Mixed-integer Programming Approach Research Articles

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.

Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning Model

In many industries, companies receive customer orders that include multiple products. To simplify the use of optimization models for planning purposes, these orders are broken down, and the quantities of each product are grouped with the same products from other orders to be completed in the same period. Consequently, traditional production planning models enforce minimum demand constraints by product and period rather than by individual orders. An important drawback of this aggregation procedure is that it requires a fixed order fulfillment period, potentially missing opportunities for more efficient resource use through early completion. This paper introduces a novel mathematical formulation that preserves the integrity of customer orders, allowing for early fulfillment when possible. We compare a traditional linear programming model with a new mixed-integer programming approach using a sawmill case study. Although more complex than the traditional model, the proposed formulation reduces costs by approximately 6% by enabling early order completion and offers greater flexibility and control over the production process. This approach leads to better resource utilization and more precise order management, presenting a valuable alternative to conventional production planning models.

Advanced Queueing and Location-Allocation Strategies for Sustainable Food Supply Chain

Background: This study presents an integrated multi-product, multi-period queuing location-allocation model for a sustainable, three-level food supply chain involving farmlands, facilities, and markets. The model employs M/M/C/K queuing systems to optimize the transportation of goods, enhancing efficiency and sustainability. A mixed-integer nonlinear programming (MINLP) approach is used to identify optimal facility locations while maximizing profitability, minimizing driver waiting times, and reducing environmental impact. Methods: The grasshopper optimization algorithm (GOA), a meta-heuristic algorithm inspired by the behavior of grasshopper swarms, is utilized to solve the model on a large scale. Numerical experiments demonstrate the effectiveness of the proposed model, particularly in solving large-scale problems where traditional methods like GAMS fall short. Results: The results indicate that the proposed model, utilizing the grasshopper optimization algorithm (GOA), effectively addresses complex and large-scale food supply chain problems. Compared to GAMS, GOA achieved similar outcomes with minimal differences in key metrics such as profitability (with a gap ranging from 0.097% to 1.11%), environmental impact (0.172% to 1.83%), and waiting time (less than 0.027%). In large-scale scenarios, GOA significantly reduced processing times, ranging from 20.45 to 64.78 s. The optimization of processing facility locations within the supply chain, based on this model, led to improved balance between cost (up to $74.2 million), environmental impact (122,112 hazardous units), and waiting time (down to 11.75 h). Sensitivity analysis further demonstrated that increases in truck arrival rates and product value had a significant impact on improving supply chain performance.

A data-driven mixed integer programming approach for joint chance-constrained optimal power flow under uncertainty

A data-driven mixed integer programming approach for joint chance-constrained optimal power flow under uncertainty

Goal-based investing with goal postponement: multistage stochastic mixed-integer programming approach

Goal-based investing with goal postponement: multistage stochastic mixed-integer programming approach

Mixed-integer disciplined convex programming approach applied to the optimal energy supply of near-zero energy buildings

Energy needs in the buildings sector accounts for 40 % of global energy demand. Therefore, the implementation of several renewable energy sources is necessary to reduce this demand. The design stage of a decentralized generation project requires quantifying the power to be installed and the energy forecast for each source throughout the useful life of the building. This study develops a novel optimization algorithm for a long-term economic function based on mixed-integer disciplined convex programming (MIDCP) which guarantees the sustainability of the building and its energy systems. The robust algorithm integrates risk management of intermittent sources, technical and economic parameters of selected technologies, and life cycle analysis (LCA) of different energy systems, including storage. Furthermore, the penetration of green hydrogen into the distributed generation mix is evaluated as an important contribution. Meteorological and energy demand variables of two antagonistic scenarios were also used as inputs to the algorithm. As a result, the optimal energy supply sizing for tertiary buildings in the two defined locations was obtained. The results of the simulations have achieved an optimal convergence of 100 % in the proposed scenarios, with a resolution time of 14 s and using a memory of about 183 MB. The simulations suggest a higher penetration of green hydrogen in scenarios where supply and investment costs decrease to gray hydrogen supply levels, reaching up to 81 % coverage of the thermal demand of the building. Hybrid energy systems under favorable conditions show a penetration of about 92 % within the distributed generation mix. The developed tool could enable decision-makers to optimally plan distributed generation projects in buildings based on economic, policy, and geographic conditions.

