This paper presents a multi-period auction for a day-ahead pool-based electricity market in which consumer payment for energy is minimized under uniform pricing. This optimization problem has been recently characteriz...
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This paper presents a multi-period auction for a day-ahead pool-based electricity market in which consumer payment for energy is minimized under uniform pricing. This optimization problem has been recently characterized as a non-separable, non-linear, mixed-integer, and combinatorial problem for which exact solution techniques are unavailable. We present a novel approach suitable for existing mixed-integerlinear solvers. A major contribution of this paper is the explicit characterization of uniform market-clearing prices as primal decision variables. The proposed methodology allows considering both quadratic and piecewise linear supply offers. In addition, the market-clearing procedure also takes into account inter-temporal operational constraints such as start-ups, ramp rates, and minimum up and down times, which may be part of generation offers. This approach provides the system operator and market agents with a valuable tool to assess consumer payment minimization versus currently used declared social welfare maximization. This conclusion is backed by simulation results obtained with off-the-shelf software. (C) 2013 Elsevier Ltd. All rights reserved.
The lower hedging problem with a minimal expected surplus risk criterion in incomplete markets is studied for American claims in finite state financial markets. It is shown that the lower hedging problem with linear e...
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The lower hedging problem with a minimal expected surplus risk criterion in incomplete markets is studied for American claims in finite state financial markets. It is shown that the lower hedging problem with linear expected surplus criterion for American contingent claims in finite state markets gives rise to a non-convex bilinearprogramming formulation which admits an exact linearization. The resulting mixed-integerlinear program can be readily processed by available software. (c) 2011 Elsevier B.V. All rights reserved.
The lower hedging problem with a minimal expected surplus risk criterion in incomplete markets is studied for American claims in finite state financial markets. It is shown that the lower hedging problem with linear e...
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The lower hedging problem with a minimal expected surplus risk criterion in incomplete markets is studied for American claims in finite state financial markets. It is shown that the lower hedging problem with linear expected surplus criterion for American contingent claims in finite state markets gives rise to a non-convex bilinearprogramming formulation which admits an exact linearization. The resulting mixed-integerlinear program can be readily processed by available software. (c) 2011 Elsevier B.V. All rights reserved.
In this article, a short-term scheduling model for cascaded hydroelectric chain plants with pumped-storage units is discussed, which considers in detail the various factors of the hydro system and units. A mixed-integ...
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In this article, a short-term scheduling model for cascaded hydroelectric chain plants with pumped-storage units is discussed, which considers in detail the various factors of the hydro system and units. A mixed-integer linear programming formulation is established. The main contribution of the article is that a systematic method is established such that the complex multivariable production functions of hydro units can be approximated by a piecewise linear function, and the characteristics of pumped-storage units are described by introducing some ancillary integer variables. Numerical testing results show that the mixed-integer linear programming formulation given in this article is efficient and effective.
This paper presents a comprehensive theoretical analysis of six distinct mixed-integerprogramming (MIP) formulations for preventive Generator Maintenance Scheduling (GMS), a critical problem for ensuring the reliabil...
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Batch sterilization with individual retorts is a common mode of operation in many food-canning plants. Although high-speed processing with continuous rotary or hydrostatic retort systems is used in very large canning ...
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Batch sterilization with individual retorts is a common mode of operation in many food-canning plants. Although high-speed processing with continuous rotary or hydrostatic retort systems is used in very large canning factories, such systems are not economically feasible in the majority of small- to medium-sized canneries. In such canneries, sterilization is carried out in a battery of retorts as a batch process. Although the unloading and reloading operations for each retort are labor intensive, a well-designed and managed plant can operate with surprising efficiency if it has the optimum number of retorts and scheduling of retort operation. The objective of this research was to present two mathematical models for sterilization scheduling in food-canning plants. The first model developed is for the case where given amount of different canned food products with specific quality requirements would be sterilized within a minimum plant operation time in an autoclave of given capacity. The second model addresses the problem of maximizing the amount of sterilized products in an autoclave of given capacity for given plant operation time. The developed models were based on mixed-integer linear programming and incorporated the possibility of simultaneous sterilization. Simultaneous sterilization applies mainly to small canneries with few retorts. In these situations, retorts often operate with only partial loads because of the small lot sizes, and they are severely under-utilized. In order to demonstrate the feasibility of the mixed-integer linear programming (MILP) models, several examples involving the sterilization of different products were included in this research. The methodology proposed in this study is of special relevance for small- and medium-sized food-canning plants that normally work with many different products at the same time.
This paper presents a novel supervised learning framework for real-time optimization of multi-parametric mixed-integer quadratic programming (mp-MIQP) problems. The framework utilizes a multi-layer perceptron (MLP) mo...
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Graph Neural Networks (GNNs) provide state-of-the-art graph learning performance, but their lack of transparency hinders our ability to understand and trust them, ultimately limiting the areas where they can be applie...
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Graph Neural Networks (GNNs) provide state-of-the-art graph learning performance, but their lack of transparency hinders our ability to understand and trust them, ultimately limiting the areas where they can be applied. Many methods exist to explain individual predictions made by GNNs, but there are fewer ways to gain more general insight into the patterns they have been trained to identify. Most existing methods for model-level GNN explanations attempt to generate graphs that exemplify these patterns, but the discreteness of graphs and the nonlinearity of deep GNNs make finding such graphs difficult. In this paper, we formulate the search for an explanatory graph as a mixed-integerprogramming (MIP) problem, in which decision variables specify the explanation graph and the objective function represents the quality of the graph as an explanation for a GNN's predictions of an entire class in the dataset. This approach, which we call MIPExplainer, allows us to directly optimize over the discrete input space and find globally optimal solutions with a minimal number of hyperparameters. MIPExplainer outperforms existing methods in finding accurate and stable explanations on both synthetic and real-world datasets. Code is available at https://***/blake-gaines/MIPExplainer.
Cutting planes (cuts) play an important role in solving mixed-integerlinear programs (MILPs), which formulate many important real-world applications. Cut selection heavily depends on (P1) which cuts to prefer and (P2...
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Cutting planes (cuts) play an important role in solving mixed-integerlinear programs (MILPs), which formulate many important real-world applications. Cut selection heavily depends on (P1) which cuts to prefer and (P2) how many cuts to select. Although modern MILP solvers tackle (P1)-(P2) by human-designed heuristics, machine learning carries the potential to learn more effective heuristics. However, many existing learning-based methods learn which cuts to prefer, neglecting the importance of learning how many cuts to select. Moreover, we observe that (P3) what order of selected cuts to prefer significantly impacts the efficiency of MILP solvers as well. To address these challenges, we propose a novel hierarchical sequence/set model (HEM) to learn cut selection policies. Specifically, HEM is a bi-level model: (1) a higher-level module that learns how many cuts to select, (2) and a lower-level module-that formulates the cut selection as a sequence/set to sequence learning problem-to learn policies selecting an ordered subset with the cardinality determined by the higher-level module. To the best of our knowledge, HEM is the first data-driven methodology that well tackles (P1)-(P3) simultaneously. Experiments demonstrate that HEM significantly improves the efficiency of solving MILPs on eleven challenging MILP benchmarks, including two Huawei's real problems.
This article addresses mixedinteger fractional signomial geometric programming (MIFSGP) problems, which have been widely used in industrial design. In this paper, first, we convert fractional signomial programming in...
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