial loss to supply chains, intellectual property breaches and supply disruptions. As a result, companies are making significant investments in their cybersecurity. However, many incidents were reported where threat actors attacked a company using the shared digital systems with its suppliers. Therefore, it is important that suppliers are selected based on their cyber resilience. This paper identifies the cyber resilience criteria and proposed a multi criteria decision making based framework to evaluate the cyber resilience of a supply chain partner. It has been also realized that investment in organizational cybersecurity alone is not sufficient to protect supply chains. Companies are now investing in increasing their supply chain cyber capabilities. In this direction, paper also proposes a mixed integer linear program (MILP) to jointly optimize supplier selection and cyber investment decisions in a supply chain based on the supplier's current cyber resilience and potential return on the cyber investments made in selected suppliers. Computational experiments are conducted to study the tradeoffs and impact of sourcing strategy, supplier capacity, cyber security investment decisions on supply chain cyber resilience. The findings underscore that an integrated decision making of supplier selection and cyber investments maximizes the supply chain cyber resilience.

Energy-efficient scheduling in an identical parallel machine environment with peak power consumption and deadline constraints

Energy-efficient scheduling is an essential means of achieving sustainability in manufacturing systems. This paper defines and addresses the problem of scheduling n jobs on m identical parallel machines in which peak power consumption and deadline constraints exist simultaneously. The objective is to maximize the total value of the selected jobs. We show that this problem is equivalent to a special case of the rectangular knapsack problem, based on which four properties are observed. To solve the problem, an effective mixed integer linear programming model is proposed based on the properties, and it is much more efficient compared to the performance of modeling methods inspired by other works. Furthermore, three effective decoding methods are proposed and embedded into genetic algorithms (GAs). Comparisons with the exact algorithm (i.e., the proposed model) show that our GAs can lead to good-quality solutions within one second for small instances. Meanwhile, experimental results for large instances indicate that the proposed GAs can obtain near-optimal or satisfactory solutions. Finally, results also show that the proposed GA-DD significantly outperforms the existing matheuristic algorithm.

Pharmaceutical capacity expansion under uncertainty: Framework and models

This work presents a methodology for capacity planning under uncertainty in general multi-stage manufacturing networks. Multiple manufacturing lines are available and the production time on each line must be divided between a set of materials. The methodology generates mixed-integer linear programming models that represent capacity expansions with economy of scale costs functions and production planning details. A deterministic model is solved to create a baseline and the impact of uncertainty is investigated by sensitivity analysis and stochastic programming. The applicability of the methodology is exemplified through two case studies derived from industrial pharmaceutical manufacturing. The methodology identifies bottlenecks that limit supply and, where required, activates, and assigns capacity expansion projects for satisfying demand subject to uncertainty. The methodology determines the best use of existing resources and the location and size of capacity expansions thereby generating a portfolio of recommendations for decision making on integrated planning of capacity and production.

A new approach for reliability modeling in green closed-loop supply chain design under post-pandemic conditions: A case study

Climate change, pandemics, and economic crises have created complex challenges for supply chains. Managing such situations requires the development of reliable decision-making frameworks. In this paper, a multi-level, multi-product, and multi-period closed-loop supply chain is studied with environmental considerations. A bi-objective mixed-integer linear programming model is presented for facility location, flow allocation, and transportation mode determination. The objectives of the model are to minimize the total cost and maximize the reliability of suppliers to meet the needs of factories. In the area of reliability engineering, a new approach is defined for modeling the probability of supplier availability considering catastrophic failures caused by pandemics, economic sanctions, and other failure modes. Furthermore, the decision-maker can handle the emission of greenhouse gases by an upper-bound constraint. In order to face the simultaneous uncertainty of demand and the maximum CO2 emission allowed, a scenario-based two-stage stochastic programming approach is proposed. The improved version of the augmented ε-constraint method, known as AUGMECON2, is used to solve the proposed model. The efficiency of the model and the proposed solution approach are investigated through a real-world case study of a battery manufacturing company in Iran.

Designing a resilient reverse network to manage the infectious healthcare waste under uncertainty: A stochastic optimization approach

The global expansion of healthcare facilities has resulted in increased levels of infectious-hazardous waste, posing serious threats to the environment and public health. Existing waste management systems can become overwhelmed during health crises, such as epidemics or natural disasters, exacerbating the problem. This study formulates a mixed-integer linear programming model for developing a resilient infectious waste management reverse network during the outbreak of the COVID-19 pandemic. Health crisis are unpredictable in nature and it is almost impossible to predict their exact behavior. Therefore, in this paper, the uncertainty of ambiguous parameters is considered using a scenario-oriented approach. To make the proposed model resilient, three strategies, including establishing new collection centers, overtime, and cooperation with third-party logistics, are introduced. The results derived from running the developed model in GAMS software using the case study data showed that the active collection center cannot serve the network alone, and to make the network more resilient, the strategy of establishing a new collection center should be selected. The findings validate the model’s utility in designing a resilient waste management network during a health crisis, emphasizing the importance of resilience in infectious healthcare waste management networks.

