Mixed Integer Nonlinear Programming Research Articles

A Modified Simulated Annealing and Enhanced Harmony Search Algorithms for the Continuous Facility Layout Problem (CFLP)

This paper focuses on solving the Continuous Facility Layout Problem (CFLP), which aims to minimize material handling costs by strategically placing facilities in a known or unknown area. The objective is to find optimal or near-optimal facility arrangements while adhering to non-overlapping and spatial constraints, thus enhancing the efficiency of production systems. The study addresses various layout scenarios, including single-row facility layout (with and without clearance), continuous layout, and unequal-area facility layout problems. To achieve this, the authors propose a mixed-integer nonlinear programming (MINLP) model tailored for continuous layouts. Two meta-heuristic algorithms are developed to optimize this model: a hybrid Simulated Annealing-Genetic Algorithm (SA-GA), which leverages genetic crossover operations, and an Enhanced Harmony Search Algorithm (EHSA), featuring dynamic parameters and a novel improvisation technique. The proposed methods provide flexible and efficient solutions for both small and large-scale layout problems, offering decision-makers practical tools for real-world applications.

A systematic methodology for selecting optimal technology for waste heat utilization in food processing industry

Utilizing waste heat that is rejected from thermal processes can greatly enhance the industry's energy balance. Identifying potential waste heat sources in the food and beverage processing industry and making estimations for their possible utilization can be an extremely challenging undertaking. To determine waste heat potentials in the food processing industry and to select an optimal technology for its utilization a novel systematic methodology based on the comprehensive energy audit and mathematical optimization has been developed. The developed mixed integer nonlinear programming model incorporates all novel and the most commonly employed technologies to utilize waste heat.The developed systematic methodology is tested on a case study, of a milk and dairy production facility. Obtained results have shown that up to 53 % of the available waste heat can be used in the scenario of limited investment costs. Otherwise, in the scenario when investment costs are not set as a limitation, 75 % of waste heat can be used, according to plant demands. Harmonising production processes is necessary to use all the waste heat. The developed systematic methodology can be applied to any food processing industry and other facilities producing waste heat because it presents a universal approach.

Optimum Planning of Carbon Capture and Storage Network Using Goal Programming

Carbon capture and storage (CCS) is a critical technology used for mitigating climate change by capturing carbon dioxide emissions from industrial sources and storing them underground to prevent their release into the atmosphere. Despite its potential, optimizing CCS systems for cost-effectiveness and efficiency improvement remains a significant challenge. In this paper, the optimization of CCS systems through the development and application of two mathematical optimization techniques is introduced. The first technique is based on using a superstructure optimization model, while the second technique relies on applying a goal programming optimization model. These models were solved using LINGO software version API 14.0.5099.166 to enhance the efficiency and cost-effectiveness of CCS systems. The first model, seeking to maximize the exchange of CO2 flowrate from sources to sinks, achieved a CO2 capture rate of 93.36% with an annual total cost of USD 1.175 billion. The second model introduced a novel mixed-integer non-linear programming (MINLP) approach for multi-objective optimization, targeting the minimization of total system cost, alternative storage, and unutilized storage while maximizing CO2 load exchange. The application of the second model, when prioritized to maximize CO2 flowrate exchange using the goal programming technique, resulted in a cost reduction of 36.46% and a CO2 capture rate of 75.87%. In contrast, when the second model prioritized minimizing the total annual cost, a 48% cost reduction was achieved, and the CO2 capture rate was decreased by 68.37%. A comparison of the two models’ results is presented. The results showed that the second model, with the priority of maximizing CO2 capture, provides the best economic–environmental objective balance, which offers notable cost reductions while keeping an efficient CO2 capture rate. This study highlights the potential of advanced mathematical modeling in increasing the feasibility of CCS as one of the very important strategies of mitigating climate change and reducing global warming.

