Cost-of-Quality Optimization via Zero-One Polynomial Programming

Optimization solvers include many options that allow users to control algorithmic aspects that may have a considerable impact on solver performance. Tuning solver options is often necessary to reduce execution time and improve solution quality. Previous studies of solver tuning techniques have focused on mixed-integer linear programming and local nonlinear programming solvers. In this paper, we investigate the potential of tuning a global optimization solver for nonlinear and mixed-integer nonlinear programming problems. In particular, derivative-free optimization (DFO) algorithms are used to find optimal values for options of the global optimization solver BARON. A set of 126 problems from the GLOBALLib and MINLPLib collections are utilized in a computational study from which we conclude that tuning options can improve the default performance of BARON for individual problems and an entire library. Additionally, we present a systematic comparison of 27 DFO solvers in terms of their ability to improve the performance of the global solver. We find that several DFO implementations are much better than others in terms of finding optimal tuning parameters.

Assessing solution quality and computational performance in the hydro unit commitment problem considering different mathematical programming approaches

An exact optimization approach for an integrated process configuration, lot-sizing, and scheduling problem

We extend recent work on solving mixed-integer nonlinear optimal control problems (MIOCPs) to the case of integer control functions subject to constraints that involve a pointwise coupling of the state with the integer controls. We extend a theorem due to [S. Sager, H. Bock, and M. Diehl, Math. Program. Ser. A, 133 (2012), pp. 1--23] to the case of MIOCPs with constraints on the integer control and show that the integrality gap vanishes in function space when the coarseness of the rounding grid is driven to zero even after adding constraints of this type. For the time-discretized problem, we extend a sum-up rounding (SUR) scheme due to [S. Sager, C. Reinelt, and H. Bock, Math. Program. Ser. A, 118 (2009), pp. 109--149] to the new problem class. Our scheme permits one to constructively obtain an $\varepsilon$-feasible and $\varepsilon$-optimal binary feasible control. We derive new, tight upper bounds on the integer control approximation error made by SUR. For unconstrained binary controls on equidistant grids, we reduce the approximation error bound from $\mathcal{O}(|\Omega|)$ to $\mathcal{O}(\log |\Omega|)$ asymptotically for $|\Omega| \to \infty$ and a fixed coarseness of the rounding grid, where $|\Omega|$ is the number of binary controls. For constrained binary controls, we show that the approximation problem is more difficult, and we give a proof of an approximation error bound of complexity $\mathcal{O}(|\Omega|)$. A numerical example compares our approach to a state-of-the-art mixed-integer nonlinear programming solver and illustrates the applicability of our results when solving MIOCPs using the direct and simultaneous approach.

Finding the optimal join order (JO) is one of the most important problems in query optimisation, and has been extensively considered in research and practise. As it involves huge search spaces, approximation approaches and heuristics are commonly used, which explore a reduced solution space at the cost of solution quality. To explore even large JO search spaces, we may consider special-purpose software, such as mixed-integer linear programming (MILP) solvers, which have successfully solved JO problems. However, even mature solvers cannot overcome the limitations of conventional hardware prompted by the end of Moore's law. We consider quantum-inspired digital annealing hardware, which takes inspiration from quantum processing units (QPUs). Unlike QPUs, which likely remain limited in size and reliability in the near and mid-term future, the digital annealer (DA) can solve large instances of mathematically encoded optimisation problems today. We derive a novel, native encoding for the JO problem tailored to this class of machines that substantially improves over known MILP and quantum-based encodings, and reduces encoding size over the state-of-the-art. By augmenting the computation with a novel readout method, we derive valid join orders for each solution obtained by the (probabilistically operating) DA. Most importantly and despite an extremely large solution space, our approach scales to practically relevant dimensions of around 50 relations and improves result quality over conventionally employed approaches, adding a novel alternative to solving the long-standing JO problem.

We consider the dynamic facility location problem with generalized modular capacities, a multiperiod facility location problem in which the costs for capacity changes may differ for all pairs of capacity levels. The problem embeds a complex cost structure and generalizes several existing facility location problems, such as those that allow temporary facility closing or capacity expansion and reduction. As the model may become very large, general-purpose mixed-integer programming (MIP) solvers are limited to solving instances of small to medium size. In this paper, we extend the generalized model to the case of multiple commodities. We propose Lagrangian heuristics, based on subgradient and bundle methods, to find good quality solutions for large-scale instances with up to 250 facility locations and 1,000 customers. To improve the final solution quality, a restricted MIP model is solved based on the information collected through the solution of the Lagrangian dual. Computational results show that the Lagrangian-based heuristics provide highly reliable results for all problem variants considered. They produce good quality solutions in short computing times even for instances where state-of-the-art MIP solvers do not find feasible solutions. The strength of the formulation also allows the method to provide tight bounds on the optimal value. Data and the online appendix are available at https://doi.org/10.1287/ijoc.2016.0738 .

