Security-constrained unit commitment (SCUC), as one of key components in power system operation, is being widely applied in vertically integrated utilities and restructured power systems. The efficient solution framew...
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Security-constrained unit commitment (SCUC), as one of key components in power system operation, is being widely applied in vertically integrated utilities and restructured power systems. The efficient solution framework is to implement iterations between a master problem (unit commitment) and subproblems (network security evaluations). In industrial applications, both Lagrangian relaxation and mixed-integer programming are commonly applied for the unit commitment problem, and both linear sensitivity factor and Benders cut methods are used to generate additional constraints in the phase of network security evaluations. This paper evaluates capabilities and performances of each algorithm through technical discussion and numerical testing. Special topics on the large-scale SCUC engine development are also discussed in this paper, such as input data screening, inactive constrains elimination, contingency management, infeasibility handling, parallel computing, and model simplification. This paper will benefit academic researchers, software developers, and system operators when they design, develop and assess effective models and algorithms for solving large-scale SCUC problems.
The p-hub center problem has extensive applications in various real-world fields such as transportation and telecommunication systems. This paper presents a new risk aversion p-hub center problem with fuzzy travel tim...
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The p-hub center problem has extensive applications in various real-world fields such as transportation and telecommunication systems. This paper presents a new risk aversion p-hub center problem with fuzzy travel times, in which value-at-risk (VaR) criterion is adopted in the formulation of objection function. For trapezoidal and normal fuzzy travel times, we first turn the original VaR p-hub center problem into its equivalent parametric mixed-integer programming problem, then develop a hybrid algorithm by incorporating genetic algorithm and local search (GALS) to solve the parametric mixed-integer programming problem. In our designed GALS, the GA is used to perform global search, while LS strategy is applied to each generated individual (or chromosome) of the population. Finally, we conduct two sets of numerical experiments and discuss the experimental results obtained by general-purpose LINGO solver, standard GA and GALS. The computational results show that the GALS achieves the better performance than LINGO solver and standard GA. (C) 2012 Elsevier B. V. All rights reserved.
The modeling of time plays a key role in the formulation of mixed-integer programming (MIP) models for scheduling, production planning, and operational supply chain planning problems. It affects the size of the model,...
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The modeling of time plays a key role in the formulation of mixed-integer programming (MIP) models for scheduling, production planning, and operational supply chain planning problems. It affects the size of the model, the computational requirements, and the quality of the solution. While the development of smaller continuous-time scheduling models, based on multiple time grids, has received considerable attention, no truly different modeling methods are available for discrete-time models. In this paper, we challenge the long-standing belief that employing a discrete modeling of time requires a common uniform grid. First, we show that multiple grids can actually be employed in discrete-time models. Second, we show that not only unit-specific but also task-specific and material-specific grids can be generated. Third, we present methods to systematically formulate discrete-time multi-grid models that allow different tasks, units, or materials to have their own time grid. We present two different algorithms to find the grid. The first algorithm determines the largest grid spacing that will not eliminate the optimal solution. The second algorithm allows the user to adjust the level of approximation;more approximate grids may have worse solutions, but many fewer binary variables. Importantly, we show that the proposed models have exactly the same types of constraints as models relying on a single uniform grid, which means that the proposed models are tight and that known solution methods can be employed. The proposed methods lead to substantial reductions in the size of the formulations and thus the computational requirements. In addition, they can yield better solutions than formulations that use approximations. We show how to select the different time grids, state the formulation, and present computational results. (C) 2013 Elsevier Ltd. All rights reserved.
In this paper, we analyse a service provider's mixed bundling problem for services such as sporting events or holiday packages. Pursuing the objective of maximising total revenue, the service provider has to deter...
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In this paper, we analyse a service provider's mixed bundling problem for services such as sporting events or holiday packages. Pursuing the objective of maximising total revenue, the service provider has to determine static prices for each single product at the beginning of the selling period. Additionally, an optimal package price has to be chosen for the bundle that comprises one unit of each single product. Because of capacity constraints, the availability of products can change over time such that consumers are forced to switch from their preferred subset of products to an alternative following dynamic substitution. We propose two mixed-integer linear programmes based on reservation prices that appropriately model the consumer choice process to address the bundling problem. It becomes evident that the determination of the optimal prices is computationally expensive even for small problem classes. Therefore, we develop metaheuristics using variable neighbourhoods. To evaluate their performance, we propose the following new approach: our extensive computational study is performed using especially generated scenarios for which the optimal product prices are known. For this purpose, we present a set of conditions for the generation of reservation prices that guarantee the optimality of the predefined prices. Based on our computational results, managerial insights are derived. (C) 2013 Elsevier B.V. All rights reserved.
Energy management in Smart Home environments is undoubtedly one of the pressing issues in the Smart Grid research field. The aim typically consists in developing a suitable engineering solution able to maximally explo...
