Integer Programming Algorithm Research Articles

A simple, efficient and versatile objective space algorithm for multiobjective integer programming

AbstractIn the last years a multitude of algorithms have been proposed to solve multiobjective integer programming problems. However, only few authors offer open-source implementations. On the other hand, new methods are typically compared to code that is publicly available, even if this code is known to be outperformed. In this paper, we aim to overcome this problem by proposing a new state-of-the-art algorithm with an open-source implementation in . The underlying method falls into the class of objective space methods, i.e., it decomposes the overall problem into a series of scalarized subproblems that can be solved with efficient single-objective IP-solvers. It keeps the number of required subproblems small by avoiding redundancies, and it can be combined with different scalarizations that all lead to comparably simple subproblems. Our algorithm bases on previous results but combines them in a new way. Numerical experiments with up to ten objectives validate that the method is efficient and that it scales well to higher dimensional problems.

Enhancing the waste heat utilization of industrial park: A heat pump-centric network integration approach for multiple heat sources and users

The industrial sector, which is characterized by high energy consumption, primarily using fossil fuels, exhibits significant carbon emissions and severe pollution. Industrial parks generate abundant waste heat with varying flow rates and multiple grades, and also include industrial users with diverse heat demand profiles. Waste heat recovery is an effective method for reducing fossil fuel consumption. However, the current waste heat recovery methods focus on single-heat-source scenarios, making them unsuitable for use in industrial parks with multiple heat sources and heating loads. To achieve efficient matching between different sources and loads, this study developed a heat-pump-centric network system and establishes a two-stage optimization method for networked waste heat utilization. First, based on matrix algebra, a method for matching the generated waste heat with heat pump combinations and heat users was developed to obtain a networked heating path. Second, an optimization model for heat pump combinations was established, and linear integer programming algorithms were employed to obtain the optimal configuration and operational plan for the heating path. Finally, energy flow analysis was conducted to elucidate the optimal energy distribution. The results show that, compared to traditional heating modes, the proposed method achieved a 55 % reduction in energy consumption with a payback period of 4.6 years. The proposed system could enhance the matching between different grades of waste heat and heating demand, thereby improving the thermal energy utilization efficiency. The proposed method demonstrates significant energy saving with efficient utilization and economic benefits and can be applied to different scenarios with multiple sources and loads.

Research on dual robot collaboration method based on improved double ant colony algorithm

Purpose This study aims to propose an efficient dual-robot task collaboration strategy to address the issue of low work efficiency and inability to meet the production needs of a single robot during construction operations. Design/methodology/approach A hybrid task allocation method based on integer programming and auction algorithms, with the aim of achieving a balanced workload between two robots has been proposed. In addition, while ensuring reasonable workload allocation between the two robots, an improved dual ant colony algorithm was used to solve the dual traveling salesman problem, and the global path planning of the two robots was determined, resulting in an efficient and collision-free path for the dual robots to operate. Meanwhile, an improved fast Random tree rapidly-exploring random tree algorithm is introduced as a local obstacle avoidance strategy. Findings The proposed method combines randomization and iteration techniques to achieve an efficient task allocation strategy for two robots, ensuring the relative optimal global path of the two robots in cooperation and solving complex local obstacle avoidance problems. Originality/value This method is applied to the scene of steel bar tying in construction work, with the workload allocation and collaborative work between two robots as evaluation indicators. The experimental results show that this method can efficiently complete the steel bar banding operation, effectively reduce the interference between the two robots and minimize the interference of obstacles in the environment.