An integrated price- and incentive-based demand response program for smart residential buildings: A robust multi-objective model

Residential buildings consume a significant amount of energy, emphasizing the importance of optimizing energy usage. Demand-side management (DSM) helps consumers and producers manage energy consumption through incentives and pricing. This study develops a new mathematical model to manage DSM in smart residential buildings. Extant literature commonly considers only a single objective function, ignores uncertainties, and applies only one price- or incentive-based program to load management in smart residential buildings. This study develops a multi-objective mixed-integer linear programming (MILP) model that applies both price- and incentive-based programs and considers uncertainties. The objectives are cost reduction, peak load minimization, user comfort improvement, and load factor maximization. This model can manage optimal schedules for household appliances and power exchange within buildings. The study shows that participating in the incentive-based program in a four-household residential complex yielded a 2 % decrease in electricity costs and a 1 % reduction in peak load while upholding comfort and load factor levels compared to non-participation. When extended to an eight-household complex, potential benefits include an 8.3 % decrease in electricity cost and a 2.6 % reduction in peak load, highlighting the program’s effectiveness in residential energy management strategies.

Mixed-integer linear programming solver using Benders decomposition assisted by a neutral-atom quantum processor

Mixed-integer linear programming solver using Benders decomposition assisted by a neutral-atom quantum processor

Decentralised protocols for autonomous mobile robots in material handling: inductive learnings from centralised controller

As customer demands for personalised items continue to grow, flexible material handling systems are becoming indispensable in manufacturing to accommodate the increasing product variety and demand fluctuations. Consequently, the adoption of autonomous mobile robots (AMRs) is on the rise, driven by their capability to autonomously respond to changes in demand. However, the myopic nature of AMRs’ autonomous decision-making may limit their ability to consider a system-wide perspective. To address this challenge, we propose an AI-based platform that extracts knowledge from a centralised agent, which makes system-wide decisions offline, and integrates this knowledge into decentralised AMRs operating online. We develop a mixed-integer linear programming model, a genetic algorithm, and a scheduling algorithm to generate centralised solutions. Additionally, we design features to convert these solutions into training instances and employ artificial neural networks to derive knowledge from them. This knowledge is then integrated into each AMR as a protocol. Through experiments, we evaluate the performance of the developed protocol, demonstrating its superiority over other dispatching rules in minimising the total weighted tardiness of transportation requests and the total waiting time of transportation requests at storages.

Multi-objective models for crop rotation planning problems

CONTEXTAgriculture is a vital component of the global economy and modern societies. It has undergone significant consolidation and transformation in response to the food supply crisis, highlighting the important relationship between humans and the environment. However, concerns remain about food security, particularly with the projected population growth of over 9.5 billion by 2050. The computerization of agri-food supply chains has emerged as a significant response to these challenges. OBJECTIVE(1) Develop a multi-objective model that explores both net return and crop diversity. (2) Solve the problem using techniques that guarantee optimality. (3) Evaluate the gain in crop diversity versus the net return of the optimized configuration. METHODSThe study presents four Multi-objective Mixed-Integer Linear Programming models with integer and binary decision variables for Crop Rotation Planning Problems. The objectives are to maximize net income and increase crop diversity and land utilization. RESULTS AND CONCLUSIONSThe study exclusively employs linear programming techniques to solve the models resulting in an optimal solution. A comparative analysis with existing models in the literature, which primarily focused on maximizing net income, yielded a noteworthy result. The proposed models demonstrate an average increase of 60% in crop diversity, with net return losses of less than 5%. SIGNIFICANCEIn conclusion, this research provides valuable information for crop rotation planning and highlights the importance of agricultural farm management and precision agriculture in addressing current challenges. The innovative nature of this research is exemplified by the use of mixed-integer linear programming techniques to solve a multi-objective problem with integer and binary variables. The obtained results demonstrate increased crop diversity and minimal economic losses, which have significant implications for several areas of agricultural science, policy, and practice.

A three-level robust scenario-based model for resilience-oriented placement of remote-controlled switches in distribution networks

This paper introduces an innovative strategy to improve the resilience of Distribution Networks (DN) following natural disasters. The approach involves a multi-stage model for the strategic placement of Remote-Controlled Switches (RCS) to expedite fault isolation and service restoration. The model integrates various resilience enhancement techniques, such as network reconfiguration and microgrid formation, throughout the pre-disaster, disaster progression, and post-disaster phases. To mitigate uncertainties related to line failures and ensure planning robustness, a novel three-level Robust Scenario-based Model (RSM) is introduced. The RSM optimizes the strategic RCS placement to enhance System Performance Criteria (SPC) in response to anticipated line failure scenarios, considering individual line vulnerabilities and disaster severity. Subsequently, the model identifies the most critical failures from each predicted scenario based on RCS placements and then recalibrates the placements to enhance DN resilience against both anticipated and critical failures. The RSM is formulated as a mixed-integer linear programming problem to maximize SPC by allocating resources optimally to serve maximum weighted loads while adhering to structural and operational constraints. The effectiveness and validity of the proposed model are demonstrated through case studies conducted on a modified IEEE 33-bus test system and a modified real DN.

