Thermal unit commitment (UC) is a nonlinear combinatorial optimization problem that minimizes total operating costs while considering system load balance, on/off restrictions and other constraints. Successfully solvin...
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Thermal unit commitment (UC) is a nonlinear combinatorial optimization problem that minimizes total operating costs while considering system load balance, on/off restrictions and other constraints. Successfully solving the thermal UC problem contributes to a more reliable power system and reduces thermal costs. This paper presents an exact mixed-integer quadratic programming (EMIQP) method for large-scale thermal UC problems. EMIQP revolutionizes the landscape by seamlessly translating the intricate nonlinear combinatorial optimization problem of UC into an exact mixed-integer quadratic formulation. This approach also elegantly reimagines on/off constraints as mixed-integer linear equations, employing both the sum and respective approaches. Our case studies unequivocally demonstrate the exceptional prowess of the EMIQP method, consistently securing the global optimum. Moreover, the mathematical-based EMIQP method produces identical results at each run, which is extremely important for UC in the real world.
The NP-hard maximum-entropy sampling problem (MESP) seeks a maximum (log-) determinant principal submatrix, of a given order, from an input covariance matrix C. We give an efficient dynamic-programming algorithm for M...
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The NP-hard maximum-entropy sampling problem (MESP) seeks a maximum (log-) determinant principal submatrix, of a given order, from an input covariance matrix C. We give an efficient dynamic-programming algorithm for MESP when C (or its inverse) is tridiagonal and generalize it to the situation where the support graph of C (or its inverse) is a spider graph with a constant number of legs (and beyond). We give a class of arrowhead covariance matrices C for which a natural greedy algorithm solves MESP. A mask M for MESP is a correlation matrix with which we pre-process C, by taking the Hadamard product M degrees C. Upper bounds on MESP with M degrees C give upper bounds on MESP with C. Most upper-bounding methods are much faster to apply, when the input matrix is tridiagonal, so we consider tridiagonal masks M (which yield tridiagonal M degrees C). We make a detailed analysis of such tridiagonal masks, and develop a combinatorial local-search based upper-bounding method that takes advantage of fast computations on tridiagonal matrices.(c) 2023 Elsevier B.V. All rights reserved.
Topology impacts important network performance metrics, including link utilization, throughput and latency, and is of central importance to network operators. However, due to the combinatorial nature of network topolo...
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Topology impacts important network performance metrics, including link utilization, throughput and latency, and is of central importance to network operators. However, due to the combinatorial nature of network topology, it is extremely difficult to obtain an optimal solution, especially since topology planning in networks also often comes with management-specific constraints. As a result, local optimization with hand-tuned heuristic methods from human experts is often adopted in practice. Yet, heuristic methods cannot cover the global topology design space while taking into account constraints, and cannot guarantee to find good solutions. In this paper, we propose a novel deep reinforcement learning (DRL) algorithm for graph searching, called DRL-GS, for network topology optimization. DRL-GS consists of three novel components, including a verifier to validate the correctness of a generated network topology, a graph neural network (GNN) to efficiently approximate topology rating, and a DRL agent to conduct a topology search. DRL-GS can efficiently search over relatively large topology space and output topology with satisfactory performance. We conduct a case study based on a real-world network scenario, and our experimental results demonstrate the superior performance of DRL-GS in terms of both efficiency and performance.
The maximum-entropy sampling problem is the NP-hard problem of maximizing the (log) determinant of an order-s principal submatrix of a given order n covariance matrix C. Exact algorithms are based on a branch-and-boun...
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The maximum-entropy sampling problem is the NP-hard problem of maximizing the (log) determinant of an order-s principal submatrix of a given order n covariance matrix C. Exact algorithms are based on a branch-and-bound framework. The problem has wide applicability in spatial statistics and in particular in environmental monitoring. Probably the best upper bound for the maximum empirically is Anstreicher???s scaled ???linx??? bound. An earlier methodology for potentially improving any upper-bounding method is by masking, that is, applying the bounding method to C ??? M, where M is any correlation matrix. We establish that the linx bound can be improved via masking by an amount that is at least linear in n, even when optimal scaling parameters are used. We also extend an earlier result that the linx bound is convex in the logarithm of a scaling parameter, making a full characterization of its behavior and providing an efficient means of calculating its limiting behavior in all cases.
The NP-hard maximum-entropy sampling problem (MESP) seeks a maximum (log-)determinant principal submatrix, of a given order, from a positive-semidefinite input matrix C. We give an efficient dynamic-programming algori...