Characterization of matrices with bounded Graver bases and depth parameters and applications to integer programming

AbstractAn intensive line of research on fixed parameter tractability of integer programming is focused on exploiting the relation between the sparsity of a constraint matrix A and the norm of the elements of its Graver basis. In particular, integer programming is fixed parameter tractable when parameterized by the primal tree-depth and the entry complexity of A, and when parameterized by the dual tree-depth and the entry complexity of A; both these parameterization imply that A is sparse, in particular, the number of its non-zero entries is linear in the number of columns or rows, respectively. We study preconditioners transforming a given matrix to a row-equivalent sparse matrix if it exists and provide structural results characterizing the existence of a sparse row-equivalent matrix in terms of the structural properties of the associated column matroid. In particular, our results imply that the $$\ell _1$$ ℓ 1 -norm of the Graver basis is bounded by a function of the maximum $$\ell _1$$ ℓ 1 -norm of a circuit of A. We use our results to design a parameterized algorithm that constructs a matrix row-equivalent to an input matrix A that has small primal/dual tree-depth and entry complexity if such a row-equivalent matrix exists. Our results yield parameterized algorithms for integer programming when parameterized by the $$\ell _1$$ ℓ 1 -norm of the Graver basis of the constraint matrix, when parameterized by the $$\ell _1$$ ℓ 1 -norm of the circuits of the constraint matrix, when parameterized by the smallest primal tree-depth and entry complexity of a matrix row-equivalent to the constraint matrix, and when parameterized by the smallest dual tree-depth and entry complexity of a matrix row-equivalent to the constraint matrix.

Digital Twin Based Resource Optimization and Dynamic Decision Making in Air Terminal Yards

Abstract With the growth of globalized trade, the efficient operation of airports is crucial. In this paper, we study the use of digital twin technology to optimize the yard resources of airports, which can improve their operational efficiency and decision-making quality. The study first constructs a digital twin framework for intelligent yard scheduling, which contains physical and virtual space and the connection between them. Data is collected through the physical perception module, while the virtual space is used for real-time simulation and optimized decision-making. The research methodology includes mixed integer programming and adaptive immune cloning algorithms for optimizing yard resource allocation and box space allocation. The experimental results show that the method can effectively reduce the total transportation distance in the air terminal yard operation and improve operation efficiency. The experiments demonstrate an average improvement in operational efficiency of around 20% and a cost reduction of around 15%. It is concluded that digital twin technology has apparent advantages in allocating resources in air terminal yards, which can achieve efficient utilization of resources and dynamic optimization of decision-making.

Retrofit Planning and Flexible Operation of Coal-Fired Units Using Stochastic Dual Dynamic Integer Programming

The continuous growth of wind power requires greater power system operational flexibility owing to the variability and uncertainty of wind power generation. Retrofitting existing coal-fired units is a demonstrated cost-effective method for improving system flexibility. This study proposes a decision support tool that provides optimal investment decisions to enhance power system operational flexibility. A novel flexibility retrofit planning (FRP) model is proposed in which the embedded operational problem is a stochastic mixed-integer nonlinear programming (SMINLP) unit commitment problem. In the operational unit commitment model, novel mixed-integer nonlinear formulations are proposed to represent the coal-fired unit attribute (minimum power output, startup and shutdown times, and maximum ramp rate) modifications after retrofitting. A new solution method based on the Benders decomposition (BD) and stochastic dual dynamic integer programming (SDDIP) algorithms is proposed to solve the proposed FRP model. The modified IEEE 39-bus, 57-bus, and 118-bus test systems were used to verify the effectiveness of the proposed model and solution method. The results demonstrate that the proposed FRP model can balance the retrofitting and operational costs to minimize the total cost and accommodate more wind generation. The proposed solution method is computationally efficient for solving FRP models.

An Integer Programming Algorithm for Constructing Maximin Distance Designs From Good Lattice Point Sets

An Integer Programming Algorithm for Constructing Maximin Distance Designs From Good Lattice Point Sets

Multi-material structural discrete variable topology optimization with minimum length scale control under mass constraint

