scholarly journals Bounds on efficient outcomes for large-scale cardinality-constrained Markowitz problems

2021 ◽  
Author(s):  
Janusz Miroforidis
Keyword(s):  
Large Scale ◽  
Technical Information ◽  
Time Limit ◽  
Mixed Integer ◽  
Portfolio Investment ◽  
Data Set ◽  
Integer Quadratic Programming ◽  
Efficient Portfolios ◽  
Mean Variance Portfolio ◽  
Mean Variance

AbstractWhen solving large-scale cardinality-constrained Markowitz mean–variance portfolio investment problems, exact solvers may be unable to derive some efficient portfolios, even within a reasonable time limit. In such cases, information on the distance from the best feasible solution, found before the optimization process has stopped, to the true efficient solution is unavailable. In this article, I demonstrate how to provide such information to the decision maker. I aim to use the concept of lower bounds and upper bounds on objective function values of an efficient portfolio, developed in my earlier works. I illustrate the proposed approach on a large-scale data set based upon real data. I address cases where a top-class commercial mixed-integer quadratic programming solver fails to provide efficient portfolios attempted to be derived by Chebyshev scalarization of the bi-objective optimization problem within a given time limit. In this case, I propose to transform purely technical information provided by the solver into information which can be used in navigation over the efficient frontier of the cardinality-constrained Markowitz mean–variance portfolio investment problem.

scholarly journals A Multistage Solution Approach for Dynamic Reactive Power Optimization Based on Interval Uncertainty

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaodong Shen ◽  
Yang Liu ◽  
Yan Liu
Keyword(s):  
Large Scale ◽  
Reactive Power ◽  
Power Optimization ◽  
Programming Model ◽  
Nonconvex Programming ◽  
Interval Uncertainty ◽  
Mixed Integer ◽  
Reactive Power Optimization ◽  
Renewable Energy Resources ◽  
Integer Quadratic Programming

In order to solve the uncertainty and randomness of the output of the renewable energy resources and the load fluctuations in the reactive power optimization, this paper presents a novel approach focusing on dealing with the issues aforementioned in dynamic reactive power optimization (DRPO). The DRPO with large amounts of renewable resources can be presented by two determinate large-scale mixed integer nonlinear nonconvex programming problems using the theory of direct interval matching and the selection of the extreme value intervals. However, it has been admitted that the large-scale mixed integer nonlinear nonconvex programming is quite difficult to solve. Therefore, in order to simplify the solution, the heuristic search and variable correction approaches are employed to relax the nonconvex power flow equations to obtain a mixed integer quadratic programming model which can be solved using software packages such as CPLEX and GUROBI. The ultimate solution and the performance of the presented approach are compared to the traditional methods based on the evaluations using IEEE 14-, 118-, and 300-bus systems. The experimental results show the effectiveness of the presented approach, which potentially can be a significant tool in DRPO research.

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.

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 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.

Structural Learning of Boltzmann Machine and its Application

2015 ◽  
Vol 785 ◽  
pp. 63-67
Author(s):  
Shamshul Bahar Yaakob ◽  
Mohd Zamri Hasan ◽  
Amran Ahmed
Keyword(s):  
Life Cycle Management ◽  
Mixed Integer ◽  
Structural Learning ◽  
Boltzmann Machine ◽  
Expected Return ◽  
Integer Quadratic Programming ◽  
Effective Selection ◽  
Mixed Integer Quadratic Programming ◽  
Mean Variance ◽  
Selection Of

This study proposed a way to solve problem efficiently which is through structural learning of Boltzmann machine. This method used mixed integer quadratic programming to solve the problem. An analysis is conducted by using the ideas of the reliability and risks of units assessed using a variance-covariance matrix and the effect and expanses of replacement are determined. In this study, the mean-variance analysis is formulated as a mathematical program with two objectives: (1) minimization of risk and (2) maximization of expected return. Lastly, the effectiveness of proposed method is illustrated by way of a life cycle management example. The result of this suggested method was demonstrated at the end. By using this method, more effective selection of results is gathered. Thus, this prove that the effectiveness of the decision making process can be reinforced.

scholarly journals Review on Reformulation of the Mean-Variance Model with Real-life Trading Restrictions

