Mixed-integer Programming Algorithm Research Articles

Determining [formula omitted]- and ([formula omitted], [formula omitted])-robustness of multiagent networks based on heuristic algorithm

The graph properties of r- and (r,s)-robustness are of importance for multiagent networks since these properties ensure consensus among agents even in the presence of a limited number of arbitrarily misbehaving agents, given sufficiently large values for the integers r and s. However, determining the exact solutions of r- and (r,s)-robustness of an arbitrary directed graph has been proven to be computationally complex NP-hard problem. In this paper, we introduce a novel method, named the Determining Robustness based Genetic Algorithm (DRSGA), for approximately calculating the r- and (r,s)-robustness using heuristic algorithm. According to graph theory in mathematical analysis, we first formalize the method for calculating the r- and (r,s)-robustness in directed graphs by utilizing a three-vertex set partition. Then, we transform these methods into a minimization problem of an n-dimensional discrete function and employ DRSGA to obtain an approximate solution. Finally, we validate the efficacy of our algorithm through a series of experiments compared to existing mixed-integer programming algorithms.

365‐day sectional work zone schedule optimization for road networks considering economies of scale and user cost

AbstractThis study proposes a methodology for deriving the optimal work zone schedule for the annual routine maintenance planning in an infrastructure asset management system considering the (i) economies of scale in work zone costs due to work zone synchronization and (ii) user costs across the road network with traffic assignments. A key aspect of the proposed methodology is the ability to derive in detail optimal work zone schedules of realistic‐scale road networks in 100 m sections for 365 days, which is beneficial in practice. To this end, an optimization model of the work zone schedule is newly formulated as a mixed‐integer programming (MIP) problem, and a novel bilevel solution method for the model utilizing the conventional solver Gurobi Optimizer with MIP algorithms such as root relaxation, dual simplex, barrier methods, and cutting planes is proposed. In application examples, the proposed methodology is applied to two real‐world road networks, which confirms that the optimal work zone schedule can be obtained in 313.7 s for a network with 2640, 100 m, sections and in 168,180 s (46 h and 43 min) for a network with 5038, 100 m, sections.

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.

Eco-Coasting Controller Using Road Grade Preview: Evaluation and Online Implementation Based on Mixed Integer Model Predictive Control

Coasting is a common method used in eco-driving to reduce fuel consumption by utilizing kinetic energy. However, in order to avoid excessive computation induced by integer coasting maneuvers, the powertrain model used in eco-driving controllers that rely on look-ahead road information has been oversimplified. This oversimplification assumes that the engine goes to idle when coasting, which significantly limits the fuel-saving potential. To address this issue, we propose an eco-coasting strategy that calculates the optimal timing and duration of coasting maneuvers using road information preview. Different from the engine-idling method, two control-oriented coasting methods, fuel cut-off method and engine start/stop method are formulated for the model-based optimal control. To evaluate and choose the best coasting mechanism for eco-coasting strategy, dynamic programming (DP) is performed to provide the globally optimal performance (i.e., benchmark results) for evaluating the engine-idling method, fuel cut-off method, and engine start/stop method. Based on the offline simulation results, the engine start/stop method consistently outperforms the fuel cut-off method in terms of both fuel consumption and travel time. This is attributed to the engine start/stop method eliminating the engine drag torque during deceleration, despite the additional energy cost required for engine restart being taken into account in the modeling, thus providing a fair evaluation. Then, the online performance of the eco-coasting strategy with engine start/stop mechanism is evaluated using Mixed Integer Model Predictive Control (MIMPC). We propose a tailored mixed-integer programming algorithm to facilitate online implementation. Simulation results show that the proposed eco-coasting strategy achieves near-optimal performance compared to DP and outperforms the rule-based method.

A scheduling model of civil aircraft maintenance stand based on spatiotemporal constraints

