Integer Constraint Programming Research Articles

Allocating Robots/Cobots to Production Systems for Productivity and Ergonomics Optimization

Collaboration between humans and robots has great promise in manufacturing systems. The utilization of cobots in a manufacturing system can improve both productivity and ergonomics. In this paper, we study the problem of how to allocate limited cobot/robots to manufacturing systems with multiple workstations so that an integrated performance measure, considering both productivity and ergonomics is optimized. Previous work on cobot/robot allocation in manufacturing systems focus on the decomposition of tasks for a single workstation into multiple work elements, and then split them between human and robots, rather than studying multi-machine systems. To bridge this gap, we consider the allocation of cobots/robots to a multi-stage manufacturing system. Specifically, we establish an integrated performance measure and formulate cobot/robot allocation into a constraint integer programming problem. With this formulation, we obtain the optimal allocation of one available cobot/robot in simulated production systems, based on the integrated performance measure of productivity and ergonomics. Furthermore, the allocation problems of production systems with multiple cobots/robots is considered and solved with a scalable algorithm. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Collaborative robots and independent robots are increasingly applied to manufacturing production systems. However, how to optimally allocate both types of robots considering both productivity and ergonomics influence has not been well studied. In this article, we established a practical optimization method to allocate cobots/robots to different workstations and split the work between cobot and human in one workstation when there are multiple workstations and a limited number of available cobots/robots in the manufacturing systems. Based on various real-world scenarios, we inferred useful insights for the robot/cobot allocation problem. To deal with the computational load when the number of workstations is large, a scalable optimization algorithm is also adopted. The case study results demonstrated the effectiveness of the proposed approach.

Global optimization of mixed-integer nonlinear programs with SCIP 8

AbstractFor over 10 years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that are particular to MINLP solving in SCIP. Further, difficulties in benchmarking global MINLP solvers are discussed and a comparison with several state-of-the-art global MINLP solvers is provided.

Enabling Research through the SCIP Optimization Suite 8.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP . The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP ’s main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP ’s application as a research tool and as a platform for further developments. Furthermore, this article gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP .

Optimal energy management of a solar-assisted heat pump water heating system with a storage system

Water heating is the fourth largest energy consumer in the commercial building sector, accounting for >40 % of the energy consumed in South Africa. Traditional electric storage tank water heaters (ESTWHs) have been the most frequently used systems in the past, owing to their low electricity costs and implementation. It was low enough at that time that energy costs were not considered. These systems have grown increasingly hostile to consumers as power prices have risen, particularly to the undesirable high morning and afternoon peaks.The indirect-expansion solar-assisted heat pump water heater (IDX-SAHPWH), for the commercial sector, to reduce energy consumption of hot water production while maintaining the users' thermal comfort level, has been proposed in this paper. The system is operated under an optimal energy control scheme, integrated with the load shifting by time-of-use (TOU) pricing plan. The comparison of the performance of the proposed optimally controlled system and the electric storage tank water heater (ESTWH) was performed through the simulation approach using the Solving Constraint Integer Programs (SCIP) solver, in the MATLAB interface optimization toolbox. The simulations reveal that the proposed system operates during off-peak hours, when power prices are lower, as compared to ESTWH system.The techno-economic analysis was conducted and presented for a project lifespan of 20 years. The proposed optimally controlled system demonstrates the cost savings obtained from the winter and summer seasons, as well as annual, as 76.0 %, 75.6 % and 75.8 %, respectively. The break-even point of the project is during the 9th month of the first year of the project, with a possible savings of 71.5 % at the end of the project's lifetime.

Building Floorplan Reconstruction Based on Integer Linear Programming

The reconstruction of the floorplan for a building requires the creation of a two-dimensional floorplan from a 3D model. This task is widely employed in interior design and decoration. In reality, the structures of indoor environments are complex with much clutter and occlusions, making it difficult to reconstruct a complete and accurate floorplan. It is well known that a suitable dataset is a key point to drive an effective algorithm, while existing datasets of floorplan reconstruction are synthetic and small. Without reliable accumulations of real datasets, the robustness of methods to real scene reconstruction is weakened. In this paper, we first annotate a large-scale realistic benchmark, which contains RGBD image sequences and 3D models of 80 indoor scenes with more than 10,000 square meters. We also introduce a framework for the floorplan reconstruction with mesh-based point cloud normalization. The loose-Manhattan constraint is performed in our optimization process, and the optimal floorplan is reconstructed via constraint integer programming. The experimental results on public and our own datasets demonstrate that the proposed method outperforms FloorNet and Floor-SP.