Topology optimization of multi-material structure has a larger design space compared with single material optimization, and it also requires efficient material selection methods to provide references for designers. The multi-material additive manufacturing ensures the manufacturability of topology design of multi-material structures, but also puts forward new manufacturability requirements, such as the minimum size of multi-material and the connection interface. This paper focuses on the development of a topology optimization algorithm for multi-material structures under the total mass constraint based on discrete variables. Recursive multiphase materials interpolation (RMMI) scheme is utilized to establish the relationship between discrete design variables and element elastic modulus and density, and sequential approximate integer programming (SAIP) and canonical relaxation algorithms are constructed to update the discrete design variables. It is shown that this method can obtain multi-material topology design with clear interface display, and has the ability of free material coexistence and degradation, which indicates that the discrete variables have more advantages than the continuous variables in the RMMI scheme. Based on this, the material selection under mass constraints is discussed in depth, and it is pointed out that the traditional determination of material coexistence or degradation in design based on specific stiffness has limitations. Thus, the present work expands the necessary conditions of material coexistence. Then, a minimum size control method of multi-material design based on post-processing is proposed to solve the minimum size geometry constraint problem by SAIP. Numerical examples show that this method can not only precisely control the minimum size of each material phase (including void phase), but also resolve the problem of interface and boundary diffusion of the multi-material phase, and significantly improve the manufacturability of multi-material design. Finally, it is applied to optimization problems with complex design domain and irregular meshes which are closer to engineering design.

An asynchronous parallel benders decomposition method for stochastic network design problems

Benders decomposition (BD) is one of the most popular solution algorithms for stochastic integer programs. The BD method decomposes stochastic problems into one master problem and multiple disjoint subproblems. It thus lends itself readily to parallelization. In almost all studies on the parallelization of this algorithm, the master problem remains idle until every subproblem is solved and vice versa. This can clearly result in an extremely inefficient parallel algorithm due to excessive idle times. On the other hand, relaxing the synchronization requirement can yield a nonconvergent or less efficient algorithm that may even underperform when compared to the sequential version. Addressing these issues, we introduce an asynchronous parallel BD method for stochastic network design problems. We show that the proposed algorithm converges to the global optimum and suggest various acceleration strategies to enhance its performance. We conduct an extensive numerical study on benchmark instances from a generic stochastic network design problem. The results indicate that using up to 20 processors, our asynchronous algorithm is on average 1.4 times faster than the conventional low-level parallel methods.

Congruency-Constrained TU Problems Beyond the Bimodular Case

A long-standing open question in integer programming is whether integer programs with constraint matrices with bounded subdeterminants are efficiently solvable. An important special case thereof are congruency-constrained integer programs [Formula: see text] with a totally unimodular constraint matrix T. Such problems are shown to be polynomial-time solvable for m = 2, which led to an efficient algorithm for integer programs with bimodular constraint matrices, that is, full-rank matrices whose n × n subdeterminants are bounded by two in absolute value. Whereas these advances heavily rely on existing results on well-known combinatorial problems with parity constraints, new approaches are needed beyond the bimodular case, that is, for m > 2. We make first progress in this direction through several new techniques. In particular, we show how to efficiently decide feasibility of congruency-constrained integer programs with a totally unimodular constraint matrix for m = 3 using a randomized algorithm. Furthermore, for general m, our techniques also allow for identifying flat directions of infeasible problems and deducing bounds on the proximity between solutions of the problem and its relaxation. Funding: This project received funding from the Swiss National Science Foundation [Grants 200021_184622 and P500PT_206742], the European Research Council under the European Union’s Horizon 2020 research and innovation program [Grant 817750], and the Deutsche Forschungsgemeinschaft (German Research Foundation) under Germany’s Excellence Strategy–GZ 2047/1 [Grant 390685813].

Integrating distributed disassembly line balancing and vehicle routing problem in supply chain: Integer programming, constraint programming, and heuristic algorithms

Today, the fast-changing demands of customers force manufacturers to adapt their systems to the variability. As a result of the recent advances in technology and transport systems, most manufacturers have begun to employ more than one distributed facility to respond rapidly to the demands of their customers. In addition, with the emergence of Industry 4.0, information exchange between systems at the same and different levels has become relatively easy. Therefore, effective management of distributed facilities by integrating processes at different levels in the supply chain can provide a significant advantage in adapting the system to customer demand dynamics. Furthermore, recycling waste products and using them in new products have become essential for environmentally friendly production. Therefore, this paper introduces integrated distributed disassembly line balancing and vehicle routing problem first time in the literature. Since the distributed disassembly centers with routing decisions of the vehicles from these centers to the factories have not been considered before, the proposed integrated study will contribute to both industry and the literature. The contribution is not only limited to the proposed integrated problem. Also, novel solution methodologies, mixed-integer linear programming, mixed-integer non-linear programming, and constraint programming models are developed to solve the problem. Besides the mathematical models, a multi-start simulated annealing algorithm is also proposed to overcome the large-size instances due to the complexity of the proposed integrated problem. The comprehensive computational analysis demonstrates that the proposed methods are very competitive in providing good-quality solutions for the problem.