PurposeMaintenance stands are the most valuable maintenance resources and provide the necessary maintenance space and maintenance facilities for aircraft maintenance. To expand the maintenance market, maintenance, repair and overhaul (MRO) urgently need to achieve a reasonable schedule between aircraft maintenance requirements and maintenance stand capability to improve aircraft maintenance continuity and reduce the risk of scratching due to aircraft movement. This study aims to design a maintenance stand scheduling (MSS) model based on spatiotemporal constraints to solve the problem of maintenance stand schedules.Design/methodology/approachTo address the problem of maintenance stand schedules, this study introduces mixed-integer programming algorithm to design the MSS model on the basis of classical hybrid flow shop structure. When designing the optimization objective function of MSS modeling, the spatiotemporal constraints are mainly considered. Specifically, first, the spatial constraints between maintenance stands are fully considered so that more aircraft can be parked in the workshop. Second, the optimization objective is designed to minimize the number of aircraft movements by defining multiple maintenance capabilities of the stand. Finally, a solution based on spatiotemporal constraints is proposed in the solving process.FindingsA set of MRO production data from Guangzhou is used as a test data set to demonstrate the effectiveness of the proposed MSS model.Originality/valueThe types of maintenance stands are defined and divided into four categories: fixed stand, temporary stand, half-body stand and engine ground test stand, which facilitates optimal modeling; a new scheduling model is designed considering both temporal constraints and spatial constraints, which can improve both the utilization of maintenance stand and safety (reduce the risk of scratching between aircraft).

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.

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.

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.

Fostering the Reuse of Manufacturing Resources for Resilient and Sustainable Supply Chains

In the current context characterized by turbulent market conditions and the increasing relevance of sustainability requirements, reconfigurable manufacturing systems (RMSs) offer great potentialities for supply chains and networks. While plenty of contributions have addressed RMSs from a technological and system-specific perspective since the mid-1990s, the research interest for the strategic potentialities of RMSs at the supply chain level is recent and mainly related to building supply chains’ resilience and sustainability. Despite the interest, methods to support supply chains to strategically exploit RMSs are still missing, while being highly needed. In this paper, a method—consisting of an index to assess machines reusability and a mixed integer programming (MIP) algorithm—is provided to support the identification of reusable and reconfigurable machine candidates at the early stage of the strategic network design. The overall method allows machines to be compared based on their reusability and geographical locations. The application of the method, as well as an example referring to the production of emergency devices during the COVID-19 pandemic are reported. The theoretical and practical implications of the study are also discussed, and, among others, strategic parameters related to machines have been identified and elaborated as enablers of supply chain reconfigurability; the proposed method supports practitioners in improving supply chain resilience and sustainability. The method also encourages practitioners towards the development and adoption of reconfigurable machines. Finally, this study also has social impacts for local communities and stimulates customer-centric collaboration among companies belonging to similar industries and sectors.

An Edge Server Placement Method Based on Reinforcement Learning.

In mobile edge computing systems, the edge server placement problem is mainly tackled as a multi-objective optimization problem and solved with mixed integer programming, heuristic or meta-heuristic algorithms, etc. These methods, however, have profound defect implications such as poor scalability, local optimal solutions, and parameter tuning difficulties. To overcome these defects, we propose a novel edge server placement algorithm based on deep q-network and reinforcement learning, dubbed DQN-ESPA, which can achieve optimal placements without relying on previous placement experience. In DQN-ESPA, the edge server placement problem is modeled as a Markov decision process, which is formalized with the state space, action space and reward function, and it is subsequently solved using a reinforcement learning algorithm. Experimental results using real datasets from Shanghai Telecom show that DQN-ESPA outperforms state-of-the-art algorithms such as simulated annealing placement algorithm (SAPA), Top-K placement algorithm (TKPA), K-Means placement algorithm (KMPA), and random placement algorithm (RPA). In particular, with a comprehensive consideration of access delay and workload balance, DQN-ESPA achieves up to 13.40% and 15.54% better placement performance for 100 and 300 edge servers respectively.

A Combined Mixed Integer Programming and Deep Neural Network-Assisted Heuristics Algorithm for the Nurse Rostering Problem

A Combined Mixed Integer Programming and Deep Neural Network-Assisted Heuristics Algorithm for the Nurse Rostering Problem

Semantically-Aware Pedestrian Intent Prediction With Barrier Functions and Mixed-Integer Quadratic Programming

We develop algorithms for inferring long-term intentions and parameters of local collision-avoidance behavior of agents in a multiagent system from their trajectories. This problem is challenging because an agent's observed trajectory only partially manifests its long-term task; it also contains adjustments made by the agent to ensure collision avoidance with other agents and obstacles in the environment. Since an observer would have no means to determine the magnitude of these adjustments, it is difficult to isolate the task-oriented component from the observed motion. To circumvent this problem, we model the agent's dynamics using a reactive optimization whose objective function captures the long-term task while its constraints capture collision-avoidance behavior. We develop two robust mixed-integer programming algorithms that infer the task and safety related parameters of this optimization problem from the positions and velocities of the agents. These algorithms are validated on synthetic datasets using parameter estimation errors, displacement errors and computation time as metrics. We further test these algorithms on a dataset of real human trajectories. We show that the learned parameters capture the true underlying pedestrian dynamics by rolling out the learned model and showing similarity between the ground truth trajectories and the reconstructed trajectories.