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Energy management in Smart Home environments is undoubtedly one of the pressing issues in the Smart Grid research field. The aim typically consists in developing a suitable engineering solution able to maximally exploit the availability of renewable resources. Due to the presence of diverse cooperating devices, a complex model, involving the characterization of nonlinear phenomena, is indeed required on purpose. In this paper an Hybrid Soft Computing algorithmic framework, where genetic, neural networks and deterministic optimization algorithms jointly operate, is proposed to perform an efficient scheduling of the electrical tasks and of the activity of energy resources, by adequately handling the inherent nonlinear aspects of the energy management model. In particular, in order to address the end-user comfort constraints, the home thermal characterization is needed: this is accomplished by a nonlinear model relating the energy demand with the required temperature profile. A genetic algorithm, based on such model, is then used to optimally allocate the energy request to match the user thermal constraints, and therefore to allow the mixed-integer deterministic optimization algorithm to determine the remaining energy management actions. From this perspective, the ability to schedule the tasks and allocate the overall energy resources over a finite time horizon is assessed by means of diverse computer simulations in realistic conditions, allowing the authors to positively conclude about the effectiveness of the proposed approach. The degree of realism of the simulated scenario is confirmed by the usage of solar energy production forecasted data, obtained by means of a neural-network based algorithm which completes the framework.
In this paper, we consider mixedinteger linear programming (MIP) formulations for piecewise linear functions (PLFs) that are evaluated when an indicator variable is turned on. We describe modifications to standard MI...
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In this paper, we consider mixedinteger linear programming (MIP) formulations for piecewise linear functions (PLFs) that are evaluated when an indicator variable is turned on. We describe modifications to standard MIP formulations for PLFs with desirable theoretical properties and superior computational performance in this context. (C) 2013 Elsevier B.V. All rights reserved.
For stochastic mixed-integer programs, we revisit the dual decomposition algorithm of Came and Schultz from a computational perspective with the aim of its parallelization. We address an important bottleneck of parall...
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For stochastic mixed-integer programs, we revisit the dual decomposition algorithm of Came and Schultz from a computational perspective with the aim of its parallelization. We address an important bottleneck of parallel execution by identifying a formulation that permits the parallel solution of the master program by using structure-exploiting interior-point solvers. Our results demonstrate the potential for parallel speedup and the importance of regularization (stabilization) in the dual optimization. Load imbalance is identified as a remaining barrier to parallel scalability. (C) 2013 Elsevier B.V. All rights reserved.
We present an exact mixed-integer programming (MIP) solution scheme where a set-covering model is used to find a small set of first-choice branching variables. In a preliminary "sampling" phase, our method q...
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We present an exact mixed-integer programming (MIP) solution scheme where a set-covering model is used to find a small set of first-choice branching variables. In a preliminary "sampling" phase, our method quickly collects a number of relevant low-cost fractional solutions that qualify as obstacles for the linear programming (LP) relaxation bound improvement. Then a set covering model is solved to detect a small subset of variables (a "backdoor," in the artificial intelligence jargon) that "cover the fractionality" of the collected fractional solutions. These backdoor variables are put in a priority branching list, and a black-box MIP solver is eventually run-in its default mode-by taking this list into account, thus avoiding any other interference with its highly optimized internal mechanisms. Computational results on a large set of instances from the literature are presented, showing that some speedup can be achieved even with respect to a state-of-the-art solver such as IBM ILOG CPLEX 12.2.
The objective of this work was to determine the location of emergency material warehouses. For the site selection problem of emergency material warehouses, the triangular fuzzy numbers are respectively demand of the d...
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The objective of this work was to determine the location of emergency material warehouses. For the site selection problem of emergency material warehouses, the triangular fuzzy numbers are respectively demand of the demand node, the distance between the warehouse and demand node and the cost of the warehouse, a bi-objective programming model was established with minimum total cost of the system and minimum distance between the selected emergency material warehouses and the demand node. Using the theories of fuzzy numbers, the fuzzy programming model was transformed into a determinate bi-objective mixedintegerprogramming model and a heuristic algorithm for this model was designed. Then, the algorithm was proven to be feasible and effective through a numerical example. Analysis results show that the location of emergency material warehouse depends heavily on the values of degree a and weight wl. Accurate information of a certain emergency activity should be collected before making the decision.
In this paper we propose improved Benders decomposition schemes for solving a remanufacturing supply chain design problem (RSCP). We introduce a set of valid inequalities in order to improve the quality of the lower b...
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In this paper we propose improved Benders decomposition schemes for solving a remanufacturing supply chain design problem (RSCP). We introduce a set of valid inequalities in order to improve the quality of the lower bound and also to accelerate the convergence of the classical Benders algorithm. We also derive quasi Pareto-optimal cuts for improving convergence and propose a Benders decomposition scheme to solve our RSCP problem. Computational experiments for randomly generated networks of up to 700 sourcing sites, 100 candidate sites for locating reprocessing facilities, and 50 reclamation facilities are presented. In general, according to our computational results, the Benders decomposition scheme based on the quasi Pareto-optimal cuts outperforms the classical algorithm with valid inequalities. (C) 2013 Elsevier Ltd. All rights reserved.
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