An enhanced energy management system for coordinated energy storage and exchange in grid-connected photovoltaic-based community microgrids

This paper introduces an enhanced coordinated community energy management system (CEMS) for a community microgrid. It is designed to optimize residential energy consumption and facilitate energy sharing among smart homes. The proposed solution integrates constrained mixed-integer programming (CMIP) approach along with advanced optimization technique and cooperative game theory-based pricing mechanism to address critical challenges in existing energy management strategies, including load scheduling and efficient peer-to-peer energy trading. The CEMS approach is adopted for grid-connected community power systems that incorporate local energy sources such as photovoltaic and battery storage systems. This solution is implemented under a time-of-use dynamic pricing model for energy transfer from the main grid to the community peers, a modified mid-market pricing mechanism for the P2P energy exchange, and feed-in tariff for energy transfer from the community peers to the main grid. Besides, seagull optimization algorithm is applied to relax the CMIP problem to get the optimal rational solution of the scheduling problem which is subjected to a rounding process to obtain the best feasible solution. The obtained results indicate a substantial reduction in electricity costs, achieving daily savings of 72.21 % and reducing grid dependency by 41.95 %. Moreover, 82.2 % of the community's energy demand was met through locally generated resources with 18.39 % enhancement of the overall CMG self-consumption ratio comparing to the reference operating scenario. Ultimately, the study demonstrates the effectiveness of the management system in improving load profiles, maximizing the use of local renewable energy sources, and reducing electricity expenses, thereby providing a sustainable and economically viable model for future smart grids.

Energy expansion planning with a human evolutionary model

This study presents a novel method for planning the expansion of transmission lines and energy storage systems while considering the interconnectedness of electricity and gas networks. We developed a two-level stochastic planning model that addresses both the expansion of transmission and battery systems in the electrical grid and the behavior of the gas network. This research explores the challenges and effects of integrating high levels of renewable energy sources while ensuring security within both networks. Our model uses a stochastic mixed-integer non-linear programming approach. To solve this complex model, we applied the Human Evolutionary Model (HEM). We tested our approach on two case studies: a simple 6-node network and the more complex IEEE RTS 24-bus network for the electricity grid, combined with 5-node and 10-node gas networks, respectively. The results demonstrate the effectiveness of our model, particularly in scenarios where connections in the power and gas networks are disrupted, preventing load shedding even when integrated network connections are cut.

Data-driven confidence bound for structural response using segmented least squares: a mixed-integer programming approach

As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set, we adopt the segmented least squares so that a data set that is not fitted well by the linear regression model can be dealt with. Since the obtained uncertainty set is nonconvex, the optimization problem solved for the uncertainty analysis is nonconvex. We recast this optimization problem as a mixed-integer programming problem to find a global optimal solution. This global optimality, together with a fundamental property of the order statistics, guarantees that the obtained bound for the structural response is conservative, in the sense that, at least a specified confidence level, probability that the structural response is in this bound is no smaller than a specified target value. We present numerical examples for three different types of skeletal structures.

Topology optimization of truss structure considering kinematic stability based on mixed-integer programming approach

Topology optimization of truss structure considering kinematic stability based on mixed-integer programming approach

Economic Dispatch of Combined Cycle Power Plant: A Mixed-Integer Programming Approach

In this article, we present a modification to the Economic Dispatch (ED) model that addresses the non-convex nature of the cost curves associated with a Combined Cycle Power Plant (CCPP). Incorporating a binary variable provides greater precision in solving the combinatorial problem in only one simulation and, most importantly, demonstrates cost minimization among the three different cost curve models for dispatching the CCPP. Our results highlight the importance of considering different demand scenarios based on a reference forecast for one day ahead. Therefore, piecewise modeling is more feasible for solving the non-convex problem, showing greater accuracy regarding the operational state of the CCPP and avoiding the cost overestimation that occurs with traditional models. Moreover, it allows the operators to manage costs better and optimize generation potential, ultimately showing economic benefits for the system operator.

Collaborative optimization of depot location, capacity and rolling stock scheduling considering maintenance requirements

Generally, when optimizing a rolling stock schedule, the locations of the depots, or places in the network where the composition changes and maintenance occurs, are assumed known. The locations where maintenance is performed naturally influence the quality of any resulting rolling stock schedules. In this paper, the problem of selecting new depot locations and their corresponding capacities is considered. A two-stage mixed integer programming approach for rolling stock scheduling with maintenance requirements is extended to account for depot selection. First, a conventional flow-based model is solved, ignoring maintenance requirements, to obtain a variety of rolling stock schedules with multiple depot locations and capacity options. Then, a maintenance feasible rolling stock schedule can be obtained by solving a series of assignment problems by using the schedules found in the first stage. The proposed methodology is tested on real-life instances, and the numerical experiments of different operational scenarios are discussed.