Age and energy aware data collection scheme for urban flood monitoring in uav-assisted Wireless Sensor Networks

Wireless Sensor Networks (WSNs) have become pivotal in numerous applications, including environmental monitoring, precision agriculture, and disaster response. In the context of urban flood monitoring, utilizing unmanned aerial vehicles (UAVs) presents unique challenges due to the dynamic and unpredictable nature of the environment. The primary challenges involve designing strategies that maximize data collection while minimizing the Age of Information (AoI) to ensure timely and accurate decision-making. Efficient data collection is crucial to capturing all relevant information and providing a comprehensive understanding of flood dynamics. Simultaneously, reducing AoI is essential, as outdated data can lead to delayed or incorrect responses, potentially worsening the situation. Addressing these challenges is critical for the effective use of WSNs in urban flood monitoring. Initially, we formulate the problem as a mixed integer non-linear programming (MINLP) problem. Further, it is solved using a Lagrangian-based branch and bound technique by converting it into an unconstrained problem. Then, for large-scale WSN, we propose a hybrid optimization technique which combines a genetic algorithm with a particle swarm optimization technique to simultaneously maximize the data collection and reduce the AoI of the collected data with the constraint of energy consumption of the UAVs. Simulation results demonstrate that our proposed algorithm outperforms existing approaches in terms of both data collection and AoI.

Bus scheduling with heterogeneous Fleets: Formulation and hybrid metaheuristic algorithms

This paper focuses on optimizing mixed-fleet bus scheduling (MFBS) with vehicles of different sizes in public transport systems. We develop a novel mixed-integer nonlinear programming (MINLP) model to address the MFBS problem by optimizing vehicle assignment and dispatching programs. The model considers user costs, operator costs, and the crowding inconvenience of standing and sitting passengers. To tackle the complexity of the MFBS problem, we employ Genetic Algorithm (GA) and Grey Wolf Optimizer (GWO). Besides, we develop two hybrid metaheuristics, including GA-SA [a combination of GA and Simulated Annealing (SA)] and GWO-SA (a combination of GWO and SA), to improve optimization capabilities for the MFBS problem. We also employ a Taguchi approach to fine-tune the metaheuristics’ parameters. We widely examine and compare the metaheuristics’ performance across various-sized samples (small, medium, and large), considering solution quality, computational time, and the result stability of each algorithm. We also compare the metaheuristics’ solutions with the optimal solutions acquired by GAMS software in small and medium-scale samples. Our findings show that the GWO-SA outperforms the other metaheuristics. Applying our model to a real bus corridor in Santiago, Chile, we find that precise dispatching plans generated by more sophisticated/advanced algorithms (GA-SA and GWO-SA) lead to larger cost savings and improved performance compared to simpler algorithms (GA and GWO). Interestingly, utilizing more advanced algorithms makes a difference in terms of fleet planning in crowded scenarios, whereas for low and medium-demand cases, simpler dispatching algorithms could be used without a drop in accuracy.

A Generalized Benders Decomposition for Mixed-Integer Nonlinear Programming: Theory and Applications

A Generalized Benders Decomposition for Mixed-Integer Nonlinear Programming: Theory and Applications

How the establishment of carbon emission trading system affects ship emission reduction strategies designed for sulfur emission control area

As the backbone of the international seaborne trade, the pollution and emission from shipping are highly concerned by governments and international organizations as well. The International Maritime Organization has designated five emission control areas (ECAs) to limit sulfur oxides emissions of ships. Meanwhile, the European Union has included the shipping industry in the EU Emission Trading System since 2024 to control their carbon emissions. The strategies like switching fuel, installing scrubber or detour, are commonly used to comply with the ECA regulation, but they may increase carbon emissions and possibly incur extra carbon trading cost. In this case, the shipping company should investigate the influence of marine emission trading system (METS) on emission reduction strategies used under ECA regulation. Therefore, this paper focuses on this problem and formulates it as a mixed-integer nonlinear programming model. Several numerical experiments are conducted to show the applicability of the proposed model. The results show that ship’s detour behavior is inevitable under the ECA regulation, which incurs more carbon emissions. When METS regulation is not considered, the optimal emission reduction strategy is installing scrubber. In contrast, when METS regulation is considered, the optimal choice may be installing scrubber or fuel switching depending on different sailing route, which indicates the effect of METS on ship emission reduction strategy. Moreover, the fleet deployment and sailing speed of scrubber installation strategy are affected by METS regulation, while the strategies of fuel switching and using LNG-powered ship are almost unaffected. This indicates that installing scrubber is more easily affected by emission control policies.

