Integer Linear Programming Solver Research Articles

Sizing and energy management of grid-connected hybrid renewable energy systems based on techno-economic predictive technique

This study intends to construct and optimally run a grid-connected hybrid renewable energy system (HRES) powering a residential building. A special techno-economic multi-objective optimization technique is used for sizing the HRES. In addition, an energy management strategy (EMS) is established as a distinct multi-objective optimization problem to minimize degradation and operating costs while improving system performance. A Bi-level mixed integer non-linear programming (BMINLP) is the framework used to formulate the two-optimization problems. Sizing problem is characterized by the higher level, on contrast; the nested EMS problem within the constraints of the size problem is presented on the lower level. For this investigation, the problem is executed via the MATLAB program. The global optimization toolbox is applied via the Multi-Objective Genetic Algorithm (MOGA) to solve the sizing optimization. While the EMS is executed using the "Intlinprg" mixed integer linear programming (MILP) solver. The technical and economic performance parameters such as degradation, renewable energy fraction (REF), operating, maintenance, and investment costs are evaluated in this study. The primary results reveal that the summer week encounters the lowest total cost and the highest REF, at roughly 99484 $ and 60 %, respectively. Furthermore, the investigation shows that the lowest degradation value attained in the same week with approximately 50.

Exact and heuristic solutions for the prize‐collecting geometric enclosure problem

AbstractIn the prize‐collecting geometric enclosure problem (PCGEP), a set of points in the plane is given, each with an associated benefit. The goal is to find a simple polygon with vertices in that maximizes the sum of the benefits of the points of enclosed by minus the perimeter of multiplied by a given nonnegative cost. The PCGEP is NP‐complete and has applications to land surveying for exploration or preservation of natural resources. In this paper, we develop the first heuristic, called PCGEP‐GR, for the PCGEP and revisit a previously proposed integer linear programming (ILP) model to solve it to optimality. We conducted a comprehensive experimental study of that heuristic and an exact algorithm based on the ILP model. We show that a new set of constraints, together with the previous set, is necessary to guarantee the correctness of the ILP model and introduce preprocessing strategies that allow us to prove optimality 40% faster on average. The proposed heuristic is able to reach the optimum in 32% of our benchmark instances and, for those with unknown optima, PCGEP‐GR was found better than or at least as good solutions as the ones obtained by the cplex ILP solver in 54% of the cases. Notwithstanding these positive results, the design of effective heuristics for the PCGEP proved to be very challenging, which also led us to obtain a result that provides the theoretical foundation for future advances in the study of this problem.

A cut-and-solve algorithm for virtual machine consolidation problem

The virtual machine consolidation problem attempts to determine which servers to be activated, how to allocate virtual machines to the activated servers, and how to migrate virtual machines among servers such that the summation of activated, allocation, and migration costs is minimized subject to the resource constraints of the servers and other practical constraints. In this paper, we first propose a new mixed integer linear programming formulation for the virtual machine consolidation problem. We show that compared with existing formulations, the proposed formulation is much more compact in terms of smaller numbers of variables or constraints, which makes it suitable for solving large-scale problems. We then develop a cut-and-solve algorithm, a tree search algorithm to efficiently solve the virtual machine consolidation problem to optimality. The proposed cut-and-solve algorithm is based on a novel relaxation of the virtual machine consolidation problem that provides a stronger lower bound than the natural continuous relaxation of the virtual machine consolidation problem, making a smaller search tree. By extensive computational experiments, we show that (i) the proposed formulation significantly outperforms existing formulations in terms of solution efficiency; (ii) compared with standard mixed integer linear programming solvers, the proposed cut-and-solve algorithm is much more efficient; and (iii) compared with an existing heuristic algorithm, the proposed cut-and-solve algorithm is better able to balance workload distribution across servers and achieve higher resource utilization.

Traveling itinerary problem in a scheduled multimodal transportation network for a fixed sequence of cities.