Exact Mixed-Integer Programming Approach for Chance-Constrained Multi-Area Reserve Sizing

Exact Mixed-Integer Programming Approach for Chance-Constrained Multi-Area Reserve Sizing

Efficient continuous piecewise linear regression for linearising univariate non-linear functions

Due to their flexibility and ability to incorporate non-linear relationships, Mixed-Integer Non-Linear Programming (MINLP) approaches for optimization are commonly presented as a solution tool for real-world problems. Within this context, piecewise linear (PWL) approximations of non-linear continuous functions are useful, as opposed to non-linear machine learning-based approaches, since they enable the application of Mixed-Integer Linear Programming techniques in the MINLP framework, as well as retaining important features of the approximated non-linear functions, such as convexity. In this work, we extend upon fast algorithmic approaches for modeling discrete data using PWL regression by tuning them to allow the modeling of continuous functions. We show that if the input function is convex, then the convexity of the resulting PWL function is guaranteed. An analysis of the runtime of the presented algorithm shows which function characteristics affect the efficiency of the model, and which classes of functions can be modeled very quickly. Experimental results show that the presented approach is significantly faster than five existing approaches for modeling non-linear functions from the literature, at least 11 times faster on the tested functions, and up to a maximum speedup of more than 328,000. The presented approach also solves six benchmark problems for the first time.

A mixed integer programming approach to improve oil spill response resource allocation in the Canadian arctic

Determining proper locations to establish emergency response facilities is a critical strategic element of pollution preparedness and response planning for oil spills in remote areas. Many location-allocation models are available in the literature, but Arctic contexts such as remoteness and environmental sensitivities are still inadequately investigated while building optimization models. A Mixed Integer Programming (MIP) based optimization model is developed to devise a location-allocation problem: maximizing weighted spill coverage considering spill size, environmental sensitivity, and response time. Strategic decisions - e.g. allocation of stockpiling resources to resource stations and which response stations to open - are incorporated into the model as decision variables. Input parameters of the model are estimated using numerical and geospatial data of potential oil spills and response stations. The model is illustrated for hypothetical oil spill scenarios in the Canadian Arctic. The model provides optimal allocation of resources and recommends best-suited locations to build response facilities. Data visualization tools including Network Diagrams and sensitivity analysis on different model configurations, show the adequacy of the proposed mathematical modelling approach to solve the given problem. Multiple facility locations have been compared to cover all possible oil spills along Arctic shipping routes, further revealing a few better locations considering realistic constraints. Decision makers can use such optimization modelling information – e.g., how many stations to build in the Arctic to adequately cover potential oil spills – to aid strategic decision-making of maritime shipping.

Optimising fleet sizing and management of shared automated vehicle (SAV) services: A mixed-integer programming approach integrating endogenous demand, congestion effects, and accept/reject mechanism impacts

Shared automated vehicles (SAV) are expected to benefit the sustainable development of urban regions and alleviate the negative impacts brought by the increasing number of private cars. In this paper, we envision a future scenario where non-pooled SAVs replace private cars and provide public on-demand mobility services to satisfy the mobility needs of a city’s residents. To help service providers make profitable fleet sizing and management decisions, we develop a mixed-integer non-linear programming model that considers the congestion effects and the mode choice of urban travellers in different income classes, between SAVs and bicycles. Our model optimises both strategic decisions (fleet size, initial fleet distribution, and service quality level) and operational decisions (trip assignment, vehicle routing, parking, and relocation). Travellers’ preference for both transport modes is described through a binary logit model and congestion effects are described by dynamically varying travel times with respect to traffic flow in a non-linear fashion. In addition, we investigate two types of accept/reject mechanisms (mandatory vs. non-mandatory acceptance) which lead to an endogenously determined acceptance rate that can affect travellers’ willingness to use SAV services. The computational challenge posed by the non-linear and non-convex nature of the model is addressed through reformulation and the use of outer-inner approximation methods combined with a breakpoint generation algorithm. We demonstrate the effectiveness of our proposed method in a case study of the city of Delft in The Netherlands, as well as a scaling analysis on three toy networks with various sizes and demand profiles. A sensitivity analysis of key parameters is carried out to assess system performance. Computational results indicate that fleet sizing decisions are influenced not only by the population’s geographical distribution and land use patterns but also by the pricing strategy, unit operating costs of the SAV fleet, network congestion level, and traveller behaviour. When the price rate of using SAVs is low, the fleet sizing decisions can also be influenced by the trip accept/reject mechanism and the travellers’ sensitivity to the service quality level. In addition, a low price of SAV service will attract more users but may not necessarily bring a higher profit because of the increased traffic congestion.