Utilizing dependence among variables in evolutionary algorithms for mixed-integer programming: A case study on multi-objective constrained portfolio optimization

Mixed-Integer Non-Linear Programming (MINLP) is not rare in real-world applications such as portfolio investment. It has brought great challenges to optimization methods due to the complicated search space that has both continuous and discrete variables. This paper considers the multi-objective constrained portfolio optimization problems that can be formulated as MINLP problems. Since each continuous variable is dependent to a discrete variable, we propose a Compressed Coding Scheme (CCS), which encodes the dependent variables into a continuous one. In this manner, we can reuse some existing search operators and the dependence among variables will be utilized while the algorithm is optimizing the compressed variables. CCS actually bridges the gap between the portfolio optimization problems and the existing optimizers, such as Multi-Objective Evolutionary Algorithms (MOEAs). The new approach is applied to two benchmark suites, involving the number of assets from 31 to 2235. The experimental results indicate that CCS is not only efficient but also robust for dealing with the multi-objective constrained portfolio optimization problems.

Exact computation of maximum rank correlation estimator

SummaryIn this paper we provide a computation algorithm to get a global solution for the maximum rank correlation estimator using the mixed integer programming (MIP) approach. We construct a new constrained optimization problem by transforming all indicator functions into binary parameters to be estimated and show that it is equivalent to the original problem. We also consider an application of the best subset rank prediction and show that the original optimization problem can be reformulated as MIP. We derive the nonasymptotic bound for the tail probability of the predictive performance measure. We investigate the performance of the MIP algorithm by an empirical example and Monte Carlo simulations.

A Biobjective Perspective for Mixed-Integer Programming

A mixed-integer programming (MIP) problem contains not only constraints but also integer restrictions. Integer restrictions divide the feasible region defined by constraints into multiple discontinuous feasible parts with different sizes. Several popular methods (e.g., rounding and truncation) have been proposed to deal with integer restrictions. Although it is easy for these methods to generate an integer, they tend to converge to an integer which is located in a feasible part with a big size. If the optimal solution is not in this feasible part, they are very likely to converge to a local optimal solution due to the loss of diversity of the population. To overcome this shortcoming, a biobjective optimization-based two-phase method is proposed in this article. In the first phase, a measure function is designed to compute the degree that a solution violates integer restrictions. By employing this measure function as the second objective function and removing integer restrictions, a MIP problem is transformed into a constrained biobjective optimization problem (CBOP). It can be proven that the Pareto optimal solution of the transformed CBOP which satisfies integer restrictions is the optimal solution of the original MIP problem. To solve the transformed CBOP, a new comparison rule is designed. After the first phase, the population can approach the Pareto optimal solution which satisfies integer restrictions. Then, the second phase is implemented to enhance the convergence precision and obtain the optimal solution. In addition, we design 12 test problems to verify the effectiveness of the proposed method. The results demonstrate that the proposed method shows better performance against five state-of-the-art evolutionary algorithms for MIP.

Exact Computation of Maximum Rank Correlation Estimator

In this paper we provide a computation algorithm to get a global solution for the maximum rank correlation estimator using the mixed integer programming (MIP) approach. We construct a new constrained optimization problem by transforming all indicator functions into binary parameters to be estimated and show that it is equivalent to the original problem. We also consider an application of the best subset rank prediction and show that the original optimization problem can be reformulated as MIP. We derive the non-asymptotic bound for the tail probability of the predictive performance measure. We investigate the performance of the MIP algorithm by an empirical example and Monte Carlo simulations.