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The NP-hard maximum-entropy sampling problem (MESP) seeks a maximum (log-)determinant principal submatrix, of a given order, from a positive-semidefinite input matrix C. We give an efficient dynamic-programming algorithm for MESP when C (or its inverse) is tridiagonal. A mask M for MESP is a correlation matrix with which we pre-process C, by taking the Hadamard product M o C. Upper bounds on MESP with M o C give upper bounds on MESP with C. Most upper-bounding methods are much faster to apply, when the input matrix is tridiagonal, so we consider tridiagonal masks M (which yield tridiagonal M o C). We analyze such tridiagonal masks, and develop a combinatorial local-search based upper-bounding method that takes advantage of fast computations on tridiagonal matrices. (C) 2021 The Authors. Published by Elsevier B.V.
The NP-hard maximum-entropy sampling problem (MESP) seeks a maximum (log-)determinant principal submatrix, of a given order, from a positive-semidefinite input matrix C. We give an efficient dynamic-programming algori...
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The NP-hard maximum-entropy sampling problem (MESP) seeks a maximum (log-)determinant principal submatrix, of a given order, from a positive-semidefinite input matrix C. We give an efficient dynamic-programming algorithm for MESP when C (or its inverse) is tridiagonal. A mask M for MESP is a correlation matrix with which we pre-process C, by taking the Hadamard product M ◦C. Upper bounds on MESP with M ◦C give upper bounds on MESP with C. Most upper-bounding methods are much faster to apply, when the input matrix is tridiagonal, so we consider tridiagonal masks M (which yield tridiagonal M ◦ C). We analyze such tridiagonal masks, and develop a combinatorial local-search based upper-bounding method that takes advantage of fast computations on tridiagonal matrices.
In this paper, a two-level algorithm is proposed to solve the distribution network reconfiguration with an objective of minimum power loss. In the first level reconfiguration, switches of maximum power loss reduction ...
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In this paper, a two-level algorithm is proposed to solve the distribution network reconfiguration with an objective of minimum power loss. In the first level reconfiguration, switches of maximum power loss reduction are disconnected by the branch exchange (BE) algorithm. Based on the results, neighbourhoods of disconnected switches are constructed by the deterministic transform method in the second level. The variable neighbourhood search (VNS) algorithm keeps searching the neighbourhoods to obtain a better solution with a lower power loss. Simulations are carried out on IEEE33 and PG&69 distribution networks to verify the superiority of the proposed algorithm. The obtained results are compared with the other methods available in the paper. It can be concluded that the presented method has both high stability and rapidity.
We provide a first demonstration of the idea that matrix-based algorithms for nonlinear combinatorial optimization problems can be efficiently implemented. Such algorithms were mainly conceived by theoretical computer...
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We provide a first demonstration of the idea that matrix-based algorithms for nonlinear combinatorial optimization problems can be efficiently implemented. Such algorithms were mainly conceived by theoretical computer scientists for proving efficiency. We are able to demonstrate the practicality of our approach by developing an implementation on a massively parallel architecture, and exploiting scalable and efficient parallel implementations of algorithms for ultra high-precision linear algebra. Additionally, we have delineated and implemented the necessary algorithmic and coding changes required in order to address problems several orders of magnitude larger, dealing with the limits of scalability from memory footprint, computational efficiency, reliability, and interconnect perspectives.
In this manuscript, a vehicle allocation problem involving a heterogeneous fleet of vehicles for delivering products from a manufacturing firm to a set of depots is considered. Each depot has a specific order quantity...
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In this manuscript, a vehicle allocation problem involving a heterogeneous fleet of vehicles for delivering products from a manufacturing firm to a set of depots is considered. Each depot has a specific order quantity and transportation costs consist of fixed and variable transportation cost. The objective is to assign the proper type and number of vehicle to each depot route to minimize the total transportation costs. It is assumed that the number of chartering vehicle types is limited. It is also assumed that a discount mechanism is applied to the vehicles renting cost. The discount mechanism is applied to the fixed cost, based on the number of vehicles to be rented. A mathematical programming model is proposed which is then converted to a mixed 0-1 integer programming model. Due to the computational complexity of the proposed mathematical model, a priority based genetic algorithm capable of solving the real world size problems was proposed. A computational experiment is conducted through which, the performance of the proposed algorithm is evaluated. The results reveal that the proposed algorithm is capable of providing the astonishing solutions with minimal computational effort, comparing with the CPLEX solutions. (C) 2016 Elsevier Ltd. All rights reserved.
We revisit the classical resource allocation problem with general convex objective functions, subject to an integer knapsack constraint. This class of problems is fundamental in discrete optimization and arises in a w...
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We revisit the classical resource allocation problem with general convex objective functions, subject to an integer knapsack constraint. This class of problems is fundamental in discrete optimization and arises in a wide variety of applications. In this paper, we propose a novel polynomial-time divide-and-conquer algorithm (called the multi-phase algorithm) and prove that it has a computational complexity of O(n log n log N), which outperforms the best known polynomial-time algorithm with O(n( log N)(2)). (C) 2015 Elsevier B.V. All rights reserved.
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