Developing an efficient and economical journey plan in multimodal transportation networks is of significant and fast-growing importance, but it is still an annoying experience for a traveler. This paper aims to find the journey plan at a combined cross-border and inter-regional level when visiting a sequence of cities while utilizing several transport modes to reduce travel costs and planning time. We study a traveling itinerary problem in a scheduled multimodal transportation network with constraints on both arcs and nodes as a new extension of the shortest path problem. We formulate a 0-1 integer linear programming model for the traveling itinerary problem and develop an exact algorithm that finds a combined cross-border and inter-regional low costs journey plan. We present case studies based on real-world transport data to illustrate the usefulness and computational efficiency of the proposed approaches. We compare the results with the previously proposed approach to demonstrate the benefits of multimodal journeys. Finally, we compare the results with the solution obtained by the general-purpose 0-1 integer linear programming solver to evaluate the computational time.

Minimum Cost Flow-Based Integrated Model for Electric Vehicle and Crew Scheduling

Vehicle and crew scheduling is vital in public transit planning. Conventionally, the issues are handled sequentially as the vehicle scheduling problem (VSP) and crew scheduling problem (CSP). However, integrating these planning steps offers additional flexibility, resulting in improved efficiency compared with sequential planning. Given the ever-growing market share of electric buses, this paper introduces a new model for integrated electric VSP and CSP, called EVCSPM. This model employs the minimum cost flow formulations for electric VSP, set partitioning for CSP, and linking constraints. Due to the nonlinear integer property of EVCSPM, we propose a method that hybrids a matching-based heuristic and integer linear programming solver, GUROBI. The numerical results demonstrate the efficiency of our methodology, and the integrated model outperforms the sequential model in real-life scenarios.

Location Privacy-Aware Offloading for MEC-Enabled IoT: Optimality and Heuristics

With the rapid development of 5G and the Internet of Things (IoT), cloud-based access mode is applied more and more in IoT scenarios. The emerging IoT applications put forward higher requirements on energy consumption and processing capacity of the network, as well as more strict privacy restrictions. The emergence of mobile edge computing solves the aforementioned user experience problems, which greatly improves execution efficiency and saves a lot of energy. However, existing studies pay more attention to issues such as energy consumption and delay, but ignore the privacy and imbalanced server load problems that mobile edge computing may cause. This paper made bandwidth resource allocation and task offloading decisions for multiple users via joint optimization, provided the privacy requirements of IoT terminals and load balancing requirements are satisfied. The objective was to minimize the total energy consumption of all terminal devices. By modeling the problem as an integer linear programming problem, the optimal solution is obtained. Considering the high computational complexity of solving integer linear programming problems, a more practical heuristic algorithm was proposed. The simulation results showed the effectiveness of the proposed optimal and heuristic schemes in reducing energy consumption, and demonstrated the importance of privacy protection.

ILP-based Substrate Routing with Mismatched Via Dimension Consideration for Wire-bonding FBGA Package Design

With the rapidly growing demand for system-level integration, package substrates have become one of the most important carriers in semiconductor industry. Fine pitch ball grid array (FBGA) packaging is a widely used technology thanks to its relative cost-effectiveness compared to other advanced packaging technologies. In addition, it is also widely used in space-constrained applications, such as mobile and handheld devices. These packaging substrate interconnections are usually customized by layout engineers taking many complex and stringent design rules into consideration. However, fully net-by-net manual design for FBGA is time-consuming and error-prone. In this article, we propose an integer linear programming (ILP)-based router for wire-bonding FBGA packaging design. Our ILP formulation not only can handle design-dependent constraints but also take the problem of mismatched via dimension into account, which is caused by the mechanical processes and greatly increases design complexity. In addition to the ILP formulation for substrate routing, three optimization stages and several ILP constraint reduction techniques are also developed to boost the run time of ILP solver. Experimental results indicate that the proposed framework can achieve high routing completion rates, which could effectively reduce the cycle time of substrate layout design. In addition, in combination with the proposed optimization strategies, 278× speedup can be achieved compared to the ILP constraint optimized router.