Sharp formulations of nonconvex piecewise linear functions to solve the economic dispatch problem with valve-point effects

Wire drawing effects in a unit with several steam admission valves produce some ripples in the unit cost characteristic. Representing the ripples as sinusoidal terms gives rise to a nonconvex cost characteristic. This paper focuses on the solution of the economic dispatch (ED) problem with the nonconvex cost functions. To this end, this work presents a new framework in which, firstly, the complex problem is tightly transformed into a set of linear programming (LP) problems using an iterative piecewise linear function (PLF) approximation especially developed for the nonconvex terms. Subsequently, five strong models including convex combination, disaggregated convex combination, multiple choice, incremental, and logarithmic techniques are proposed to represent the set of built LP problems as a mixed-integer programming (MIP) problem which efficiently can be solved by a robust powerful algorithm. Then, the obtained solution from the MIP algorithm is used to warm-start an enhanced nonlinear programming (NLP) model and to further improve the solution. In extensive experiments, we compare the performance of the presented methods in terms of solution quality, computational efficiency, and consistency with other approaches in the literature of the nonconvex ED. The tight PLF approximation and the five sharp and generally locally ideal MIP formulation techniques in conjunction with the existing efficient MIP and NLP algorithms result in the strong solution framework which can find a global or a virtually global solution and surpass the state-of-the-art methods in the area of the nonconvex ED in all considered case studies.

Fast mixed integer optimization (FMIO) for high dose rate brachytherapy

The purpose of this work was to develop an efficient quadratic mixed integer programming algorithm for high dose rate (HDR) brachytherapy treatment planning problems and integrate the algorithm into an open-source Monte Carlo based treatment planning software, RapidBrachyMCTPS. The mixed-integer algorithm yields a globally optimum solution to the dose volume histogram (DVH) based problem and, unlike other methods, is not susceptible to local minimum trapping. A hybrid linear-quadratic penalty model coupled to a mixed integer programming model was used to optimize treatment plans for 10 prostate cancer patients. Dose distributions for each dwell position were calculated with RapidBrachyMCTPS with type A uncertainties less than 0.2% in voxels within the planning target volume (PTV). The optimization process was divided into two parts. First, the data was preprocessed, in which the problem size was reduced by eliminating voxels that had negligible impact on the solution (e.g. far from the dwell position). Second, the best combination of dwell times to obtain a plan with the highest score was found. The dwell positions and dose volume constraints were used as input to a commercial mixed integer optimizer (Gurobi Optimization, Inc.). A penalty-based criterion was adopted for the scoring. The voxel-reduction technique successfully reduced the problem size by an average of 91%, without loss of quality. The preprocessing of the optimization process required on average 4 s and solving for the global maximum required on average 33 s. The total optimization time averaged 37 s, which is a substantial improvement over the ∼15 min optimization time reported in published literature. The plan quality was evaluated by evaluating dose volume metrics, including PTV D 90, rectum and bladder D 1cc and urethra D 0.1cc . In conclusion, fast mixed integer optimization is an order of magnitude faster than current mixed-integer approaches for solving HDR brachytherapy treatment planning problems with DVH based metrics.

New models and efficient methods for single-product disassembly lot-sizing problem with surplus inventory decisions

ABSTRACT This paper addresses the problem of disassembly lot-sizing for the single-product type. Due to some specific characteristics of disassembly systems, surplus inventory can be generated while satisfying the demand for the components. Disposal decisions are considered here to avoid inventory accumulations throughout the planning horizon. Three new mixed-integer programming (MIP) formulations are proposed to model the problem. The formulations differ from each other concerning the quality of the lower bound provided by their linear relaxation, which is an important issue in MIP resolution methods. Two efficient heuristics are also investigated for real-case applications when MIP algorithms are not relevant. The three formulations and the performance of the heuristics are compared based on new randomly generated instances for disassembly lot-sizing problems. As a managerial insight, the disposal decisions in disassembly lot-sizing models are relevant to save inventory costs.

Security-Constraint Unit Commitment for AC/DC Transmission Systems with Voltage Stability Constraint

Due to the inherent characteristics of weaker voltage supporting ability, line-commutated converter based HVDC technologies have significant effects on AC/DC hybrid power grid’s voltage stability. These has led to new challenges for power grid operators in terms of ensuring power system security. To address these challenges, a unit commitment of receiving-end in AC/DC hybrid grid is presented in this paper. In the proposed model, we employ static voltage stability constraints to guarantee enough voltage supporting capacity from thermal plants at HVDC feed-in area. Based on the characteristics of the model, Benders decomposition and mixed integer programming algorithm are used to get the optimal transmission power of HVDC and schedule of thermal generators. The study is done by considering IEEE-39 and Jiangsu power grid in eastern China, containing two and three HVDC transmission projections respectively. Numerical results on two benchmark problems illustrate the effectiveness of the proposed algorithm, both in terms of convergence rate and solution quality.