Covariate balancing for high-dimensional samples in controlled experiments

In controlled experiments, achieving covariate balancing across all groups is crucial as it ensures that the estimated treatment effects are not confounded by the effects of covariates. This study proposes a mixed-integer nonlinear programming model to address the covariate balancing problem. Specifically, we introduce a new covariate imbalance measure, which is the maximum discrepancy in both the first and second central moments between any two groups. The second central moment can effectively capture the correlation of covariates in a physical sense, which is crucial for partitioning high-dimensional samples. A mixed-integer nonlinear programming model is constructed to minimize the proposed measure to obtain the optimal partitioning results. The nonlinear model is then linearized to accelerate the optimization process. We conduct computational experiments based on simulated datasets, including one-dimensional, two-dimensional, and three-dimensional Gaussian distributed samples, and a real clinic trial dataset. Compared to the conventional discrepancy-based method, our method achieves a 54.81% and a 40.6% reduction in the maximum discrepancy of partitioning results in the two-dimensional simulated Gaussian samples and the real clinic trial dataset, respectively. These results demonstrate the superiority of the proposed model in partitioning high-dimensional samples with correlated covariates compared with the conventional discrepancy-based method.

Enhancing the Reliability of Weak-Grid-Tied Residential Communities Using Risk-Based Home Energy Management Systems under Market Price Uncertainty

This paper evaluates the reliability of smart home energy management systems (SHEMSs) in a residential community with an unreliable power grid and power shortages. Unlike the previous works, which mainly focused on cost analysis, this research assesses the reliability of SHEMSs for different backup power sources, including photovoltaic systems (PVs), battery storage systems (BSSs), electric vehicles (EVs), and diesel generators (DGs). The impact of these changes on the daily cost and the balance of energy source contribution in providing electrical energy to household loads, particularly during power outage hours, is also evaluated. To address the uncertainty of electricity market prices, a risk management approach based on conditional value at risk is applied. Additionally, the study highlights the impact of community size on energy costs and reliability. The proposed model is formulated as a mixed-integer nonlinear programming problem and is solved using GAMS. The effectiveness of the proposed risk-based optimization approach is demonstrated through comprehensive cost and reliability analysis. The results reveal that when electric vehicles are used as backup power sources, the energy index of reliability (EIR) is not affected by market price variations and shows significant improvement, reaching approximately 99.9% across all scenarios.

Optimal management in island microgrids using D-FACTS devices with large-scale two-population algorithm

Amidst the increasing complexity of microgrid optimization, characterized by numerous decision variables and intricate non-linear relationships, there is a pressing need for highly efficient algorithms. This study introduces a tailored Mixed Integer Nonlinear Programming (MINLP) model that optimizes the charging and discharging schedules of electric vehicles (EVs) and energy storage systems (ESS) while incorporating Distributed Flexible AC Transmission System (D-FACTS) devices. To address these challenges, a novel approach based on the Large-Scale Two-Population Algorithm (LSTPA) is proposed. The model's effectiveness was evaluated using a 33-node microgrid, where the proposed method achieved a total purchased energy of 1.2 MWh, a voltage deviation of 0.0357 p.u, and a CPU time of 551 s, outperforming traditional methods like NSGA-II, PSO, and JAYA. Additionally, in a 69-node microgrid, the approach resulted in a total purchased energy of 0.3 MWh and a voltage deviation of 0.0078 p.u. These results demonstrate the superior performance of the proposed method in terms of energy efficiency, voltage stability, and computational time, advancing the efficiency of microgrid management.

