Binary Integer Programming Research Articles

A 0/1 Constrained Optimization Solving Sample Average Approximation for Chance Constrained Programming

Sample average approximation (SAA) is a tractable approach for dealing with chance constrained programming, a challenging stochastic optimization problem. The constraint of SAA is characterized by the 0/1 loss function, which results in considerable complexities in devising numerical algorithms. Most existing methods have been devised based on reformulations of SAA, such as binary integer programming or relaxed problems. However, the development of viable methods to directly tackle SAA remains elusive, let alone providing theoretical guarantees. In this paper, we investigate a general 0/1 constrained optimization, providing a new way to address SAA rather than its reformulations. Specifically, starting with deriving the Bouligand tangent and Fréchet normal cones of the 0/1 constraint, we establish several optimality conditions. One of them can be equivalently expressed by a system of equations, enabling the development of a semismooth Newton-type algorithm. The algorithm demonstrates a locally superlinear or quadratic convergence rate under standard assumptions along with nice numerical performance compared with several leading solvers. Funding: This research was supported by the National Key R&D Program of China [Grant 2023YFA1011100], the Fundamental Research Funds for the Central Universities, and the National Natural Science Foundation of China [Grant 12271309].

Two-set inequalities for the binary knapsack polyhedra

This paper presents two-set inequalities, a class of valid inequalities for knapsack and multiple knapsack problems. Two-set inequalities are generated from two arbitrary sets of variables from a knapsack constraint. This class of cutting planes is not a traditional type of lifting since a valid inequality over a restricted space is not required to start. Furthermore, they cannot be derived using any existing lifting technique. The paper presents a quadratic algorithm to efficiently generate many two-set inequalities. Conditions for facet-defining two-set inequalities are also derived. Computational experiments tested these inequalities as pre-processing cuts versus CPLEX, a high-performance mathematical programming solver, at default settings. Overall, two-set inequalities reduced the time to solve some benchmark multiple knapsack instances to up to 80%. Computational results also showed the potential of this new class of cutting planes to solve computationally challenging binary integer programs.

Analytical model and swapping policy assessment of a vertical lift module – buffer integrated storage system

To meet the rising demands of global trade and e-commerce, efficient warehousing relies on integrated and cooperative material handling systems. This paper investigates the extension of Vertical Lift Module (VLM) storage capability with a Buffer System and assesses the impact of this integration on performance. We developed an analytical model to calculate the expected dual command cycles, forming the basis for evaluating the VLM – Buffer integrated storage system’s performance. Our research emphasises minimising unnecessary swaps between the VLM and the Buffer System to enhance throughput performance. We introduce the Look Ahead Strategy (LAS) to minimise inter-system swaps and develop a Binary Integer Program (BIP) to benchmark its performance. The results indicate that LAS performs on par with BIP, due to its ability to consider product popularity during the final selection of the outbound swapping tote. Through a comprehensive analysis of the analytical model with an empirical correction, utilising Pareto-based order sequences, the results show deviations of less than 1% on average, affirming the analytical model’s accuracy. Our research provides insights on using the VLM-Buffer integrated storage system, emphasising efficient tote swapping policies like LAS for enhanced warehouse operations, and allows managers to assess system performance through scenario-based analyses.

Strategic placement of volunteer responder system defibrillators.

Volunteer responder systems (VRS) alert and guide nearby lay rescuers towards the location of an emergency. An application of such a system is to out-of-hospital cardiac arrests, where early cardiopulmonary resuscitation (CPR) and defibrillation with an automated external defibrillator (AED) are crucial for improving survival rates. However, many AEDs remain underutilized due to poor location choices, while other areas lack adequate AED coverage. In this paper, we present a comprehensive data-driven algorithmic approach to optimize deployment of (additional) public-access AEDs to be used in a VRS. Alongside a binary integer programming (BIP) formulation, we consider two heuristic methods, namely Greedy and Greedy Randomized Adaptive Search Procedure (GRASP), to solve the gradual Maximal Covering Location (MCLP) problem with partial coverage for AED deployment. We develop realistic gradually decreasing coverage functions for volunteers going on foot, by bike, or by car. A spatial probability distribution of cardiac arrest is estimated using kernel density estimation to be used as input for the models and to evaluate the solutions. We apply our approach to 29 real-world instances (municipalities) in the Netherlands. We show that GRASP can obtain near-optimal solutions for large problem instances in significantly less time than the exact method. The results indicate that relocating existing AEDs improves the weighted average coverage from 36% to 49% across all municipalities, with relative improvements ranging from 1% to 175%. For most municipalities, strategically placing 5 to 10 additional AEDs can already provide substantial improvements.