Train rescheduling for large-scale disruptions in a large-scale railway network

This paper studies the problem of rescheduling trains in a large-scale railway network with the characteristics of long distance, long time horizon and a large number of trains, where a disruption causes the paralysis of a significant part of the network for a long duration. As rescheduling measures we consider train reordering and retiming as well as the option of rerouting trains along alternative paths in the railway network. Although rerouting was not previously employed in large-scale long-distance networks, we show its benefit in reducing passenger delays. We formulate the problem as an integer linear programming (ILP) model on a space–time network with the goal of minimizing the total passenger delay and the number of passengers that could not reach their destination. In order to effectively solve the ILP model for real-world instances, we propose a heuristic algorithm (LR-H), based on the Lagrangian relaxation (LR) of a subset of constraints in the ILP model. LR allows decomposing the problem into a series of independent train-based subproblems which are easy to solve. Due to the large number of constraints and to cope with the real-time requirement, LR-H employs dynamic constraint-generation.We tested LR-H on railway networks of different sizes under several disruption scenarios: first, we compared the results obtained by LR-H on a small-size instance with those found by the general-purpose ILP solver GUROBI, showing that LR-H can find near-optimal solutions in significantly shorter computing times. Then, we applied LR-H to a real-world instance of a railway network in China with 350 trains in different disruption scenarios. The experimental results show that, LR-H can obtain near-optimal solutions with an average optimality gap of 2.27% in an average computing time of about 300 s.

Renewable Hydrogen Energy Communities layouts towards off-grid operation

Solar hydrogen technology, i.e. producing green hydrogen by electrolysis fed by solar panels, is gaining attention as studies show it can compete with traditional electric batteries. Contemporary, the interest in the realization of Renewable Energy Community driven by the recent adoption in almost all the EU Countries of the RED II Directive is increasing. To match innovative technologies and new business models making the energy demand and the production closer in terms of time and space, the feasibility of Renewable Hydrogen Energy Community is explored. To determine the profitability of these solutions and size and operate the energy system, energy and economic analyses are needed as well as the optimization of its performance. A building complex with 180 kWp of PhotoVoltaics was studied using hourly real data on energy loads and production. Storage capacities ranging from 500 to 2000 kWh were simulated for hydrogen and electric battery options. The cost of investment and operation was also analyzed for the years 2020, 2030, and 2040 to evaluate changes in technology readiness level as well as accounting for the strong changes in electricity tariff due to the geopolitical issues effects on the market. The analysis was conducted using the DECAPLAN™ digital platform, which employs a mixed integer linear programming solver. Finally, the dispatch on hourly base has been compared for the same two months in 2019, 2020 and 2021 corresponding to pre, during and after pandemic restrictions.

Synthesizing MILP Constraints for Efficient and Robust Optimization

While mixed integer linear programming (MILP) solvers are routinely used to solve a wide range of important science and engineering problems, it remains a challenging task for end users to write correct and efficient MILP constraints, especially for problems specified using the inherently non-linear Boolean logic operations. To overcome this challenge, we propose a syntax guided synthesis (SyGuS) method capable of generating high-quality MILP constraints from the specifications expressed using arbitrary combinations of Boolean logic operations. At the center of our method is an extensible domain specification language (DSL) whose expressiveness may be improved by adding new integer variables as decision variables, together with an iterative procedure for synthesizing linear constraints from non-linear Boolean logic operations using these integer variables. To make the synthesis method efficient, we also propose an over-approximation technique for soundly proving the correctness of the synthesized linear constraints, and an under-approximation technique for safely pruning away the incorrect constraints. We have implemented and evaluated the method on a wide range of benchmark specifications from statistics, machine learning, and data science applications. The experimental results show that the method is efficient in handling these benchmarks, and the quality of the synthesized MILP constraints is close to, or higher than, that of manually-written constraints in terms of both compactness and solving time.