Data-driven collaborative healthcare resource allocation in pandemics

Severe shortages of healthcare resources are major challenges in pandemics, especially in their early stages. To improve emergency management efficiency, this paper proposes a novel rolling predict-then-optimize framework that includes three interactive modules, i.e., data-driven demand prediction, healthcare resource allocation, and parameter rolling update. Such a framework uses historical data to dynamically update the control parameters of the proposed Net-SEIHRD model, which predicts the healthcare needs of each region by jointly considering government interventions and cross-regional travel behaviors. Based on the forecasted healthcare resource demand in real-time, an optimization model is then formulated to realize coordinated resource allocation across multiple regions by minimizing the total generalized cost. To facilitate model solving, the proposed mixed integer nonlinear programming model is converted into an equivalent mixed integer linear model by using some linearization techniques. Finally, the proposed method is applied to the SARS-CoV-2 emergency response and collaborative allocation of healthcare resources in Shanghai, China. The results show that the proposed prediction model can effectively predict the peak and scale of the spread of the virus. Compared with the traditional LM and SEIHR models, the prediction accuracy of the Net-SEIHRD model is improved by 10.76% and 24.11%, respectively. Moreover, coordinated relief activities across regions, such as patient transfer and drug-sharing can improve the efficiency of pandemic control and save social costs.

Adaptive Privacy-Preserving Coded Computing with Hierarchical Task Partitioning.

Coded computing is recognized as a promising solution to address the privacy leakage problem and the straggling effect in distributed computing. This technique leverages coding theory to recover computation tasks using results from a subset of workers. In this paper, we propose the adaptive privacy-preserving coded computing (APCC) strategy, designed to be applicable to various types of computation tasks, including polynomial and non-polynomial functions, and to adaptively provide accurate or approximated results. We prove the optimality of APCC in terms of encoding rate, defined as the ratio between the computation loads of tasks before and after encoding, based on the optimal recovery threshold of Lagrange Coded Computing. We demonstrate that APCC guarantees information-theoretical data privacy preservation. Mitigation of the straggling effect in APCC is achieved through hierarchical task partitioning and task cancellation, which further reduces computation delays by enabling straggling workers to return partial results of assigned tasks, compared to conventional coded computing strategies. The hierarchical task partitioning problems are formulated as mixed-integer nonlinear programming (MINLP) problems with the objective of minimizing task completion delay. We propose a low-complexity maximum value descent (MVD) algorithm to optimally solve these problems. The simulation results show that APCC can reduce the task completion delay by a range of 20.3% to 47.5% when compared to other state-of-the-art benchmarks.

Optimizing Supply Chain Design under Demand Uncertainty with Quantity Discount Policy

In typical business situations, sellers usually offer discount schemes to buyers to increase overall profitability. This study aims to design a supply chain network under uncertainty of demand by integrating an all-unit quantity discount policy. The objective is to maximize the profit of the entire supply chain. The proposed model is formulated as a mixed integer nonlinear programming model, which is subsequently linearized into a mixed integer linear programming model and hence able to obtain a global solution. Numerical examples in the manufacturing supply chain where customer demand follows normal distributions are used to assess the effect of quantity discount policies. Key findings demonstrate that the integration of quantity discount policies significantly reduces total supply chain costs and improves inventory management under demand uncertainty, and decision makers need to decide a balance level between service levels and profits.

Energy Efficiency Maximization for Multi-UAV-IRS-Assisted Marine Vehicle Systems

Mobile edge computing is envisioned as a prospective technology for supporting time-sensitive and computation-intensive applications in marine vehicle systems. However, the offloading performance is highly impacted by the poor wireless channel. Recently, an Unmanned Aerial Vehicle (UAV) equipped with an Intelligent Reflecting Surface (IRS), i.e., UIRS, has drawn attention due to its capability to control wireless signals so as to improve the data rate. In this paper, we consider a multi-UIRS-assisted marine vehicle system where UIRSs are deployed to assist in the computation offloading of Unmanned Surface Vehicles (USVs). To improve energy efficiency, the optimization problem of the association relationships, computation resources of USVs, multi-UIRS phase shifts, and multi-UIRS trajectories is formulated. To solve the mixed-integer nonlinear programming problem, we decompose it into two layers and propose an integrated convex optimization and deep reinforcement learning algorithm to attain the near-optimal solution. Specifically, the inner layer solves the discrete variables by using the convex optimization based on Dinkelbach and relaxation methods, and the outer layer optimizes the continuous variables based on the Multi-Agent Twin Delayed Deep Deterministic Policy Gradient (MATD3). The numerical results demonstrate that the proposed algorithm can effectively improve the energy efficiency of the multi-UIRS-assisted marine vehicle system in comparison with the benchmarks.