Co-digestion of water hyacinth, municipal solid waste and cow dung: A methane optimised biogas–liquid petroleum gas hybrid system

Fossil fuels are still the major source of energy in developing countries, howbeit expensive and environmentally unsustainable. Co-digestion substrate proportions and the respective biogas potentials for a huge number of biomaterials for anaerobic digestion are yet to be ascertained let alone optimised. This paper presents a novel methane-optimised biogas–liquid petroleum gas hybrid system concept. Herein this research, biogas is produced from the anaerobic co-digestion of water hyacinth, municipal solid waste and cow dung. A model that incorporated seasonal variations of biomass feedstocks was developed; an optimisation problem was formulated and solved using the Optimisation Interface tool (OptiTool) in combination with the Solving Constraint Integer Programs (SCIP) toolbox in Matrix Laboratory (MATLAB). The biogas production reactions are optimised in such a way that the methane component of the biogas is maximised, and the other components minimised by the integration of a model which necessitates the feed in of optimal substrate masses as per the ratios ascertained for the substrates considered thereby yielding a high quality combustible biogas product. The methane-optimised biogas is channelled towards some community gas demand and liquid petroleum gas comes in to fill the discrepancy between the methane-optimised biogas and the gas demand. Consideration of seasonality changes in the availability of substrates in the modelling and optimisation led to an increase of 174.58% in annual biogas output. A 6.97% annual lowest cost savings was realised in winter and 18.24% annual highest cost savings was realised in summer from the methane-optimised biogas–liquid petroleum gas hybrid system.

Implementing the branch-and-cut approach for a general purpose Benders’ decomposition framework

Benders’ decomposition is a popular mathematical and constraint programming algorithm that is widely applied to exploit problem structure arising from real-world applications. While useful for exploiting structure in mathematical and constraint programs, the use of Benders’ decomposition typically requires significant implementation effort to achieve an effective solution algorithm. Traditionally, Benders’ decomposition has been viewed as a problem specific algorithm, which has limited the development of general purpose algorithms and software solutions. This paper presents a general purpose Benders’ decomposition algorithm that is capable of handling many classes of mathematical and constraint programs and provides extensive flexibility in the implementation and use of this algorithm. A branch-and-cut approach for Benders’ decomposition has been implemented within the constraint integer programming solver SCIP using a plugin-based design to allow for a wide variety of extensions and customisations to the algorithm. The effectiveness of the Benders’ decomposition algorithm and available enhancement techniques is assessed in a comprehensive computational study.

An Optimal Generation Scheduling Approach Based on Linear Relaxation and Mixed Integer Programming

This paper proposes an optimal generation scheduling approach based on linear relaxation and mixed integer programming, which is used to solve the generation dispatch problem. The quadratic transmission loss constraint of each transmission line is converted into linear constraints by using the linear relaxation and mixed integer programming technique. Consequently, the original optimal generation scheduling problem is formulated as a quadratic programming or mixed integer quadratic programming problem that can be solved by commercial optimization solver. In order to improve the efficiency of algorithm, this paper further analyses the generation scheduling model and deletes the redundant variables and constraints. Three test systems, including IEEE 30-node system, IEEE 118-node system, and Polish 2746-node system, are employed to examine the effectiveness of the proposed method. The comparative results obtained by the proposed method, quadratically constrained quadratic programming method (QCQP), and solving constraint integer programs solver (SCIP) verify the effectiveness of the proposed method in solving the optimal generation scheduling problem.

Optimal tank sizing and operation of energy-water supply systems in residences

Energy and water insecurities are global challenges, especially in arid and semi-arid regions. This paper proposes an optimal energy-water nexus management approach in residences using alternative energy and water resources, these alternatives are rainwater harvesting system, greywater recycling system, water storage, and gravity-fed distribution system. The Solving Constraint Integer Programming (SCIP) solver, in MATLAB’s OPTI toolbox, is used to solve the multi-objective optimization problem. Simulation results show that the optimal tank sizing and system operations will minimize the capital and operational cost of the system. The solver produced a potable water savings of 20.5% and an energy savings of 62.54%.