An optimization framework for solving large scale multidemand multidimensional knapsack problem instances employing a novel core identification heuristic

By applying the core concept to solve a binary integer program (BIP), certain variables of the BIP are fixed to their anticipated values in the optimal solution. In contrast, the remaining variables, called core variables, are used to construct and solve a core problem (CP) instead of the BIP. A new approach for identifying CP utilizing a local branching (LB) alike constraint is presented in this article. By including the LB-like constraint in the linear programming relaxation of the BIP, this method transfers batches of variables to the set of core variables by analyzing changes to their reduced costs. This approach is sensitive to problem hardness because more variables are moved to the core set for hard problems compared to easy ones. This novel core identification approach is embedded in a multi-stage framework to solve the multidemand, multidimensional knapsack problems (MDMKP), where at each stage, more variables are added to the previous stage CP. The default branch and bound of CPLEX20.10 is used to solve the first stage, and a tabu search algorithm is used to solve subsequent stages until all variables are added to CP in the last stage. The new framework has shown equivalent to superior results compared to the state-of-the-art algorithms in solving large MDMKP instances having 500 and 1,000 variables.

Constructing renewable energy sphere for efficient search

In the field of renewable energy (RE), traditional methods for understanding, development, and education have heavily relied on 2D table formats for data retrieval and presentation. However, these formats suffer from inefficiency and an inability to fully capture the relationships between variables. In response to this challenge, Li et al. (2022) demonstrated that their therapeutic 3D sphere system significantly outperformed the therapeutic 2D table in query processing time. Furthermore, Shih et al. (2020) utilized a T-test to underscore the superiority of the TED Talks sphere over the TED Talks 2D table format website in terms of convenience, query processing efficiency, usefulness, and intuitiveness. Building upon this foundation, this study referenced and enhanced the work of Li et al. by introducing a three-dimensional spherical visualization model driven by cluster-based binary integer programming (BIP). This novel approach resulted in a 58% reduction in information retrieval time and achieved an impressive 86.4% user satisfaction rating. It is worth noting that compared to the previous Systematic Review and Synthesis (SRS), user satisfaction experienced a significant 19% improvement. This improvement enhances the search efficiency for RE information, thereby fostering public awareness and development of RE. Taking energy supply-demand balance sheets as an example, this study demonstrates that the spherical retrieval system (SRS) constructed by the visualization 3D spherical model resolves the issue of inefficient retrieval in 2D table formats, and the newly added functionality of highlighting objects on the spherical surface intuitively illustrates the one-to-many relationships between individual RE supply and demand. To optimize hardware and software performance, data mining techniques are employed to cluster supply data, reducing complexity, and improving optimization efficiency. The experiment is that testers search for the same targets and compared the proposed 3D SRS with the Taiwan Power Company (Taipower) 2D website in terms of retrieval speed and accuracy. The statistical results of the T-test indicate that the proposed 3D SRS is more effective and accurate than the Taipower 2D website. The research findings indicate: 1. The new 3D SRS reduces query time by 58%. 2. Adopting the k-means algorithm for clustering and batch optimization can transform from an initially infeasible solution to finding the optimal solution within 12 s. This method also reduces computer software and hardware costs, providing effective solutions for relevant applications. These technologies can be used for the education, promotion, publicity, and dissemination of RE.

Solving the project scheduling problem with dependent resource constraints

ABSTRACT Most resource-constrained project scheduling problems consider resources that are independent of the job processing sequence. However, solving project scheduling problems in some industrial manufacturing is challenging because the required resources depend on the job processing sequence in existing scheduling approaches. To address this issue, this paper proposes a dependent resource-constrained project scheduling problem formulated with two types of models: a conceptual model and a binary integer programming model. The performance of four proposed algorithms – binary integer programming, reduced subproblem of the binary integer programming, job sequence assignment, and job as early as possible – is tested on 68 combinations of numerical simulation experiments. The computational results show that the job as early as possible algorithm can find a better approximate solution for solving real-world problems. This achievement aids project managers in generating activity schedules and finding the approximate minimum makespan for a project with dependent resource constraints.

How to optimize service-oriented cloud manufacturing

Within the context of Industry 4.0, service-oriented cloud manufacturing has emerged as a paradigm of significant interest, noted for enhancing manufacturing efficacy through integration, flexibility, and customization. The challenges of service selection and optimization, alongside transportation optimization, are pivotal for the effective implementation of service-oriented cloud manufacturing. This study explores an integrated problem that incorporates both sequential and parallel structures. To address this intricate issue, a binary-integer programming model is proposed, aiming to minimize the cumulative costs, including both manufacturing and transportation expenses. The validity and effectiveness of the proposed model are demonstrated through a real-world case study in mold manufacturing. Analysis of the experimental results provides managerial insights, which could inform the implementation and improvement of service-oriented cloud manufacturing strategies.

