Single Linear Optimization Research Articles

A multi-quantile regression time series model with interquantile lipschitz regularization for wind power probabilistic forecasting

Modern decision-making processes require uncertainty-aware models, especially those relying on non-symmetric costs and risk-averse profiles. The objective of this work is to propose a dynamic model for the conditional non-parametric distribution function (CDF) to generate probabilistic forecasts for a renewable generation time series. To do that, we propose an adaptive non-parametric time-series model driven by a regularized multiple-quantile-regression (MQR) framework. In our approach, all regression models are jointly estimated through a single linear optimization problem that finds the global-optimal parameters in polynomial time. An innovative feature of our work is the consideration of a Lipschitz regularization of the first derivative of coefficients in the quantile space, which imposes coefficient smoothness. The proposed regularization induces a coupling effect among quantiles creating a single non-parametric CDF model with improved out-of-sample performance. A case study with realistic wind-power generation data from the Brazilian system shows: 1) the regularization model is capable to improve the performance of MQR probabilistic forecasts, and 2) our MQR model outperforms five relevant benchmarks: two based on the MQR framework, and three based on parametric models, namely, SARIMA, and GAS with Beta and Weibull CDF.

Quantitative Resilience of Linear Driftless Systems.

This paper introduces the notion of quantitative resilience of a control system. Following prior work, we study linear driftless systems enduring a loss of control authority over some of their actuators. Such a malfunction results in actuators producing possibly undesirable inputs over which the controller has real-time readings but no control. By definition, a system is resilient if it can still reach a target after a partial loss of control authority. However, after a malfunction, a resilient system might be significantly slower to reach a target compared to its initial capabilities. We quantify this loss of performance through the new concept of quantitative resilience. We define such a metric as the maximal ratio of the minimal times required to reach any target for the initial and malfunctioning systems. Naïve computation of quantitative resilience directly from the definition is a complex task as it requires solving four nested, possibly nonlinear, optimization problems. The main technical contribution of this work is to provide an efficient method to compute quantitative resilience. Relying on control theory and on two novel geometric results we reduce the computation of quantitative resilience to a single linear optimization problem. We demonstrate our method on an opinion dynamics scenario.

An Ensemble Learning Framework for Model Fitting and Evaluation in Inverse Linear Optimization

We develop a generalized inverse optimization framework for fitting the cost vector of a single linear optimization problem given multiple observed decisions. This setting is motivated by ensemble learning, where building consensus from base learners can yield better predictions. We unify several models in the inverse optimization literature under a single framework and derive assumption-free and exact solution methods for each one. We extend a goodness-of-fit metric previously introduced for the problem with a single observed decision to this new setting and demonstrate several important properties. Finally, we demonstrate our framework in a novel inverse optimization-driven procedure for automated radiation therapy treatment planning. Here, the inverse optimization model leverages an ensemble of dose predictions from different machine learning models to construct a consensus treatment plan that outperforms baseline methods. The consensus plan yields better trade-offs between the competing clinical criteria used for plan evaluation.

Comparison of Predictions Between an EMG-Assisted Approach and Two Optimization-Driven Approaches for Lumbar Spine Loading During Walking With Backpack Loads.

The efficacy of two optimization-driven biomechanical modeling approaches has been compared with an electromyography-assisted optimization (EMGAO) approach to predict lumbar spine loading while walking with backpack loads. The EMGAO approach adopts more variables in the optimization process and is complex in data collection and processing, whereas optimization-driven approaches are simple and include the fewest possible variables. However, few studies have been conducted on the efficacy of using the optimization-driven approach to predict lumbar spine loading while walking with backpack loads. Anthropometric information of 10 healthy male adults as well as their kinematic, kinetic, and electromyographic data acquired while they walked with various backpack loads (no-load, 5%, 10%, 15%, and 20% of body weight) served as inputs into the model for predicting lumbosacral joint compression forces. The efficacy of two optimization-driven models, namely double linear optimization with constraints on muscle intensity and single linear optimization without any constraints, was investigated by comparing the resulting force profile with that provided by a current EMGAO approach. The double and single linear optimization approaches predicted mean deviations in peak force of -5.1%, and -19.2% as well as root-mean-square differences in force profile of 16.2%, and 25.4%, respectively. The double linear optimization approach was a relatively comparable estimator to the EMGAO approach in terms of its consistency, slight bias, and efficiency for predicting peak lumbosacral joint compression forces. The double linear optimization approach is a useful biomechanical model for estimating peak lumbar compression forces while walking with backpack loads.