Optimizing the reinforcement of buildings and structures in automatic design processes

Introduction. Reinforcement is one of the most important processes in designing reinforced concrete structures. The need to optimize the reinforcement process arises from the constant increase in the volume and complexity of construction projects, as well as from the economy and efficiency requirements. In this regard, automatic design processes are becoming increasingly relevant, being conducive to significant acceleration and improvement of the quality of these works. Other areas of civil and industrial construction are also adopting automatic design processes in order to reduce construction and production costs. Mixed Integer Programming (MIP), Simplex Method (SM), and Genetic Algorithm (GA) are commonly used.Aim: to develop an algorithm for optimizing the reinforcement process of reinforced concrete structures of buildings and structures and to design a program for automating the process.Materials and methods. The paper relies upon the results of the calculations performed by the authors in the Lira program. Furthermore, the authors created a digital information model of the building in the Revit program. The Python programming language was used to test the results. A ready-made solution was created in C# using RevitAPI.Results. The paper substantiates the relevance and demonstrates the feasibility of optimization of technological solutions in the process of designing buildings and structures made of reinforced concrete according to the criterion “reliability – efficiency”. To this end, existing design software was integrated into a single modeling and design module, and the necessary software was proposed for development. The genetic algorithm was chosen as the main method for optimizing the reinforcement of structures. Tools for processing the calculation results, creating a duplicate of the calculation model in the design environment and analyzing the calculations were elaborated.Conclusion. The selected genetic algorithm accelerates the design process, and saves time when designing reinforced concrete structures. The results of the study are instrumental in developing the software for the automation of reinforcement.

Medium-term multi-stage distributionally robust scheduling of hydro–wind–solar complementary systems in electricity markets considering multiple time-scale uncertainties

Joint trading of hydro–wind–solar complementary systems (HWSCSs) in the electricity market (EM) helps to reduce the imbalance cost and increase profits. However, multiple energy resources and market price uncertainties affect the trading strategies. Existing medium-term (MT) scheduling approaches assume that the probability distribution of the random variable is perfectly known. Short-term variations were also ignored, which led to revenue loss and trading risk. To address the above issues, this paper proposes an MT multi-stage distributionally robust optimization (MDRO) scheduling approach for a price-taking HWSCS in the EM. Firstly, hourly unit commitment (HUC) constraints are incorporated into the MT scheduling model to accurately capture short-term variations. A novel ambiguity set is designed based on the modified chi-square distance to address probability distribution uncertainties at two different time scales. Subsequently, an MDRO scheduling model is proposed to optimize the trading strategy. Finally, the proposed MDRO model is converted to a large-scale multi-stage integer programming problem based on linearization and reformation. The stochastic dual dynamic integer programming algorithm is modified to ensure computational tractability. Xiluodu-Xiangjiaba HWSCS, located in the Jinsha River in China, was selected as a case study. The results show that: 1) the MDRO model is more robust to distributional uncertainties than the multi-stage stochastic programming (MSSP) model. When the probability distribution of the random variable changes, the MDRO model yields a higher expected revenue (+2.43%) and a lower standard deviation (-60.8%) of revenue, which illustrates lower trading risk. 2) Compared with MSSP, deterministic, two-stage stochastic programming, and distributionally robust optimization models, the MDRO model exhibits the best out-of-sample performance in terms of the highest expected revenue and lowest trading risk. 3) Incorporating HUC constraints into the MDRO model helps to increase the total revenue (+3.53%) and energy generation (+3.31%) at the expense of increasing the computational burden.