Linear programming (LP) and mixed integer linear programming (MILP) problems belong among very important class of problems that find their applications in various managerial consequences. The aim of the paper is to discuss computational performance of current optimization packages for solving large scale LP and MILP optimization problems. Current market with LP and MILP solvers is quite extensive. Probably among the most powerful solvers GUROBI 6.0, IBM ILOG CPLEX 12.6.1, and XPRESS Optimizer 27.01 belong. Their attractiveness for academic research is given, except their computational performance, by their free availability for academic purposes. The solvers are tested on the set of selected problems from MIPLIB 2010 library that contains 361 test instances of different hardness (easy, hard, and not solved).

We present a novel hybrid algorithm for training Deep Neural Networks that combines the state-of-the-art Gradient Descent (GD) method with a Mixed Integer Linear Programming (MILP) solver, outperforming GD and variants in terms of accuracy, as well as resource and data efficiency for both regression and classification tasks. Our GD+Solver hybrid algorithm, called GDSolver, works as follows: given a DNN D as input, GDSolver invokes GD to partially train D until it gets stuck in a local minima, at which point GDSolver invokes an MILP solver to exhaustively search a region of the loss landscape around the weight assignments of D’s final layer parameters with the goal of tunnelling through and escaping the local minima. The process is repeated until desired accuracy is achieved. In our experiments, we find that GDSolver not only scales well to additional data and very large model sizes, but also outperforms all other competing methods in terms of rates of convergence and data efficiency. For regression tasks, GDSolver produced models that, on average, had 31.5% lower MSE in 48% less time, and for classification tasks on MNIST and CIFAR10, GDSolver was able to achieve the highest accuracy over all competing methods, using only 50% of the training data that GD baselines required.

We study the reduction of bounded reachability analysis of timed automata (TA) to a Mixed Integer Linear Programming (MILP) problem. While bounded model checking of timed automata has been explored in the literature based on the satisfiability of Boolean constraint formulas over linear arithmetic constraints verified using SAT Modulo Theory (SMT) solvers, the approach presented in this paper opens up the alternative of using MILP solvers. We present some preliminary results comparing the two approaches and provide ideas on how linear optimization can be useful for analyzing the behavior of TA. The results are supported by a prototype implementation which relies either on a MILP solver (Gurobi) or an SMT solver (MathSAT). Certain techniques for reducing the search space and improving the performance are also discussed.

This article presents a planning problem in a distribution network incorporating two levels inventory management of perishable products, lot-sizing, multi-sourcing and transport capacity with a homogeneous fleet of vehicles. A mixed integer linear programming (MILP) and a greedy heuristic are developed to solve this real planning problem. There are some instances for which the solver cannot give a good lower bound within the limited time and for other instances it takes a lot of time to solve MILP. The greedy heuristic is an alternative to the mixed integer linear program to quickly solve some large instances taking into account original and difficult constraints. For some instances the gap between the solutions of the solver (MILP) and the heuristic becomes quite significant. The variable neighborhood descent (VND), the iterated local search (ILS) and the multi-start iterated local search (MS-ILS) are implemented. These methods are included in an APS (Advanced Planning System) and compared with a MILP solver. The instances are derived from actual data or built using a random generator of instances to have wider diversity for computational evaluation. The VND significantly improves the quality of solutions.

