scholarly journals Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded

2020 ◽  
Author(s):  
Miten Mistry ◽  
Dimitrios Letsios ◽  
Gerhard Krennrich ◽  
Robert M. Lee ◽  
Ruth Misener
Keyword(s):  
Large Scale ◽  
Optimization Problem ◽  
Regression Tree ◽  
Penalty Functions ◽  
Discrete Models ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Data Set ◽  
Chemical Catalysis ◽  
Feasible Solutions

Decision trees usefully represent sparse, high-dimensional, and noisy data. Having learned a function from these data, we may want to thereafter integrate the function into a larger decision-making problem, for example, for picking the best chemical process catalyst. We study a large-scale, industrially relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted trees and penalty functions mitigating risk. This mixed-integer optimization problem with convex penalty terms broadly applies to optimizing pretrained regression tree models. Decision makers may wish to optimize discrete models to repurpose legacy predictive models or they may wish to optimize a discrete model that accurately represents a data set. We develop several heuristic methods to find feasible solutions and an exact branch-and-bound algorithm leveraging structural properties of the gradient-boosted trees and penalty functions. We computationally test our methods on a concrete mixture design instance and a chemical catalysis industrial instance.

scholarly journals An Algorithm for Rescheduling of Trains under Planned Track Closures

2021 ◽  
Vol 11 (5) ◽  
pp. 2334
Author(s):  
Grzegorz Filcek ◽  
Dariusz Gąsior ◽  
Maciej Hojda ◽  
Jerzy Józefczyk
Keyword(s):  
Optimization Problem ◽  
Broad Class ◽  
Mixed Integer ◽  
Time Shift ◽  
Integer Optimization ◽  
Train Rescheduling ◽  
Feasible Solutions ◽  
The Given ◽  
Np Hardness

This work considered a joint problem of train rescheduling and closure planning. The derivation of a new train run schedule and the determination of a closure plan not only must guarantee the satisfaction of all the given constraints but also must optimize the number of accepted closures, the number of approved train runs, and the total time shift between the resultant and the original schedule. Presented is a novel nonlinear mixed integer optimization problem which is valid for a broad class of railway networks. A multi-level hierarchical heuristic algorithm is introduced due to the NP-hardness of the considered optimization problem. The algorithm is able, on an iterative basis, to jointly select closures and train runs, along with the derivation of a train schedule. Results obtained by the algorithm, launched for the conducted experiments, confirm its ability to provide acceptable and feasible solutions in a reasonable amount of time.

scholarly journals Partially distributed outer approximation

2021 ◽  
Author(s):  
Alexander Murray ◽  
Timm Faulwasser ◽  
Veit Hagenmeyer ◽  
Mario E. Villanueva ◽  
Boris Houska
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Outer Approximation ◽  
Mixed Integer ◽  
Global Optimality ◽  
Integer Optimization ◽  
Global Minimizers ◽  
Outer Approximation Method ◽  
Coupling Constraints ◽  
Outer Approximation Algorithm

AbstractThis paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.

Loss reduction as a Mixed Integer optimization problem

2009 ◽  
Author(s):  
Stephane Fliscounakis ◽  
Fabrice Zaoui ◽  
Marie-Pierre Houry ◽  
Emilie Milin
Keyword(s):  
Optimization Problem ◽  
Mixed Integer ◽  
Loss Reduction ◽  
Integer Optimization ◽  
Mixed Integer Optimization

scholarly journals Benchmarks for Current Linear and Mixed Integer Optimization Solvers

2015 ◽  
Vol 63 (6) ◽  
pp. 1923-1928 ◽  
Author(s):  
Josef Jablonský
Keyword(s):  
Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Large Scale ◽  
Optimization Problems ◽  
Academic Research ◽  
Mixed Integer ◽  
Important Class ◽  
Integer Optimization ◽  
Computational Performance ◽  
Optimization Solvers

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).

scholarly journals The Airlift Planning Problem

2019 ◽  
Vol 53 (3) ◽  
pp. 773-795
Author(s):  
Dimitris Bertsimas ◽  
Allison Chang ◽  
Velibor V. Mišić ◽  
Nishanth Mundru
Keyword(s):  
Large Scale ◽  
Programming Model ◽  
Simulated Data ◽  
Mixed Integer ◽  
Planning Problem ◽  
Weight Restrictions ◽  
Total Delay ◽  
Data Set ◽  
Scale Optimization ◽  
Airlift Planning