Model predictive control strategy applied to different types of building for space heating

In recent years, the concept of energy-efficient buildings has attracted widespread attention due to growing energy consumption in different types of buildings. The application of thermal energy storage (TES) systems, especially latent heat energy storage (LHES), has become a promising approach to improve thermal efficiency of buildings and hence reduce CO2 emissions. One way to achieve this, could be by implementing a model predictive control (MPC) strategy, using weather and electricity cost predictions. To this end, a heat exchanger unit containing a phase change material (PCM) as a LHES medium, thermally charged by solar energy was incorporated into three versions of a standard building. This paper reports on the use of EnergyPlus software to simulate the heating demand profile of these buildings, with Solving Constraint Integer Programs (SCIP) as the optimization tool. After applying MPC strategy, the energy costs of different building types were evaluated. Furthermore, the effect of prediction horizon and decision time step of MPC strategy, and PCM mass capacity on the performance of the MPC were all investigated in 1 and 7-day simulations. Results showed that by increasing the prediction horizon and PCM mass, more cost saving could be obtained. However, in terms of decision time step, although the study revealed that increasing it led to a higher energy saving, it made the system more sensitive to sharp changes as it failed to provide an accurate reading of the parameters and variables.

Test-sequence optimisation by survival analysis

Testing is an indispensable process for ensuring product quality in production systems. Reducing the time and cost spent on testing whilst minimising the risk of not detecting faults is an essential problem of process engineering. The optimisation of complex testing processes consisting of independent test steps is considered. Survival analysis-based models of an elementary test to efficiently combine the time-dependent outcome of the tests and costs related to the operation of the testing system were developed. A mixed integer non-linear programming (MINLP) model to formalize how the total cost of testing depends on the sequence and the parameters of the elementary test steps was proposed. To provide an efficient formalization of the scheduling problem and avoid difficulties due to the relaxation of the integer variables, the MINLP model as a P-graph representation-based process network synthesis problem was considered. The applicability of the methodology is demonstrated by a realistic case study taken from the computer manufacturing industry. With the application of the optimal test times and sequence provided by the SCIP (Solving Constraint Integer Programs) solver, 0.1–5% of the cost of the testing can be saved.

FiberSCIP—A Shared Memory Parallelization of SCIP

Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a mixed-integer linear programming solver and constraint integer programming framework available in source code. There is a parallel extension of SCIP named ParaSCIP, which parallelizes SCIP on massively parallel distributed memory computing environments. This paper describes FiberSCIP, which is yet another parallel extension of SCIP to utilize multi-threaded parallel computation on shared memory computing environments, and has the following contributions: First, we present the basic concept of having two parallel extensions, and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator), including an implementation of deterministic parallelization. Second, we discuss the difficulties in achieving a good performance that utilizes all resources on an actual computing environment, and the difficulties of performance evaluation of the parallel solvers. Third, we present a way to evaluate the performance of new algorithms and parameter settings of the parallel extensions. Finally, we demonstrate the current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer nonlinear programs (MINLPs) in parallel. The online appendix is available at https://doi.org/10.1287/ijoc.2017.0762 .

SCIP: global optimization of mixed-integer nonlinear programs in a branch-and-cut framework

This paper describes the extensions that were added to the constraint integer programming framework SCIP in order to enable it to solve convex and nonconvex mixed-integer nonlinear programs (MINLPs) to global optimality. SCIP implements a spatial branch-and-bound algorithm based on a linear outer-approximation, which is computed by convex over- and underestimation of nonconvex functions. An expression graph representation of nonlinear constraints allows for bound tightening, structure analysis, and reformulation. Primal heuristics are employed throughout the solving process to find feasible solutions early. We provide insights into the performance impact of individual MINLP solver components via a detailed computational study over a large and heterogeneous test set.

