Real-world problems are often nonconvex and involve integer variables, representing vexing challenges to be tackled using state-of-the-art solvers. We introduce a mathematical identity-based ...reformulation of a class of polynomial integer nonlinear optimization (PINLO) problems using a technique that linearizes polynomial functions of separable and bounded integer variables of any degree. We also introduce an alternative reformulation and conduct computational experiments to understand their performance against leading commercial global optimization solvers. Computational experiments reveal that our integer linear optimization reformulations are computationally tractable for solving large PINLO problems via Gurobi (up to 10,000 constraints and 20,000 variables). This is much larger than current leading commercial global optimization solvers such as BARON, thereby demonstrating its promise for use in real-world applications of integer linear optimization with a polynomial objective function.
We study the mixed-integer optimization (MIO) approach to feature subset selection in nonlinear kernel support vector machines (SVMs) for binary classification. To measure the performance of subset ...selection, we use the distance between two classes (DBTC) in a high-dimensional feature space based on the Gaussian kernel function. However, DBTC to be maximized as an objective function is nonlinear, nonconvex and nonconcave. Despite the difficulty of linearizing such a nonlinear function in general, our major contribution is to propose a mixed-integer linear optimization (MILO) formulation to maximize DBTC for feature subset selection, and this MILO problem can be solved to optimality using optimization software. We also derive a reduced version of the MILO problem to accelerate our MILO computations. Experimental results show good computational efficiency for our MILO formulation with the reduced problem. Moreover, our method can often outperform the linear-SVM-based MILO formulation and recursive feature elimination in prediction performance, especially when there are relatively few data instances.
This paper introduces a new supervised Bayesian approach to hyperspectral image segmentation with active learning, which consists of two main steps. First, we use a multinomial logistic regression ...(MLR) model to learn the class posterior probability distributions. This is done by using a recently introduced logistic regression via splitting and augmented Lagrangian algorithm. Second, we use the information acquired in the previous step to segment the hyperspectral image using a multilevel logistic prior that encodes the spatial information. In order to reduce the cost of acquiring large training sets, active learning is performed based on the MLR posterior probabilities. Another contribution of this paper is the introduction of a new active sampling approach, called modified breaking ties, which is able to provide an unbiased sampling. Furthermore, we have implemented our proposed method in an efficient way. For instance, in order to obtain the time-consuming maximum a posteriori segmentation, we use the α-expansion min-cut-based integer optimization algorithm. The state-of-the-art performance of the proposed approach is illustrated using both simulated and real hyperspectral data sets in a number of experimental comparisons with recently introduced hyperspectral image analysis methods.
Using empirical models to predict whether sections within pipes have defects can save inspection costs and, potentially, avoid oil spills. Optimal Classification Tree (OCT) formulations offer ...potentially desirable combinations of interpretability and prediction accuracy on unseen pipes. Approaches based on powerful state-of-the-art OCT formulations have enabled researchers to solve decision tree problems optimally instead of using traditional sub-optimal greedy approaches. Yet, the recently proposed formulations also have limitations. Some of the most recent formulations require a large number of decision variables and constraints leading to computational inefficiencies. Previous formulations have optimal solutions with undesirable or invalid tree structures which may depend on the particular software implementation. Additionally, some formulations always grow a full tree even when desirable parsimonious tree options are available. This article proposes the Modified Optimal Classification Tree (M-OCT) formulation with novel leaf-branch-interaction constraints, which could stabilize the previous formulation and reduce the chance of invalid tree structures when generating optimal trees. By incorporating the idea of binary encoding of thresholds from a previous article, we reduce the total number of binary variables. We then extend M-OCT to construct a novel formulation called Binary Node Penalty Optimal Classification Tree (BNP-OCT) with binary splits and node complexity constraints, which support efficiency in standard branch-and-cut solvers and prevents the overfitting issue when learning the optimal tree models. We compare the proposed methods with alternatives including standard formulations using 15 standard data sets. In addition, we use 750 test cases to compare the computational stability of pre-existing formulations to those involving the proposed leaf-branch constraints. We demonstrate that the proposed formulation offers advantages in accuracy, computational efficiency, and structural stability. We also describe how the proposed methods are able to achieve 94% classification accuracy on balanced test sets for unseen pipes.
•Optimal classification trees offer interpretable and accurate classification but have stability problems.•Leaf-branch-interaction constraints stabilize mixed integer formulation and validity.•Binary encoding of threshold variables increases the computational efficiency.•Case study illustrates the practical benefits for classifying potential pipeline defects.
An actively managed portfolio almost never beats the market in the long term. Thus, many investors often resort to passively managed portfolios whose aim is to follow a certain financial index. The ...task of building such passive portfolios aiming also to minimize the transaction costs is called Index Tracking (IT), where the goal is to track the index by holding only a small subset of assets in the index. As such, it is an NP-hard problem and becomes unfeasible to solve exactly for indices with more than 100 assets. In this work, we present a novel hybrid simulated annealing method that can efficiently solve the IT problem for large indices and is flexible enough to adapt to financially relevant constraints. By tracking the S&P-500 index between the years 2011 and 2018 we show that our algorithm is capable of finding optimal solutions in the in-sample period of past returns and can be tuned to provide optimal returns in the out-of-sample period of future returns. Finally, we focus on the task of holding an IT portfolio during one year and rebalancing the portfolio every month. Here, our hybrid simulated annealing algorithm is capable of producing financially optimal portfolios already for small subsets of assets and using reasonable computational resources, making it an appropriate tool for financial managers.