New Ways in Municipal Flood Mitigation: a Mixed-Integer Programming Approach and its Practical Application

Adapting to the consequences of climate change is one of the central challenges faced by humanity in the next decades. One of these consequences are intense heavy rain events, which can cause severe damage to buildings due to flooding. In this paper, we present the first use of optimization techniques that scales well enough to be applicable for supporting decision-making in planning precautionary measures for flash floods caused by heavy rain events in realistic scenarios. Our mixed-integer programming model has been implemented as an innovative decision support tool in the form of a web application, which has already been used by more than 30 engineering offices, municipalities, universities, and other institutions. The model aims to minimize the damage caused in the case of a heavy rain event by taking best-possible actions subject to a limited budget and constraints on the cooperation of residents. We further present an efficient, graph-based representation and preprocessing of the surface terrain, a combinatorial algorithm for computing an initial solution of the mixed-integer program, and computational results obtained on real-word data from different municipalities.

Prioriactions: Multi‐action management planning in R

AbstractDesigning effective conservation strategies requires deciding not only where to locate conservation actions (i.e. which territorial units should be priortized), but also which type actions should be deployed. For most of conservation planning contexts, deciding where and what to do usually yields a complex and computationally challenging decision‐making setting. Although the resulting optimization problems have typically been tackled using heuristic approaches, recent advances in mixed integer programming (MIP) solver technology have turned MIP‐based approaches into a practical alternative for solving complex conservation planning problems.We introduce theRpackageprioriactions, which allows solving complex conservation planning problems comprising prioritization and action deployment decisions.prioriactionsfeatures a MIP approach that allows formulating and solving optimally (or nearly optimally) a wide class of conservation planning problems (characterized by different spatial and functional constraints and requirements). Furthermore, the package allows using a variety of commercial and open‐source exact solvers enhancing its usability as well as its practical effectiveness.Here, we present a comprehensive description of the main functions available inprioriactions. This package has a workflow of three straightforward steps: (a) validation of the input data, using theinputData()function that prepares input; (b) the creation of a prioritization model, using theproblem()function, allows the creation of two types of common models: theminimization of coststo achieve a recovery target andmaximizing the recovery benefitsgiven a limited budget; and (c) to solve of the model, using thesolve()function.Theprioriactionspackage provides a user‐friendly platform for addressing different multi‐actions management problems, allowing to identify more rigorously, transparently and in a reproducible way the spatial deployment of management actions.

Computation of Systemic Risk Measures: A Mixed-Integer Programming Approach

Mixed-Integer Programming Formulations for Systemic Risk Measures Measurement and allocation of systemic risk have become important tasks in interconnected financial networks. In “Computation of Systemic Risk Measures: A Mixed-Integer Programming Approach,” Ararat and Meimanjan consider a clearing model that considers external assets and business costs of a bank simultaneously by extending the Rogers–Veraart network model with default costs. They prove that clearing payment vectors can be calculated by solving mixed-integer programming problems in which the existence of business costs and default costs are represented by binary variables. The systemic risk measure corresponding to this model yields nonconvex sets of capital allocation vectors. The authors compute these nonconvex sets by solving a multiobjective optimization problem whose scalarizations are two-stage mixed-integer programming problems with an expectation constraint. The computational procedure is versatile enough to accommodate other applications of systemic risk where the risk factors are aggregated by solving a general mixed-integer programming problem.

A Stochastic Optimization Approach to Energy-Efficient Underground Timetabling Under Uncertain Dwell and Running Times

We consider a problem from the context of energy-efficient underground railway timetabling, in which an existing timetable draft is improved by slightly changing departure and running times. In practice, synchronization between accelerating and braking trains to utilize regenerative braking plays a major role for the energy efficiency of a timetable. Because deviations from a planned timetable may lead to unnecessarily high energy consumption during actual operation, we include operational uncertainties in our model to create a timetable that remains energy efficient, even if deviations from the nominal timetable occur. To solve the problem, we use a scenario expansion model in conjunction with a Benders decomposition approach. As an alternative to solving the Benders subproblems, we present a heuristic sparse cut that can be computed efficiently. The resulting sparse-cut heuristic produces high-quality solutions on a set of real-world instances stemming from the Nürnberg underground system, outperforming the integrated mixed-integer programming approach as well as the basic Benders approach. Additionally, we evaluate two static recovery strategies—shortening dwell times as well as shortening dwell and running times—to determine the cost and benefit of handling delays using a simple static rule. In our experiments, we are able to reduce the energy consumption by up to 9.4% and confirm that delay recovery via shortening dwell times is an energy-efficient and effective way to increase punctuality at low cost in terms of energy. Funding: This research was supported by the Bavarian Ministry of Economic Affairs, Regional Development and Energy through the Center for Analytics – Data – Applications (ADA-Center) within the framework of “BAYERN DIGITAL II” (20-3410-2-9-8).