Multiplayer Homicidal Chauffeur reach-avoid games: A pursuit enclosure function approach

This paper presents a multiplayer Homicidal Chauffeur reach-avoid differential game, which involves Dubins-car pursuers and simple-motion evaders. The goal of the pursuers is to cooperatively protect a planar convex region from the evaders, who strive to reach the region. We propose a cooperative strategy for the pursuers based on subgames for multiple pursuers against one evader and optimal task allocation. We introduce pursuit enclosure functions (PEFs) and propose a new enclosure region pursuit (ERP) winning approach that supports the forward analysis for the strategy synthesis in the subgames. We show that if a pursuit coalition is able to defend the region against an evader under the ERP winning, then no more than two pursuers in the coalition are necessarily needed. We also propose a steer-to-ERP approach to certify the ERP winning and synthesize the ERP winning strategy. To implement the strategy, we introduce a positional PEF and provide the necessary parameters, states, and strategies that ensure the ERP winning for both one pursuer and two pursuers against one evader. Additionally, we formulate a binary integer program using the subgame outcomes to maximize the captured evaders in the ERP winning for the pursuit task allocation. Finally, we propose a multiplayer receding-horizon strategy where the ERP winnings are checked in each horizon, the task is allocated, and the strategies of the pursuers are determined. Numerical examples are provided to illustrate the results.

Valorant Haven Strategy Using BIP and Weighted Graph

Strategy in a competitive video game is needed to reach a successful game, for example, Valorant. Route planning is one of the strategies in playing games. In consideration of making a new strategy, this research develops a binary integer programming (BIP) model to generating optimal route depending on passable paths, travel time, kills, and survivability. By using POM QM for Windows to compute the model, we obtained optimal modified routes that can be combined in the role and agent composition.

Augmenting input-output system under the curse of dimensionality: AHP-RAS integration and algorithm simulation

ABSTRACT In the estimation of input-output tables, one frequently encountered challenge is the aggregation of sectors in initial tables, which complicates the estimation of more detailed tables due to missing data—a phenomenon referred to as the “curse of dimensionality” when augmenting from lower to higher dimensions. We propose an AHP-RAS method to address the substantial data deficiencies encountered in the expansion of input-output tables. The method applies the Analytical Hierarchy Process (AHP) to transform the subjective relative importance of sectors into input coefficients using Pairwise Comparison Matrices (PCM) and eigenvector methods. Subsequently, it incorporates the RAS approach to supplement objective data, thereby integrating subjective judgement and objective information to tackle the curse of dimensionality. Unlike traditional AHP methods, this study employs binary integer programming to decompose large-scale matrices into subsets, making the AHP technique applicable to input-output tables with a broader range of sectors. We employ Monte Carlo simulation techniques to evaluate the robustness of the proposed methodology, specifically assessing the impacts of subjective judgement, objective data utilization, and the variation in sector numbers. Overall, the method overcomes the curse of dimensionality, yielding coefficients within an acceptable error margin, thereby demonstrating a significant advancement in the field of input-output analysis.

StructuredMesh: 3-D Structured Optimization of Façade Components on Photogrammetric Mesh Models Using Binary Integer Programming

StructuredMesh: 3-D Structured Optimization of Façade Components on Photogrammetric Mesh Models Using Binary Integer Programming

Dynamic box assignment planning in log yards

The situation on the log yard changes seasonally and also over the years. The quantities of assortments to be stored, their number and also the type of wood can change. To respond to this, we have developed a dynamic log yard planning model for assigning roundwood to specific ejection boxes and storage areas in order to minimise the overall transport distances of the loaded transportation vehicles on the log yard, including any possible re-allocation of assortments. The study centres on the log yard of a medium-sized hardwood sawmill in Europe, with actual cutting data from a six-month period. We are comparing a multi-period binary integer program with a model that operates on a period per period basis and a solution approach that splits the problem into two subproblems and solves them sequentially. The models undergo testing with decreasing space capacities at the storage boxes on the log yard and are compared. If capacity is continuously decreasing from 100% to 80%, then period per period planning is on average 13% worse than multi-period planning. We also investigate how the solutions change when twice as many or half as many assortments are stored at the log yard. In addition, we study how much the solutions improve when logs can be removed from the storage boxes to clear them and release them for other material in the following period.