Recent years have seen an unprecedented growth in the use of sensor data to guide wind farm operations and maintenance. Emerging sensor-driven approaches typically focus on optimal maintenance ...procedures for single turbine systems, or model multiple turbines in wind farms as single component entities. In reality, turbines are composed of multiple components that dynamically interact throughout their lifetime. These interactions are central for realistic assessment and control of turbine failure risks. In this paper, an integrated framework that combines i) real-time degradation models used for predicting remaining life distribution of each component, with ii) mixed integer optimization models and solution algorithms used for identifying optimal wind farm maintenance and operations is proposed. Maintenance decisions identify optimal times to repair every component, which in turn, determine the failure risk of the turbines. More specifically, optimization models that characterize a turbine's failure time as the first time that one of its constituent components fail - a systems reliability concept called competing risk is developed. The resulting turbine failures impact the optimization of wind farm operations and revenue. Extensive experiments conducted for multiple wind farms with 300 wind turbines - 1200 components - showcases the performance of the proposed framework over conventional methods.
•A condition-based maintenance and operations model is proposed for wind farms.•Component and turbine dependencies on failure risks and maintenance are modeled.•A tailored solution algorithm is proposed to ensure computational scalability.•A comprehensive experimental framework is developed via degradation and wind data.•The proposed approach provides significant improvements over benchmark models.
Unit commitment (UC) stands out as a significant challenge in electrical power systems. With the rapid growth in power demand and the pressing issues of fossil fuel scarcity and global warming, it ...has become crucial to enhance the utilization of renewable energy sources. This study focuses on addressing the UC problem by incorporating a wind farm and proposes a modified version of the metaheuristic African vultures optimization algorithm (AVOA) in binary form, utilizing the sigmoid transfer function. The modified AVOA employs multiple phase‐shift tactics to overcome premature local optima. By determining the on/off status of generating units, the modified AVOA improves the algorithm's effectiveness. Additionally, the paper develops an auto‐regressive moving average model (ARMA) to forecast wind speeds, with the AVOA assisting in selecting the optimal orders (q and p) of the ARMA model. This is done using historical wind speed data to capture uncertainty in the wind speed. The wind power is then calculated using various models and integrated into the UC problem. The effectiveness of the modified AVOA is examined on the IEEE 30‐bus system. The binary AVOA (BAVOA) outperforms several algorithms presented in the case study, demonstrating its superiority. Furthermore, the results indicate that BAVOA delivers superior outcomes within the discrete search space when compared to the continuous search space.
This paper investigates a solution for the unit commitment (UC) combined with a wind farm by modifying the metaheuristic African vultures optimization algorithm (AVOA) into a binary version using the sigmoid transfer function. An auto regressive moving average model (ARMA) is built to forecast the wind speed, its orders of the q and p are selected using the AVOA. The wind power is calculated using different models and integrated into the UC.
We study gas network problems with compressors and control valves under uncertainty that can be formulated as two‐stage robust optimization problems. Uncertain data are present in the physical ...parameters of the pipes as well as in the overall demand. We show how to exploit the special decomposable structure of the problem to reformulate the two‐stage problem as a single‐stage robust optimization problem. The right‐hand side of the single‐stage problem can be precomputed by solving a series of optimization problems and multiple elements of the right‐hand side can be combined into one optimization task. The practical feasibility and effectiveness of our approach is demonstrated with benchmarks on several gas network instances, among them a realistic model of the Greek natural gas network. Overall, aggregation and preprocessing allow us to quickly solve large gas network instances under uncertainty for the price of slightly more conservative solutions.
•Introduces novel hybrid techno-economic optimization method for distributed energy systems and microgrids.•Method guarantees result feasibility, especially during outage and islanded ...situations.•Compares to the state-of-art approach in literature.•Introduces novel state-of-charge constraint for reduced models to approximate multiple outage days.•Method shown to produce significant runtime savings with high optimality and robustness.
Recently, researchers have begun to study hybrid approaches to Microgrid techno-economic planning, where a reduced model optimizes the DER selection and sizing is combined with a full model that optimizes operation and dispatch. Though providing significant computation time savings, these hybrid models are susceptible to infeasibilities, when the size of the DER is insufficient to meet the energy balance in the full model during macrogrid outages. In this work, a novel hybrid optimization framework is introduced, specifically designed for resilience to macrogrid outages. The framework solves the same optimization problem twice, where the second solution using full data is informed by the first solution using representative data to size and select DER. This framework includes a novel constraint on the state of charge for storage devices, which allows the representation of multiple repeated days of grid outage, despite a single 24-h profile being optimized in the representative model. Multiple approaches to the hybrid optimization are compared in terms of their computation time, optimality, and robustness against infeasibilities. Through a case study on three real Microgrid designs, we show that allowing optimizing the DER sizing in both stages of the hybrid design, dubbed minimum investment optimization (MIO), provides the greatest degree of optimality, guarantees robustness, and provides significant time savings over the benchmark optimization.
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