Day-ahead multi-criteria energy management of a smart home under different electrical rationing scenarios

With the recent global energy crisis, some countries have implemented electrical rationing (ER), making it necessary for smart homes to play a pivotal role in optimizing energy consumption and contributing to sustainable practices. To effectively manage smart home consumption, a stochastic programming approach for a grid-connected smart home energy management system (SHEMS) is proposed in this paper. The system includes PV, battery, diesel, and gas-based heating/cooling systems (HCS). Additionally, a demand response program (DRP) has been employed under time-of-use tariffs in the Syrian energy market. The main objective is to minimize the day-ahead expected cost and consumer discomfort by optimizing the operation of dispatchable units and loads. To manage the risks associated with the expected cost due to potential uncertainties in PV energy generation and electrical rationing programs, the conditional value-at-risk (CVaR) approach is adopted. Two methods are proposed to model the uncertainty in PV energy generation; interval bands and interval-based scenarios. The problem is modeled as a mixed-integer non-linear programming (MINLP) model, and coded in GAMS to test different cases. Based on the results obtained, substantial reductions reached 56.2% in worst-case cost scenarios when employing concurrent DRP-risk management.

Batch-sizing and machinability data systems for milling operations: An optimal sustainable cost of quality approach

Nowadays, manufacturers make every effort to achieve a higher quality of their products at an attractive cost. With all the introduced legislation and incentives in the developed world to address global warming, machining shops in the West also strive to cut greenhouse emissions. This article offers an optimal approach to the micro Computer-Aided Process Planning (CAPP) problem to optimize the internal quality cost and buffering effect while keeping the environmental impact low. To optimize the machining parameters, the mathematical model is developed for different milling operations, face, side, and peripheral. cutting speed, feed rate, axial depth of cut, radial depth of cut, nose radius, and batch sizing while maximizing profit and meeting customer demand. A Mixed-Integer Nonlinear Programming (MINLP) model is formulated and solved using Classical Constrained Nonlinear Optimization (CCNO) and Genetic Algorithms (GAs). Surface roughness, used as a metric to evaluate the desired quality level of a finished machined part type, is modeled as a Gaussian random variable to model the surface roughness of the machined part utilizing a cumulative normal distribution. The ratio of rework and scrap is calculated in terms of the surface roughness of the machined part shifting away from the target and exceeding upper and lower specification limits. The internal failure cost model, addressing both scrap and rework, is developed based on Taguchi’s quadratic loss function. CCNO is employed to validate the results obtained by GAs, relaxing the lot-sizing integrality constraint and, thus, the convexity of the produced relaxed model. An iterative method employing a developed multi-regression model is used to solve for the expended power consumption (an inherent highly nonlinear environmental criterion of the developed model) within both GAs and CCNO. This study reveals that the machining parameters substantially impact the cost components of the objective function as well as the scrap and rework quantities. A stringent quality cost target can force the model to optimize the feed rate and nose radius to minimize the internal failure quality cost while improving the environmental impact, including direct and indirect power consumption and CO2 emissions considerations.

Home energy management system for residential fuel cell-based combined heat and power system

The goal of this paper is to propose an optimization scheme for enhancing power dispatch and load scheduling for residential fuel cell-based combined heat and power systems (FC-CHPS) using mixed integer linear programming (MILP), considering the lifetime degradation of both the fuel cell system (FCS) and battery energy storage systems (BESS). The scheme is applied in the home energy management system that oversees the electric and thermal power of residential FC-CHPS. First, the nonlinearity in the relationship between the natural gas consumption and output electric power, and between the residual thermal power and output electric power of the fuel cell system (FCS) in the FC-CHPS is approximated using piecewise linearization. Then, the piecewise linearization is integrated with MILP to derive optimal power dispatch and load scheduling solutions, while accounting for the nonlinearity of the FCS. Next, cost functions representing the lifetime degradation of FCS and BESS are formulated. These cost functions result in nonlinear optimization constraints. Therefore, innovative methods are proposed to linearize these constraints, allowing the continued use of MILP as the optimization method and factoring in the lifetime degradation of FCS and BESS. Compared to the mixed-integer non-linear programming (MINLP) method that does not linearize the non-linearity in the FCS or the lifetime degradation of the FCS and BESS, the proposed MILP scheme achieves the identical objective function value. Furthermore, the computation time for the proposed MILP scheme is 99.94 % lower than that required by the MINLP method. The proposed scheme provides accurate results in short computation times.