Testing initial solutions in a variable neighbourhood search for binary integer programming problems

Testing initial solutions in a variable neighbourhood search for binary integer programming problems

A two-phase method for compaction path planning and control of the impact roller

Compaction efficiency and quality are extraordinarily significant for branch-line airport construction engineering. However, a human-determined compaction path is generally adopted during the compaction, negatively impacting compaction efficiency and quality. A two-phase approach to the compaction path is proposed to address the problem. The first phase focuses on the establishment of a model to optimize the impact roller’s complete-coverage compaction path (CCCP) to improve compaction efficiency. In this phase, the optimization problem of the CCCP is equivalent to the traveling salesman problem (TSP). Next, the optimization of the CCCP is formulated and solved as a binary integer programming problem. Finally, a method for determining the optimal traversal compaction sequence is proposed to obtain the optimal CCCP based on the secondary development of the Gurobi optimizer. In the second phase, to guarantee the compaction quality, the path navigation modulus is designed to precisely control the compaction path. Combining the compaction path planning with the path control, an integrated system is developed to provide a better service for practical earthwork compaction engineering in airport construction. The results of the simulation experiment and field experiment indicate that the CCCP determined by the proposed optimization method in the first phase can improve the compaction efficiency compared to the human-determined compaction path. In addition, the developed system can effectively generate the CCCP. Meanwhile, the developed system can provide a visual path navigation and precise path control during the compaction to ensure the compaction quality, verifying that the proposed method can offer a novel idea for compaction path control.

Schedules and Waitlists and Integer Programs, Oh My!

Summary Student class schedules often involve significant scheduling conflicts and can be challenging to resolve. Three scheduling problems common to students, advisors, and deans at universities include building a schedule, changing schedules for multiple students due to a course cancelation, and finding seats for students on waitlists for multiple courses. This paper presents binary integer programs to solve each, building in complexity.

Penjadwalan staf PT. Adi Sarana Logistik Divisi Outbound Unit Picker dan Dispatcher berdasarkan Minimisasi Jam lembur

PT. Adi Sarana Logistik (PT ASL) is a company engaged in the warehouse and logistics sector, which delivers many packages daily. Previously, manual scheduling took a long time, and there were violations of working hours regulations. The research was conducted at the outbound division, in picker and dispatcher units for leaders and operational staff, where the number of operational staff varies each month, so there are four schedules were produced where this study aims to minimize overtime hours for each level of staffs and units by Goal Programming and Binary Integer Programming which are completed with LINGO 18.0. The results of this study have been implemented in the company, where the schedule only takes a few seconds, while previously, it took 1-2 days. The scheduling carried out in this study is in October 2022, where all employees for leaders and staff in each unit have 22 working days, nine days off, 1 hour of overtime, and follow the rules.

Methods for the graph realization problem

Abstract The graph realization problem seeks an answer to how and under what conditions a graph can be constructed if we know the degrees of its vertices. The problem was widely studied by many authors and in many ways, but there are still new ideas and solutions. In this sense, the paper presents the known necessary and su cient conditions for realization with the description in pseudocode of the corresponding algorithms. Two cases to solve the realization problem are treated: finding one solution, and finding all solutions. In this latter case a parallel approach is presented too, and how to exclude isomorphic graphs from solutions. We are also discussing algorithms using binary integer programming and flow networks. In the case of a bigraphical list with equal out- and in-degree sequences a modified Edmonds–Karp algorithm is presented such that the resulting graph will be always symmetric without containing loops. This algorithm solves the problem of graph realization in the case of undirected graphs using flow networks.

High-speed train timetable optimization based on space–time network model and quantum simulator

Timetable scheduling is a combinatorial optimization problem that presents formidable challenges for classical computers. This paper introduces a pioneering methodology for addressing the high-speed train timetabling problem through quantum computing. Initially, a comprehensive binary integer programming model, grounded in the space–time network, is proposed (M1). To manage the intricacy of model M1, a knapsack problem reformulation is employed to establish a simplified binary integer programming model (M2). Both M1 and M2 are subsequently converted into quadratic unconstrained binary optimization (QUBO) models to harness the potential of quantum computing. Several techniques, including the Gurobi solver, simulated annealing, and the coherent Ising machine (CIM) quantum simulator, are deployed to solve the model across four distinct scenarios of varying complexity. The findings indicate that CIM quantum simulator outperforms the simulated annealing method in terms of solution quality for medium-scale problems.

Profit Maximization for Cache-Enabled Vehicular Mobile Edge Computing Networks

In this paper, we investigate a multiuser cache-enabled vehicular mobile edge computing (MEC) network, where one edge server (ES) has some caching and computing capabilities to assist the task computing from the vehicular users. The introduce of caching into the MEC network significantly affects the system performance such as the latency, energy consumption and profit at the ES, which imposes a critical challenge on the system design and optimization. To solve this challenge, we firstly design the vehicular MEC network in a non-competitive environment by maximizing the profit of the ES with a predetermined threshold of user QoE, and jointly exploit the caching and computing resources in the network. We then model the optimization problem into a binary integer programming problem, and adopt the cross entropy (CE) method to obtain the effective offloading and caching decision with a low complexity. Simulation results are finally presented to verify that the proposed scheme can achieve the near optimal performance of the conventional branch and bound (BnB) scheme, while sharply reduce the computational complexity compared to the BnB.