Model-based approach for optimizing the storage management of bio-repositories

Systematically collected samples of human tissue and fluids (e.g. blood, urine) play a key role in biomedical research. Biomaterial banks aim at collecting such biomaterials systematically and providing long-term availability of samples, which have to be kept constantly frozen at low temperatures. Therefore, storage management has to meet critical constraints in order to maintain high quality of the samples. The project aims at supporting the application of optimization and simulation algorithms for storage management. The approach has to provide means for adapting the algorithms flexibly and systematically to different or changing settings of biomaterial management and, therefore, aims at implementing a model-based framework to specify and run the algorithms.The process of establishing an optimization/simulation model for a given Biomaterial bank supported by the project starts with acquiring separately a model (1) of biomaterial handling and (2) of the optimization or simulation approach. The models for specific situations are derived from generic ontologies. A subsequent model mapping step assigns components representing aspects of biomaterial handling and storage to roles in a suitable optimization or simulation scheme. The mapping then enables the semi-automatic generation of optimization and simulation code. In the case of offline optimization problems, the framework produces program code that can be processed by an existing generic solver for mixed integer optimization programs (Zuse Institute Mathematical Programming Language code to be processed by the solver Solving Constraint Integer Programs). In the case of online problems, i.e., problems with an ongoing production of new information relevant for the optimization, the approach generates Java code suitable for processing by an existing simulation kernel (SimKit).The mapping module has been verified by reproducing a given solution for the Capacitated Facility Problem. Preliminary results of simulation runs show antagonistic effects of sorting bio-specimens by sample type: Sorting decreases the number of freezer opening operations while it increases fragmentation. The project is the first to adopt ontology-based modeling and model mapping for systematically exploring optimization and simulation approaches to biomaterial storage management. The results of simulation runs not only demonstrate the feasibility of the approach, but yield first practical insights (e.g. the effect of sorting samples).

Modeling energy consumption in automated vacuum waste collection systems

In a world where resources are scarce and urban areas consume the vast majority of these resources, it is vital to make cities greener and more sustainable. A smart city is a city in which information and communications technology are merged with traditional infrastructures, coordinated and integrated using new digital technologies. The increasing amount of waste generated, and the collection and treatment of waste poses a major challenge to modern urban planning in general, and to smart cities in particular. To cope with this problem, automated vacuum waste collection (AVWC) uses air suction on a closed network of underground pipes to transport waste from the drop off points scattered throughout the city to a central collection point, reducing greenhouse gas emissions and the inconveniences of conventional methods (odours, noise, etc.). Since a significant part of the cost of operating AVWC systems is energy consumption, we have developed a model with the aim of applying constraint programming technology to schedule the daily emptying sequences of the drop off points in such a way that energy consumption is minimized. In this paper we describe how the problem of deciding the drop off points that should be emptied at a given time can be modeled as a constraint integer programming (CIP) problem. Moreover, we report on experiments using real data from AVWC systems installed in different cities that provide empirical evidence that CIP offers a suitable technology for reducing energy consumption in AVWC.

Integer Programming for Bayesian Network Structure Learning

Bayesian networks provide an attractive representation of structured probabilistic information. There is thus much interest in ‘learning’ BNs from data. In this paper the problem of learning a Bayesian network using integer programming is presented. The SCIP (Solving Constraint Integer Programming) framework is used to do this. Although cutting planes are a key ingredient in our approach, primal heuristics and efficient propagation are also important.

Valid Linear Programming Bounds for Exact Mixed-Integer Programming

Fast computation of valid linear programming (LP) bounds serves as an important subroutine for solving mixed-integer programming problems exactly. We introduce a new method for computing valid LP bounds designed for this application. The algorithm corrects approximate LP dual solutions to be exactly feasible, giving a valid bound. Solutions are repaired by performing a projection and a shift to ensure all constraints are satisfied; bound computations are accelerated by reusing structural information through the branch-and-bound tree. We demonstrate this method to be widely applicable and faster than solving a sequence of exact LPs. Several variations of the algorithm are described and computationally evaluated in an exact branch-and-bound algorithm within the mixed-integer programming framework SCIP (Solving Constraint Integer Programming).

SCIP: solving constraint integer programs

Constraint integer programming (CIP) is a novel paradigm which integrates constraint programming (CP), mixed integer programming (MIP), and satisfiability (SAT) modeling and solving techniques. In this paper we discuss the software framework and solver SCIP (Solving Constraint Integer Programs), which is free for academic and non-commercial use and can be downloaded in source code. This paper gives an overview of the main design concepts of SCIP and how it can be used to solve constraint integer programs. To illustrate the performance and flexibility of SCIP, we apply it to two different problem classes. First, we consider mixed integer programming and show by computational experiments that SCIP is almost competitive to specialized commercial MIP solvers, even though SCIP supports the more general constraint integer programming paradigm. We develop new ingredients that improve current MIP solving technology. As a second application, we employ SCIP to solve chip design verification problems as they arise in the logic design of integrated circuits. This application goes far beyond traditional MIP solving, as it includes several highly non-linear constraints, which can be handled nicely within the constraint integer programming framework. We show anecdotally how the different solving techniques from MIP, CP, and SAT work together inside SCIP to deal with such constraint classes. Finally, experimental results show that our approach outperforms current state-of-the-art techniques for proving the validity of properties on circuits containing arithmetic.