Health care decision makers often have a limited understanding of the costs associated with quality improvement efforts. However, such information is vital for managers to make appropriate operational and financial decisions to ensure high quality health care services. We used the Cost of Quality (COQ) model to estimate the cost of quality-related activities at the Makerere University-Johns Hopkins University (MU-JHU) Laboratory in Uganda. Using data collected from January 1, 2007–December 31, 2007, we allocated the direct costs associated with quality-related activities in the laboratory across COQ’s cost categories: prevention, appraisal, internal failures, and external failures. We found that approximately 94% of total COQ was spent on costs of “good quality” (prevention and appraisal), while 6% was spent on costs of “poor quality” (internal and external failures). The high percentage of COQ spent on prevention and appraisal activities is consistent with efforts to ensure high quality laboratory results. Future studies should try to link COQ to health outcomes and quantify “hidden” failure costs. This CE update introduces the Cost of Quality (COQ) model and illustrates how it can be applied to a clinical laboratory setting to help managers and executives make more informed decisions about spending on quality-related activities. We begin with an overview of the COQ concept and its 4 main cost categories, followed by an illustration of how the model can be applied in a medical laboratory setting. We then discuss some of the advantages and limitations of this methodology and provide suggestions for future research. * COQ : Cost of Quality MU-JHU : Makerere University-Johns Hopkins University IOM : Institute of Medicine P-A-F : prevention-appraisal-failure CAP : College of American Pathology PCR : polymerase chain reaction QA : quality assurance LIS : laboratory Information System EQA : External Quality Assurance CSC : Customer Service Concern PM : preventive maintenance QC : Quality Control PIR : Process Improvements Reports GLP : good laboratory practices GAAP : generally accepted accounting principles

With rising energy costs and concerns about environmental sustainability, there is a growing need to deploy Home Energy Management Systems (HEMS) that can efficiently manage household energy consumption. This paper proposes a new supervised-learning-based strategy for optimal energy scheduling of an HEMS that considers the integration of energy storage systems (ESS) and electric vehicles (EVs). The proposed supervised-learning-based HEMS framework aims to optimize the energy costs of households by forecasting the energy demand and simultaneously scheduling the charging and discharging operations of ESS and EV. From the scenarios extracted from historical data, the HEMS optimization problem is solved using a mixed-integer linear programming (MILP) solver to collect the datasets on the optimal actions of the ESS and EV. Accordingly, a supervised learning method is used to learn the optimal actions of the MILP solver using deep neural networks (DNNs). Well-trained DNNs act as decision-making tools that are subsequently applied to predict near-optimal actions for ESS and EV based on real-time data. The effectiveness of the proposed method is demonstrated through simulation results and compared with deep reinforcement learning-based and forecasting-based methods. The results show that the proposed method can significantly reduce energy costs and improve the efficiency of ESS and EV operations. Overall, the proposed supervised-learning-based HEMS offers a practical and effective solution for residential energy management.

In apparel manufacturing, cut pieces produced by the cutting process are a key input work-in-process (WIP) to the bottleneck sewing process. However, an excessive inventory of cut pieces not only requires extra storage space but also creates difficulties with shop floor control. This study determines the ideal cutting times of fabric lays by minimising the cut piece inventory under the constraint that sufficient cut pieces are produced in time to satisfy the bottleneck usage. This study proposes a mixed integer programming (MIP) model and a heuristic method to solve the problem. The solutions for most test instances of the problem that are calculated by the heuristic method are not as good as those by the MIP solver; however, the heuristic method computation times are negligible. The experiments show that the MIP model’s efficiency significantly improves by starting from an initial solution provided by the proposed heuristic method.

Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They often provide good feasible solutions early and help to reduce the time needed to prove optimality. In this paper, we present a scheme for start heuristics that can be executed without previous knowledge of an LP solution or a previously found integer feasible solution. It uses global structures available within MIP solvers to iteratively fix integer variables and propagate these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. If sufficiently many variables can be fixed that way, the resulting problem is solved first as an LP, and then as an auxiliary MIP if the rounded LP solution does not provide a feasible solution already. We present three primal heuristics that use this scheme based on different global structures. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about 60% of the instances and by this, help to improve several performance measures for MIP solvers, including the primal integral and the average solving time.

In order to utilize the network resources efficiently, many traffic engineering schemes have been proposed to distribute the loads on links by controlling traffic routes. Traffic engineering based on tunneling can finely control traffic by setting a route of each flow explicitly. In the tunneling-based traffic engineering scheme, it is not easy to choose the best tunnel node pairs and the best flow allocation to the tunnels. In this paper, we propose a method to calculate an optimal solution in terms of the number of tunnels that can mitigate network congestion or the ratio of each flow on the links in a given network topology. We formulate the problems as mixed integer programming (MIP) and obtain optimal solutions using a high speed MIP solver. We have conducted experiments in the two kinds of problems on two network topologies. We calculate optimal solutions using a MIP solver, and evaluate the calculation time and improvement of network congestion by adding tunnels.