The U.S. Transportation Command (USTRANSCOM) is responsible for planning and executing the transportation of U.S. military personnel and cargo by air, land, and sea. The airlift planning problem faced by the air component of USTRANSCOM is to decide how requirements (passengers and cargo) will be assigned to the available aircraft fleet and the sequence of pickups and drop-offs that each aircraft will perform to ensure that the requirements are delivered with minimal delay and with maximum utilization of the available aircraft. This problem is of significant interest to USTRANSCOM because of the highly time-sensitive nature of the requirements that are typically designated for delivery by airlift, as well as the very high cost of airlift operations. At the same time, the airlift planning problem is extremely difficult to solve because of the combinatorial nature of the problem and the numerous constraints present in the problem (such as weight restrictions and crew rest requirements). In this paper, we propose an approach for solving the airlift planning problem faced by USTRANSCOM based on modern, large-scale optimization. Our approach relies on solving a large-scale mixed-integer programming model that disentangles the assignment decision (which aircraft will pickup and deliver which requirement) from the sequencing decision (in what order the aircraft will pickup and deliver its assigned requirements), using a combination of heuristics and column generation. Through computational experiments with both a simulated data set and a planning data set provided by USTRANSCOM, we show that our approach leads to high-quality solutions for realistic instances (e.g., 100 aircraft and 100 requirements) within operationally feasible time frames. Compared with a baseline approach that emulates current practice at USTRANSCOM, our approach leads to reductions in total delay and aircraft time of 8%–12% in simulated data instances and 16%–40% in USTRANSCOM’s planning instances.

Mixed-integer optimization methods for online scheduling in large-scale HVAC systems

2019 ◽  
Vol 14 (4) ◽  
pp. 889-924 ◽  
Author(s):  
Michael J. Risbeck ◽  
Christos T. Maravelias ◽  
James B. Rawlings ◽  
Robert D. Turney
Keyword(s):  
Large Scale ◽  
Optimization Methods ◽  
Hvac Systems ◽  
Online Scheduling ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Mixed Integer Optimization

scholarly journals Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems

2020 ◽  
Author(s):  
Álinson S. Xavier ◽  
Feng Qiu ◽  
Shabbir Ahmed
Keyword(s):  
Machine Learning ◽  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Large Scale ◽  
Unit Commitment ◽  
Energy Sector ◽  
Mixed Integer ◽  
Data Set ◽  
Computational Performance

Security-constrained unit commitment (SCUC) is a fundamental problem in power systems and electricity markets. In practical settings, SCUC is repeatedly solved via mixed-integer linear programming (MIP), sometimes multiple times per day, with only minor changes in input data. In this work, we propose a number of machine learning techniques to effectively extract information from previously solved instances in order to significantly improve the computational performance of MIP solvers when solving similar instances in the future. Based on statistical data, we predict redundant constraints in the formulation, good initial feasible solutions, and affine subspaces where the optimal solution is likely to lie, leading to a significant reduction in problem size. Computational results on a diverse set of realistic and large-scale instances show that using the proposed techniques, SCUC can be solved on average 4.3 times faster with optimality guarantees and 10.2 times faster without optimality guarantees, with no observed reduction in solution quality. Out-of-distribution experiments provide evidence that the method is somewhat robust against data-set shift. Summary of Contribution. The paper describes a novel computational method, based on a combination of mixed-integer linear programming (MILP) and machine learning (ML), to solve a challenging and fundamental optimization problem in the energy sector. The method advances the state-of-the-art, not only for this particular problem, but also, more generally, in solving discrete optimization problems via ML. We expect that the techniques presented can be readily used by practitioners in the energy sector and adapted, by researchers in other fields, to other challenging operations research problems that are solved routinely.

scholarly journals Comparison of penalty functions on a penalty approach to mixed-integer optimization

2016 ◽  
Author(s):  
Rogério B. Francisco ◽  
M. Fernanda P. Costa ◽  
Ana Maria A. C. Rocha ◽  
Edite M. G. P. Fernandes
Keyword(s):  
Penalty Functions ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Penalty Approach

scholarly journals Stability by the vector criterion of a mixed integer optimization problem with quadratic criterial fun ctions

2020 ◽  
pp. 15-21
Author(s):  
Т.Т. Lebedeva ◽  
◽  
N.V. Semenova ◽  
T.I. Sergienko ◽  
◽  
...  
Keyword(s):  
Initial Data ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Mixed Integer ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Vector Criterion

The article is devoted to the study of qualitative characteristics of different concepts of stability of vector problems of mixed-integer optimization, namely, to identifying the conditions under which the set of Pareto-optimal solutions of the problem possesses some property of invariance defined in advance in relation to the external influences on initial data of the problem. We investigate the questions of stability with respect to data perturbations in a vector criterion of mixed-integer optimization problem. The necessary and sufficient conditions of stability of three types for a problem of finding the solutions of the Pareto set are found. Such conditions guarantee that the small variations of initial data of vector criterion: 1) do not result in new Paretooptimal solutions, 2) save all Pareto-optimal solutions of the problem and can admit new solutions, 3) do not change the set of Pareto-optimal solutions of the initial problem.

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