An MINLP-based decision-making tool to help microbreweries improve energy efficiency and reduce carbon footprint through retrofits

Microbreweries have greater production costs per litre of beer compared to large breweries, as well as higher carbon footprints. Due to the range of different retrofit technologies available and the different capacities and configurations of microbreweries, it is not always clear what retrofits will improve operations. Therefore, this work proposes a novel mixed-integer nonlinear programming decision-making tool to be used by any microbrewery, that determines the technoeconomic feasibility and sizing of energy efficiency-improving retrofits, including solar and wind power, battery storage, anaerobic digestion, boiler type selection, heat integration by heat storage, and carbon capture via dual-function materials. The model was demonstrated on a real UK microbrewery case study. The model gave an optimal configuration of a 10 m3 anaerobic digester, 30 solar panels outputting 380 W each, an 800 W wind turbine and a 2.3 m3 heat storage tank, reducing annual operating costs by 62.9 % and carbon dioxide emissions by 77.1 % with a payback period of 8 years. The tool is designed to be flexible for use by any microbrewery in any location with any brewing recipe and allow the owner(s) to develop more profitable and sustainable microbreweries.Tweetable abstractMicrobreweries can implement mathematically optimised renewable energy, heat integration and anaerobic digestion to reduce operating costs by 62.9 % and carbon emissions by 77.1 %.

A quadratically constrained mixed-integer non-linear programming model for multiple sink distributions

Rising traffic congestion and fuel costs pose significant challenges for supply chains with numerous retailers. This paper addresses these challenges by optimizing transportation routes for processed tomatoes within a long-haul and intercity distribution network. We use the heterogeneous capacitated vehicle routing problem framework to create a new quadratically constrained mixed-integer non-linear programming model that aims to meet demand at multiple destinations while minimizing transportation costs. Our model incorporates real-time data and route optimization strategies that consider traffic conditions based on freight time and route diversions for expedited deliveries. It aims to devise an optimal transportation schedule that minimizes fuel, operational, and maintenance costs while ensuring efficient delivery of tomato paste. By applying this model to a real-world case study, we estimate a significant 27.59% reduction in transportation costs, dropping them from GH¢20,270 ($1,638.91) to GH¢14,676 ($1,186.61) on average. This highlights the effectiveness of our strategy in lowering costs while maintaining smooth and efficient deliveries.

ReLU surrogates in mixed-integer MPC for irrigation scheduling

Efficient water management in agriculture is important for mitigating the growing freshwater scarcity crisis. Mixed-integer Model Predictive Control (MPC) has emerged as an effective approach for addressing the complex scheduling problems in agricultural irrigation. However, the computational complexity of mixed-integer MPC still poses a significant challenge, particularly in large-scale applications. This study proposes an approach to enhance the computational efficiency of mixed-integer MPC-based irrigation schedulers by employing Rectified Linear Unit (ReLU) surrogate models to describe the soil moisture dynamics of the agricultural field. By leveraging the mixed-integer linear representation of the ReLU operator, the proposed approach transforms the mixed-integer MPC-based scheduler with a quadratic cost function into a mixed-integer quadratic program, which is the simplest class of mixed-integer nonlinear programming problems that can be efficiently solved using global optimization solvers. The effectiveness of this approach is demonstrated through comparative studies conducted on a large-scale agricultural field across two growing seasons, involving other machine learning surrogate models, specifically Long Short-Term Memory (LSTM) networks, and the triggered irrigation scheduling method. The ReLU-based approach significantly reduces solution times—by up to 99.5%—while achieving comparable performance to the LSTM approach in terms of water savings and Irrigation Water Use Efficiency (IWUE). Moreover, the ReLU-based approach achieves enhanced performance in terms of irrigation water savings and IWUE compared to the triggered approach.