Quantum-Inspired Digital Annealing for Join Ordering

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 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.

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.

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.

Chapter 13 - Emerging clouds

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.

This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To tackle the nonlinearity in the constraint, we alternatively fix a subset of decision variables and optimize the remaining ones via Mixed Integer Linear Programming (MILP). We solve the MILP problem at each iteration via an off-the-shelf MILP solver. Our experimental results show that our method significantly outperforms existing heuristic methods, employing either independent optimization or joint optimization strategies. We have also verified the generalization ability of our method over grid environments with various sizes and its high robustness to the algorithm setting.

Efficient optimization of a large-scale biorefinery system using a novel decomposition based approach

We present an efficient polynomial-time approximation scheme (EPTAS) for the problem of scheduling jobs on parallel uniform machines that improves all previously known EPTAS for the problem. Our algorithm uses a Mixed Integer Linear Program (MILP) formulation for a relaxed version of the problem. We simplify the MILP by repeatedly removing carefully selected sets of jobs and machines until all integer variables have been removed. Then, we build up the solution through the use of a dynamic programming approach, enumeration, and linear program solving. Notable about our approach is that our algorithm only uses an LP solver, different from previous EPTAS approaches where MILP solvers are necessary.

This article introduces a Hybrid Intervention Scheme Based Optimization (HIBO) algorithm solving an Optimal Reactive Power Management (ORPM) problem in real-time using a Mixed Integer Linear Programming (MILP) solver. The ORPM problem presented here contains a linear objective function containing four objectives separated using a set of static penalty factors for each area. The non-linear optimization problem has been assumed linear by localizing the search for solution, this is done by introducing a penalty on the change from the original state or the base case scenario. Thereby, optimizing the non-linear ORPM in linear steps makes it a fast solver for small changes in power system state. A contingency analysis (for N-1 voltage violations) is included for ensuring the safety and reliability of the power system. The results are used to update the ORPM problem or stop if the system is secure. The optimization variables used to represent transformer taps and shunt device switches are handled as discrete integers and remaining variables as continuous real numbers. The intervention scheme, objectives and constraints used in the HIBO have been derived through surveys conducted at a transmission system control center and are supported using literature. Validation of the HIBO algorithm was performed on the Dutch transmission network model after dividing it into four regional areas. Convergence characteristics of the HIBO algorithm are compared using results. From the results, it is concluded that the HIBO algorithm is a competitive optimization solver, suitable for deployment in the secondary voltage control scheme within system operations domain for transmission system operators.

Tweakable block cipher (TBC) is an extension of conventional block cipher. We study how to build a TBC based on generalized Feistel structure (GFS), a classical block cipher construction. While known dedicated TBC proposals are based on substitution-permutation network (SPN), GFS has not been used for building TBC. In particular, we take 64-bit GFS block cipher TWINE and try to make it tweakable with a minimum change. To find a best one from a large number of candidates, we performed a comprehensive search with a help of mixed integer linear programming (MILP) solver. As a result, our proposal Tweakable TWINE is quite efficient, has the same number of rounds as TWINE with extremely simple tweak schedule.

In this paper we explore the possibility of deriving consensus rankings by solving consensus optimization problems, characterizing consensus rankings as suitable complete order relations minimizing the average Kemeny-Snell distance to the individual rankings. This optimization problem can be expressed as a binary programming (BP) problem which can typically be solved reasonably efficiently. The underlying theory is discussed in Sect. 1. Applications of the proposed method given in Sect. 2 include a comparison to other mathematical programming (MP) approaches using the data set of Tse [9] and establishing a consensus ranking of marketing journals identified by domain experts from a subset of the Harzing journal quality list [2]. In Sect. 3 we discuss computational details and present the results of a benchmark experiment comparing the performance of the commercial solver CPLEX to three open source mixed integer linear programming (MILP) solvers

Energy conversion from renewable energy has been possible due to extra-market supporting policies. The extra-market approach survives for low penetration levels, but as energy from wind penetration increases the extra-market policies are expected to become untenable. A wind power producer (WPP) should expect full competition in deregulated electricity market, i.e., has to have an offer strategy to be competitive. A WPP has to face uncertainties on available wind energy and market prices. Uncertainties have to be conveniently addressed; otherwise a decrease on the financial results is expected. A stochastic programming approach is presented to suitable address those uncertainties. The problem formulation is approached in the way of writing equations in order to benefit from the well-established mixed integer linear program (MILP) solvers in order to compute an offering strategy. A case study with data from the Iberian Electricity Market is used to illustrate the effectiveness of the proposed approach.

Modern industrial robots are increasingly deployed in dynamic environments, where unpredictable events are expected to impact the robot’s operation. Under these conditions, runtime task replanning is required to avoid failures and unnecessary stops, while keeping up productivity. Task replanning is a long-sighted complement to path replanning, which is mostly concerned with avoiding unexpected obstacles that can lead to potentially unsafe situations. This paper focuses on task replanning as a way to dynamically adjust the robot behaviour to the continuously evolving environment in which it is deployed. Analogously to probabilistic roadmaps used in path planning, we propose the concept of Task roadmaps as a method to replan tasks by leveraging an offline generated search space. A graph-based model of the robot application is converted to a task scheduling problem to be solved by a proposed Branch and Bound (B&B) approach and two benchmark approaches: Mixed Integer Linear Programming (MILP) and Planning Domain Definition Language (PDDL). The B&B approach is proposed to compute the task roadmap, which is then reused to replan for unforeseeable events. The optimality and efficiency of this replanning approach are demonstrated in a simulation-based experiment with a mobile manipulator in a kitting application. In this study, the proposed B&B Task Roadmap replanning approach is significantly faster than a MILP solver and a PDDL based planner.