Compact linear programs for 2SAT

For each integer n we present an explicit formulation of a compact linear program, with O(n3) variables and constraints, which determines the satisfiability of any 2SAT formula with n boolean variables by a single linear optimization. This contrasts with the fact that the natural polytope for this problem, formed from the convex hull of all satisfiable formulas and their satisfying assignments, has superpolynomial extension complexity. Our formulation is based on multicommodity flows. We also discuss connections of these results to the stable matching problem.

A Linearly Convergent Variant of the Conditional Gradient Algorithm under Strong Convexity, with Applications to Online and Stochastic Optimization

Linear optimization is many times algorithmically simpler than nonlinear convex optimization. Linear optimization over matroid polytopes, matching polytopes, and path polytopes are examples of problems for which we have simple and efficient combinatorial algorithms but whose nonlinear convex counterpart is harder and admits significantly less efficient algorithms. This motivates the computational model of convex optimization, including the offline, online, and stochastic settings, using a linear optimization oracle. In this computational model we give several new results that improve on the previous state of the art. Our main result is a novel conditional gradient algorithm for smooth and strongly convex optimization over polyhedral sets that performs only a single linear optimization step over the domain on each iteration and enjoys a linear convergence rate. This gives an exponential improvement in convergence rate over previous results. Based on this new conditional gradient algorithm we give the first...

Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints

We discuss some difficulties in determining valid upper bounds in spatial branch-and-bound methods for global minimization in the presence of nonconvex constraints. In fact, two examples illustrate that standard techniques for the construction of upper bounds may fail in this setting. Instead, we propose to perturb infeasible iterates along Mangasarian–Fromovitz directions to feasible points whose objective function values serve as upper bounds. These directions may be calculated by the solution of a single linear optimization problem per iteration. Preliminary numerical results indicate that our enhanced algorithm solves optimization problems where a standard branch-and-bound method does not converge to the correct optimal value.

Series-parallel Hybrid Vehicle Control Strategy Design and Optimization Using Real-valued Genetic Algorithm

Despite the series-parallel hybrid electric vehicle inherits the performance advantages from both series and parallel hybrid electric vehicle, few researches about the series-parallel hybrid electric vehicle have been revealed because of its complex construction and control strategy. In this paper, a series-parallel hybrid electric bus as well as its control strategy is revealed, and a control parameter optimization approach using the real-valued genetic algorithm is proposed. The optimization objective is to minimize the fuel consumption while sustain the battery state of charge, a tangent penalty function of state of charge(SOC) is embodied in the objective function to recast this multi-objective nonlinear optimization problem as a single linear optimization problem. For this strategy, the vehicle operating mode is switched based on the vehicle speed, and an "optimal line" typed strategy is designed for the parallel control. The optimization parameters include the speed threshold for mode switching, the highest state of charge allowed, the lowest state of charge allowed and the scale factor of the engine optimal torque to the engine maximum torque at a rotational speed. They are optimized through numerical experiments based on real-value genes, arithmetic crossover and mutation operators. The hybrid bus has been evaluated at the Chinese Transit Bus City Driving Cycle via road test, in which a control area network-based monitor system was used to trace the driving schedule. The test result shows that this approach is feasible for the control parameter optimization. This approach can be applied to not only the novel construction presented in this paper, but also other types of hybrid electric vehicles.

A graphical characterization of the efficient set for convex multiobjective problems

In this paper, a graphical characterization, in the decision space, of the properly efficient solutions of a convex multiobjective problem is derived. This characterization takes into account the relative position of the gradients of the objective functions and the active constraints at the given feasible solution. The unconstrained case with two objective functions and with any number of functions and the general constrained case are studied separately. In some cases, these results can provide a visualization of the efficient set, for problems with two or three variables. Besides, a proper efficiency test for general convex multiobjective problems is derived, which consists of solving a single linear optimization problem.