The United Kingdom electricity market mechanism: A tool for a battery energy storage system optimal dispatching

In this paper, the role of a Battery Energy Storage System (BESS) in the United Kingdom (UK) electricity market is investigated. Such device is selected since research works related to the topic demonstrate that BESSs help facing challenges caused by renewable energy sources increasing penetration in the power systems’ field. Indeed, in the next future, BESSs will assume a relevant role thanks to their fast response time. In the present paper, an optimization model is implemented to encode the UK market rules and output the optimal set of offers on day-ahead and intraday markets, dynamic frequency response services and imbalance settlement. The market rules are formalised in a mathematical model considering market temporal sequencing and BESS technical limitations. The tool also models the state of energy management, necessary since BESSs are energy limited assets. Objective function and constraints are linearized to define a Mixed Integer Linear Programming problem to reduce the computational burden and to integrate the model in the Energy Management System previously developed at University of Genoa. Specific tests are performed including and excluding ancillary services to evaluate the related advantages. The obtained outcomes reveal that ancillary services are the most convenient options within all the implemented scenarios.

Efficient Operation Algorithm of UAVs for Tourist Safety: Case of the Hallasan Mountain Trail in Jeju Island

Tourist safety is one of the most important factors for tourists when choosing a tourism destination. Jeju Island’s Hallasan Mountain Trail is a trail that connects the mid-slope of Hallasan, the main mountain on Jeju volcanic island, and boasts very beautiful scenery. However, tourist safety has become an issue as accidents continue to occur every year. In this study, an efficient operation algorithm that can minimize the total cost with a mixed-integer linear programming (MILP) model is developed, considering the introduction of a UAV patrol system on the Hallasan Mountain Trail, which is difficult to access by vehicles. The application of different speeds for patrol and nonpatrol routes, the selection of candidate sites for UAV stations with easy vehicle access, and the sensitivity analysis of patrol speed and maximum operation time considering the performance improvement of UAVs are the contributions of this study. The results show that stations are installed as close as possible to the trail courses and that lower-performance UAVs are utilized that can patrol the trail courses at a given time. The sensitivity analysis also confirmed that the total cost can be minimized by reducing the number of stations and UAVs or replacing higher-performance UAVs with lower-performance UAVs.

A hybrid quantum–classical algorithm for mixed-integer optimization in power systems

Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks for power system applications. The main issue of these formulations is the computational complexity of the solution algorithms, as they are considered NP-Hard problems. Quantum computing has been tested as a potential solution towards reducing the computational burden imposed by these problems, providing promising results, motivating the can be used to speedup the solution of MILPs. In this work, we present a general framework for solving power system optimization problems with a Quantum Computer (QC), which leverages mathematical tools and QCs’ sampling ability to provide accelerated solutions. Our guiding applications are the optimal transmission switching and the verification of neural networks trained to solve a DC Optimal Power Flow. Specifically, using an accelerated version of Benders Decomposition , we split a given MILP into an Integer Master Problem and a linear Subproblem and solve it through a hybrid “quantum–classical” approach, getting the best of both worlds. We provide 2 use cases, and benchmark the developed framework against other classical and hybrid methodologies, to demonstrate the opportunities and challenges of hybrid quantum–classical algorithms for power system mixed integer optimization problems.

An MILP model based on a processing strategy of complex multisource constraints for the short-term peak shaving operation of large-scale cascaded hydropower plants

Hydropower with flexible regulation plays an important role in short-term peak shaving operations. However, short-term peak shaving operation is a challenging problem due to the large scale, the nonconvex and nonlinear characteristics, and the complex multisource tasks. This study proposes a mixed integer linear programming (MILP) model, termed MILPoPSC, based on a processing strategy for complex multisource constraints, tailored for short-term peak shaving in large-scale cascaded hydropower plants. The MILP model, designed to incorporate multisource tasks by abstracting them into constraints, ensures that task requirements are met. A novel multisource constraint transformation method is introduced to derive constraint expressions related to power flow, facilitating the unification of constrained variables. Additionally, a classification and integration method based on restriction mode and set theory is proposed to improve solving efficiency by integrating constrains of the same type. The proposed method was applied to 7 hydropower cascade plants in the Wujiang River. The results showed that the linearization method and the processing strategy of complex multisource constraints can successfully reduce the complexity of the MILP model without affecting the solution quality. This indicates that MILPoPSC has good practical value for the short-term peak shaving operation of large-scale cascaded hydropower plants in China.