Optimal Scheduling of Rainwater Collection Vehicles: Mixed Integer Programming and Genetic Algorithms

Due to climate change, some areas in the world witnessed higher levels of heavy rain than the capacity of the wastewater system of the streets. Therefore, water tankers are used for the dewatering process to take the extra rainwater from the streets to keep a smooth flow of vehicles and to use the water in agriculture and industry. Water is taken to a water treatment plant. Performing the dewatering process as fast as possible, especially in crowded streets, was ignored by researchers. In this study, at first, the problem was solved using two mixed integer programming (MIP) models. A new variant of identical parallel machine scheduling with job splitting is proposed for the first time, where one or at most two tankers can work at the same flood location at the same time. This is performed in the second model. However, the first model considers dividing the dewatering processes into two phases, where the first one, which is more urgent, is to reduce the amount of floodwater. The second one is for dewatering the rest of the water. Then two genetic algorithms (GAs) were used to solve faster the two MIP models, which are NP-hard problems. At first, the MIP and GA models were applied to small-sized problems. Then GA was used for large practical data sets. Results showed that for small problems, MIP and GA gave optimal solutions in a reasonable number of iterations, while for larger problems, good solutions were obtained in a reasonable number of iterations.

Multi-stage distributionally robust optimization for hybrid energy storage in regional integrated energy system considering robustness and nonanticipativity

Hybrid energy storage system (HESS) has advantages in coping with the uncertainty of renewable energy and improving the stability of regional integrated energy systems (RIES). Few of the current HESS uncertainty scheduling methods consider both robustness and nonanticipativity, which may result in scheduling strategies that are not feasible in practice. Therefore, this research constructs a HESS (containing electric, thermal, hydrogen and natural gas storage devices) and forms a hybrid energy storage operator (IHESO) with an independent market position based on the HESS to provide energy services. Subsequently, a novel multi-stage distributionally robust optimization (MSDRO) method is established to maximize HESS revenue. Robustness and nonanticipativity can be satisfied in the uncertainty scheduling process of this method. After that, the stochastic dual dynamic integer programming (SDDiP) algorithm is introduced to solve multi-stage nested problems of complex systems. Finally, simulations are conducted in the actual system of three seasons and five scenarios. The conclusions are as follows: 1) The scheduling strategy provided by the MSDRO model and SDDiP algorithm can ensure effective operation based on satisfying robustness and nonanticipativity. 2) Compared with MSO, TSDRO and MSRO, the method proposed can improve the HESS economy and stability, increase renewable energy consumption and reduce carbon emissions.

Interdicting Attack Plans with Boundedly Rational Players and Multiple Attackers: An Adversarial Risk Analysis Approach

Cybersecurity planning supports the selection of and implementation of security controls in resource-constrained settings to manage risk. Doing so requires considering adaptive adversaries with different levels of strategic sophistication in modeling efforts to support risk management. However, most models in the literature only consider rational or nonstrategic adversaries. Therefore, we study how to inform defensive decision making to mitigate the risk from boundedly rational players, with a particular focus on making integrated, interdependent planning decisions. To achieve this goal, we introduce a modeling framework for selecting a portfolio of security mitigations that interdict adversarial attack plans that uses a structured approach for risk analysis. Our approach adapts adversarial risk analysis and cognitive hierarchy theory to consider a maximum-reliability path interdiction problem with a single defender and multiple attackers who have different goals and levels of strategic sophistication. Instead of enumerating all possible attacks and defenses, we introduce a solution technique based on integer programming and approximation algorithms to iteratively solve the defender’s and attackers’ problems. A case study illustrates the proposed models and provides insights into defensive planning. Funding: A. Peper and L. A. Albert were supported in part by the National Science Foundation [Grant 2000986].

Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm

One of the most important theories in linear programming is the dualistic theory and its basic idea is that for every linear model has dual linear model, so that solving the original linear model gives a solution to the dual model. Therefore, when we solving the linear programming model, we actually obtain solutions for two linear models. In this research, we present a study of the models. The neutrosophic dual and the binary simplex algorithm, which works to find the optimal solution for the original and dual models at the same time. The importance of this algorithm is evident in that it is relied upon in several operations research topics, such as integer programming algorithms, some nonlinear programming algorithms, and sensitivity analysis in linear programming...