Access mechanism for period flows of non-deterministic end systems for time-sensitive networks

The IEEE 802.1Qbv standard schedules time-triggered (TT) flows (i.e., period flows) in a fixed TT Window each period. However,period flows generated by non-deterministic end systems exhibit significant jitter, whichleads to a mismatch between the generation times and the scheduled TT Windows. In the worst case scenario, this mismatch can cause an additional send delay of approximately one period in the flow. In this study,we model the send delay issue due to the maximum send delay requirement for all frames in a period flow not being satisfied simultaneously, and measure the jitter of period flows in a typical non-deterministic end system. Moreover, we propose an access mechanism for jittered period flows to schedule multiple conflict-free TT Windows in each period of flows at the source end system and control the send delay within the required delay tolerance. This mechanism enables deterministic access to jittered period flows, providing a prerequisite for reliable end-to-end transmission in the network. Moreover, this mechanism adopts a multi-objective integer linear programming (MILP) solver to optimize the TT Windows schedule. Furthermore, we establish the constraints and objective functions for the MILP solver and evaluate the mechanism with actual sampled frames in a real non-deterministic end system. Compared with the conventional fixed single TT Window and worst-case delay analysis mechanisms, the proposed mechanism satisfies the send delay requirements and considerably reduces the buffer usage at the source end system.

Conditional TMDTO as a MILP Instance

Conditional Time-Memory-Data Trade-off (TMDTO) attack given by Biryukov and Shamir can be reduced to the following problem: “Find the minimum number of state bits that should be fixed in order to recover the maximum number of state bits by utilizing the keystream bits and value of rest of the state bits”. As per our literature survey, existing algorithms search for state bits that should be fixed (as minimum as possible) in order to recover the maximum possible state bits directly through the keystream bits. However, those algorithms are cipher specific and require extensive manual effort in analyzing the keystream bit equations. In this manuscript, we have constructed an automated framework that is easy to implement and solves the above problem (for the case when bits are fixed to 0) for any NLFSR based stream cipher with better complexity, thereby reducing manual efforts. However, we do not claim any global optimum for fixed bits. We tried to reduce the number of fixed bits as much as possible. To show that our algorithm is applicable to a majority of NLFSR based stream ciphers, we implement it on three different stream ciphers: LIZARD, GRAIN-128a and ESPRESSO. It improves all existing TMDTO results on these ciphers. The framework involves modelling keystream bit equations into a set of linear constraints, which is then solved by using a Mixed Integer Linear Programming (MILP) solver, Gurobi. The advantages of our automated framework over other methods are that we can achieve better results with far less effort, and it can be applied to any stream cipher of a similar structure with very ease. To the best of our knowledge, our MILP model is the first work that converts the conditional TMDTO of a stream cipher into a linear optimization problem. As a consequence, for LIZARD cipher, we reduce the number of fixed bits by 20 bits from the previous best result when the number of recovered bits is 18. In the case of GRAIN-128a, the highest reduction in the number of fixed bits is by 34 bits when the number of recovered bits is 35. Lastly, for ESPRESSO cipher, the reduction is by 7 bits when the number of recovered bits is 35.

Minimizing the makespan and carbon emissions in the green flexible job shop scheduling problem with learning effects

One of the most difficult challenges for modern manufacturing is reducing carbon emissions. This paper focuses on the green scheduling problem in a flexible job shop system, taking into account energy consumption and worker learning effects. With the objective of simultaneously minimizing the makespan and total carbon emissions, the green flexible job shop scheduling problem (GFJSP) is formulated as a mixed integer linear multiobjective optimization model. Then, the improved multiobjective sparrow search algorithm (IMOSSA) is developed to find the optimal solution. Finally, we conduct computational experiments, including a comparison between IMOSSA and the nondominated sorting genetic algorithm II (NSGA-II), Jaya and the mixed integer linear programming (MILP) solver of CPLEX. The results demonstrate that IMOSSA has high precision, good convergence and excellent performance in solving the GFJSP in low-carbon manufacturing systems.