2017 ◽  
Vol 14 (1) ◽  
pp. 40
Author(s):  
Feng Li
Keyword(s):  
Computing Time ◽  
Real Life ◽  
Mixed Integer ◽  
Variance Model ◽  
Integer Quadratic Programming ◽  
Continuous Relaxation ◽  
Perspective Reformulation ◽  
Mixed Integer Quadratic Programming ◽  
Trading Restrictions ◽  
Mean Variance

In this paper, we consider a class of portfolio selection problems with cardinality and minimum buy-in threshold constraints in real-life which can be formulated as mixed-integer quadratic programming (MIQP). Two reformulation methods that generate the same tight continuous relaxation of original problem are compared in the context under the branch-and-bound algorithm, one is the Perspective Reformulation and another is the Lift-and-Convexification Reformulation (LCR). Computational results show that the (PC) is more competitive than the (LCR) method in terms of computing time and nodes in MIQP solver CPLEX 12.7, what's more, this outperformance becomes more obvious as the size of instances grows.

Structural Learning of Boltzmann Machine: An Application

2015 ◽  
Vol 793 ◽  
pp. 657-662
Author(s):  
Shamshul Bahar Yaakob ◽  
Zamri Hassan ◽  
Syed Akhmal Syed Jamalil
Keyword(s):  
Variance Analysis ◽  
Mixed Integer ◽  
Structural Learning ◽  
Boltzmann Machine ◽  
Expected Return ◽  
Integer Quadratic Programming ◽  
Effective Selection ◽  
Mixed Integer Quadratic Programming ◽  
Mean Variance ◽  
Selection Of

In order to solve a problem efficiently, we propose the structural learning of Boltzmann machine. The proposed method enables us to solve the problem defined in terms of mixed integer quadratic programming. In this research, an analysis is performed by using the concepts of the reliability and risks of units evaluated using a variance-covariance matrix and also the effect and expanses of replacement are measured. Mean-variance analysis is formulated as a mathematical programming with two objectives to minimize the risk and maximize the expected return. Finally, we employ a Boltzmann machine to solve the mean-variance analysis efficiently. At the end, the result of our method was exemplified. This method enables us to obtain a more effective selection of results and enhanced the effectiveness of the decision making process.

scholarly journals Exposing hidden alternative backbone conformations in X-ray crystallography using qFit

2015 ◽  
Author(s):  
Daniel A Keedy ◽  
James Fraser ◽  
Henry van den Bedem
Keyword(s):  
High Resolution ◽  
Electron Density ◽  
Large Scale ◽  
Molecular Mechanisms ◽  
Model Building ◽  
Mixed Integer ◽  
X Ray ◽  
Integer Quadratic Programming ◽  
Chain Conformations ◽  
Building Program

Proteins must move between different conformations of their native ensemble to perform their functions. Crystal structures obtained from high-resolution X-ray diffraction data reflect this heterogeneity as a spatial and temporal conformational average. Although movement between natively populated alternative conformations can be critical for characterizing molecular mechanisms, it is challenging to identify these conformations within electron density maps. Alternative side chain conformations are generally well separated into distinct rotameric conformations, but alternative backbone conformations can overlap at several atomic positions. Our model building program qFit uses mixed integer quadratic programming (MIQP) to evaluate an extremely large number of combinations of sidechain conformers and backbone fragments to locally explain the electron density. Here, we describe two major modeling enhancements to qFit: peptide flips and alternative glycine conformations. We find that peptide flips fall into four stereotypical clusters and are enriched in glycine residues at the n+1 position. The potential for insights uncovered by new peptide flips and glycine conformations is exemplified by HIV protease, where different inhibitors are associated with peptide flips in the “flap” regions adjacent to the inhibitor binding site. Our results paint a picture of peptide flips as conformational switches, often enabled by glycine flexibility, that result in dramatic local rearrangements. Our results furthermore demonstrate the power of large-scale computational analysis to provide new insights into conformational heterogeneity. Overall, improved modeling of backbone heterogeneity with high-resolution X-ray data will connect dynamics to the structure-function relationship and help drive new design strategies for inhibitors of biomedically important systems.

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