A combined mixed integer programming and deep neural network-assisted heuristics algorithm for the nurse rostering problem

The objective of the nurse rostering problem (NRP) is to obtain a scheduling plan that optimizes the allocation of human resources, effectively reducing work pressure on nurses and improving work efficiency and quality. Because various constraints must be considered during scheduling, the NRP is complicated and known to be NP-hard. Existing research has not combined learning mechanisms with NRP. This study constructively explores the possibility of combining an optimization method and a learning mechanism to automatically produce feasible solutions and proposes a feature vector and a reconstruction mechanism to assist in this exploration. We aim to learn a policy that is generalizable for NRPs of various sizes and design a hybrid algorithm with learning and optimization methods to solve the general NRP. The algorithm has two main parts: a deep neural network (DNN) improvement part and a reconstruction part. In the DNN improvement part, a feature vector is used to describe heterogeneous NRP solutions and normalizes these solutions to the same dimension. Then, the DNN model determines the best heuristic for approximating the local optimal solution. The method reconstructs the structure of the current solution with embedded mixed integer programming (MIP), quickly escaping the local optimum and enhancing the diversity of the search process, increasing the likelihood of determining an optimal solution. Different experiments and statistical tests were conducted by comparing various configurations and approaches. The detailed computational and statistical results demonstrate the competitive performance of the proposed method.

Optimal operation of a single unit in a pumping station based on a combination of orthogonal experiment and 0-1 integer programming algorithm

Abstract The frequent start–stop scheme in the operation management of large pumping stations causes several problems, e.g., energy consumption and a potential safety hazard. We therefore established a mathematical model for the optimal operation of a large-scale pumping station considering the start-stop loss of machine. The objectives of the optimization model included electricity charges for a pumping station operation and the start-stop loss of a pumping station. The blade angle and start-stop scheme were taken into account as the double-decision variables, while the target water extraction (equality constraint), start-stop scheme, and power were the constraint conditions. A combination of an orthogonal experiment and a 0-1 integer programming algorithm was proposed to explore the optimal solution of the model. A real case of a single-unit pump station in China was applied to prove the effectiveness of the algorithm. The results showed that the optimization efficiency of the proposed algorithm was 4%–10% higher than that of the genetic algorithm. Additionally, the maximum optimization benefit was obtained when there were fewer than three start-stops during the operation process. The proposed algorithm provided a reference for similar complex nonlinear models.

Multi-baseline phase unwrapping with robust branch and bound pure integer programming algorithm

Phase unwrapping (PU) represents a crucial bottleneck restricting the practical application of InSAR technique. According to the relationship between the same relative elevation and each interferometric phase differential, a new robust branch and bound pure integer programming phase unwrapping (BB-PIP-PU) algorithm for multi-baseline InSAR based on operations research is proposed. This algorithm constructs an N dimensional space with the ambiguity number as the axis. It takes the intercept of the ith ambiguity number axis as the objective function, and the directed ray intersecting the N-1 dimensional plane as the constraint condition. Firstly, it takes the optimal solution of ith ambiguity number axis as the solution starting point. Then, it increments by one pixel successively to verify whether the solution set composed of the remaining ambiguity numbers meets the integer condition, until the condition is established. Finally, the optimal integer solution of the N ambiguity numbers is determined. To improve noise robustness, a rectangular window is innovatively designed to replace ambiguity number at the center mutation point with ambiguity number with the highest frequency in the rectangular window. The significant advantages of this algorithm are that it has better unwrapping ability in the abrupt topographic change region, compared with the branch-cut, LS and MCF algorithms. Moreover, it weakens the baseline requirement of interferometric pairs, compared with the CRT algorithm. Finally, experimental results on both simulated and real data illustrate the good performance of our approach in terms of the effectiveness, universality, reliability, and noise robustness ability.