Hierarchical multi-agent control framework for energy efficiency and carbon emission reduction in multi-zone buildings

Centralized optimization approaches to trade-off between comfort, energy and carbon emissions are widely adopted in the control of building heating, ventilation, and air-conditioning (HVAC) systems. However, the high computational complexity in each control horizon, single point of failure risks, and the limited number of zones to control make the centralized approach unattractive. Unlike centralized controls, multi-agent control (MAC) systems are flexible and modular. This paper proposes a scalable multi-agent based distributed approach for optimized control of a multi-zone smart building based on a set of local agents which represent individual zones in the building, coordinated by a central agent. For each control horizon, the coordinator minimizes the overall carbon emissions and assigns an individual energy budget to each local agent. Each local agent minimizes the discomfort in its zone while respecting the energy budget assigned by the coordinator. We propose a heuristic search based on a genetic algorithm to find the optimized control sequences in each zone, and formulate an integer linear programming (ILP) model for the coordinator problem which can be solved using an ILP solver. For a representative winter test day, the proposed methodology gave an energy savings of 8.8% and reduced the carbon footprint by 23.4%.

A bi-criteria moving-target travelling salesman problem under uncertainty

This article concerns a variant of moving target travelling salesman problem where the number and locations of targets vary with time and realizations of random trajectories. Managerial objectives are to maximize the number of visits to different targets and to minimize the total travel distance. Employing a linear value function for finding supported Pareto-efficient solutions, we develop a two-stage stochastic programming model. We propose an iterative randomized dynamic programming (RDP) algorithm which converges to a global optimum with probability one. Each iteration in RDP involves a randomized backward and forward recursion stage as well as options for improving any given schedule: swaps of targets and optimization of timing for visits. An integer linear programming (ILP) model is developed and solved by a standard ILP solver to evaluate the performance of RDP on instances of real data for scheduling an environmental surveillance boat to visit ships navigating in the Baltic Sea. Due to a huge number of binary variables, the ILP model in practice becomes intractable. For small to medium size data sets, the Pareto-efficiency of solutions found by RDP and ILP solver are equal within a reasonable tolerance; however, RDP is significantly faster and able to deal with large-scale problems in practice.

MULTI-OBJECTIVE OPTIMIZATION MODEL FOR A MULTI-DEPOT MIXED FLEET ELECTRIC VEHICLE SCHEDULING PROBLEM WITH REAL-WORLD CONSTRAINTS

This paper presents the problem of public transport planning in terms of the optimal use of the available fleet of vehicles and reductions in operational costs and environmental impact. The research takes into account the large fleet of vehicles of various types that are typically found in large cities, including the increasingly widely used electric buses, many depots, and numerous limitations of urban public transport. The mathematical multi-criteria mathematical model formulated in this work considers many important criteria, including technical, economic, and environmental criteria. The preliminary results of the Mixed Integer Linear Programming solver for the proposed model on both theoretical data and real data from urban public transport show the possibility of the practical application of this solver to the transport problems of medium-sized cities with up to two depots, a heterogeneous fleet of vehicles, and up to about 1500 daily timetable trips. Further research directions have been formulated with regard to larger transport systems and new dedicated heuristic algorithms.

Optimizing Number, Placement, and Backhaul Connectivity of Multi-UAV Networks

Multi unmanned aerial vehicle (UAV) network is a promising solution to providing wireless coverage to ground users in challenging rural areas (such as Internet of Things (IoT) devices in farmlands), where the traditional cellular networks are sparse or unavailable. A key challenge in such networks is the 3-D placement of all UAV base stations (BSs) such that the formed multi-UAV network: 1) utilizes a minimum number of UAVs while ensuring—2) backhaul connectivity directly (or via other UAVs) to the nearby terrestrial BS; and 3) wireless coverage to all ground users in the area of operation. This joint backhaul-and-coverage-aware drone deployment (BoaRD) problem is largely unaddressed in the literature and, thus, is the focus of this article. We first formulate the BoaRD problem as integer linear programming (ILP). However, the problem is NP-hard and, therefore, we propose a low complexity algorithm with a provable performance guarantee to solve the problem efficiently. Our simulation study shows that the Proposed algorithm performs very close to that of the Optimal algorithm (solved using ILP solver) for smaller scenarios, where the area size and the number of users are relatively small. For larger scenarios, where the area size and the number of users are relatively large, the proposed algorithm greatly outperforms the baseline approaches—Backhaul-aware Greedy and random algorithm, respectively, by up to 17% and 95% in utilizing fewer UAVs while ensuring 100% ground-user coverage and backhaul connectivity for all deployed UAVs across all considered simulation setting.

SuperBall: A New Approach for MILP Modelings of Boolean Functions

Mixed Integer Linear Programming (MILP) solver has become one of the most powerful tools of searching for cryptographic characteristics. It has great significance to study the influencing factors of the efficiency of MILP models. For this goal, different types of MILP models should be constructed and carefully studied. As Boolean functions are the fundamental cryptographic components, in this paper, we study the descriptive models of Boolean functions. Here, a descriptive model of a Boolean function refers to a set of integer linear inequalities, where the set of the binary solutions to these inequalities is exactly the support of this Boolean function. Previously, it is hard to construct various types of descriptive models for study, one important reason is that only a few kinds of inequalities can be generated. On seeing this, a new approach, called SuperBall, is proposed to generate inequalities. The SuperBall approach is based on the method of undetermined coefficients, and it could generate almost all kinds of inequalities by appending appropriate constraints. Besides, the Sasaki-Todo Algorithm is also improved to construct the descriptive models from a set of candidate inequalities by considering both their sizes and strengths, while the strengths of descriptive models have not been considered in the previous works. As applications, we constructed several types of descriptive models for the Sboxes of Liliput, SKINNY-128, and AES. The experimental results first prove that the diversity of the inequalities generated by the SuperBall approach is good. More importantly, the results show that the strengths of descriptive model do affect the efficiencies, and although there is not a type of descriptive model having the best efficiency in all experiments, we did find a specific type of descriptive model which has the minimal size and relatively large strength, and the descriptive models of this type have better efficiencies in most of our experiments.

Speeding up neural network robustness verification via algorithm configuration and an optimised mixed integer linear programming solver portfolio

Despite their great success in recent years, neural networks have been found to be vulnerable to adversarial attacks. These attacks are often based on slight perturbations of given inputs that cause them to be misclassified. Several methods have been proposed to formally prove robustness of a given network against such attacks. However, these methods typically give rise to high computational demands, which severely limit their scalability. Recent state-of-the-art approaches state the verification task as a minimisation problem, which is formulated and solved as a mixed-integer linear programming (MIP) problem. We extend this approach by leveraging automated algorithm configuration techniques and, more specifically, construct a portfolio of MIP solver configurations optimised for the neural network verification task. We test this approach on two recent, state-of-the-art MIP-based verification engines, mathrm {MIPVerify} and mathrm {Venus}, and achieve substantial improvements in CPU time by average factors of up to 4.7 and 10.3, respectively.

A Penalty Branch-and-Bound Method for Mixed Binary Linear Complementarity Problems

Linear complementarity problems (LCPs) are an important modeling tool for many practically relevant situations and also have many important applications in mathematics itself. Although the continuous version of the problem is extremely well-studied, much less is known about mixed-integer LCPs (MILCPs) in which some variables have to be integer-valued in a solution. In particular, almost no tailored algorithms are known besides reformulations of the problem that allow us to apply general purpose mixed integer linear programming solvers. In this paper, we present, theoretically analyze, enhance, and test a novel branch-and-bound method for MILCPs. The main property of this method is that we do not “branch” on constraints as usual but by adding suitably chosen penalty terms to the objective function. By doing so, we can either provably compute an MILCP solution if one exists or compute an approximate solution that minimizes an infeasibility measure combining integrality and complementarity conditions. We enhance the method by MILCP-tailored valid inequalities, node selection strategies, branching rules, and warm-starting techniques. The resulting algorithm is shown to clearly outperform two benchmark approaches from the literature. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: M. De Santis acknowledges support within the project RM120172A2970290, which has received funding from Sapienza, University of Rome. M. Schmidt thanks the Deutsche Forschungsgemeinschaft (DFG) for its support within project A05 and B08 in the “SFB TRR 154 Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks.” L. Winkel is supported by the DFG within the Research Training Group 2126: “Algorithmic Optimization.” Supplemental Material: The online supplementary material is available at https://doi.org/10.1287/ijoc.2022.1216 .