A new solution procedure for the discrete VAR optimization of a power distribution system is presented in this paper. In order to obtain an optimal discrete solution within a reasonable time, a mixed-integer programmi...
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A new solution procedure for the discrete VAR optimization of a power distribution system is presented in this paper. In order to obtain an optimal discrete solution within a reasonable time, a mixed-integer programming method combined with an expert system is proposed to achieve these requirements. The proposed expert system helps the system planning engineers to allocate an appropriate initial feasible solution, and to decide the position of transformer tap settings as well as the number of capacitor units. From three solution stages using the linear programming approach, the expert system approach, and the mixed-integer programming approach, the discrete VAR optimization problem is promptly solved. Numerical simulations of a small-scale system and a practical system are demonstrated with significant results. The results demonstrate the effectiveness and improvement of the proposed method to solve the VAR optimization problem in a power distribution system.
Material storage locations incurring minimum transportation costs in construction are a common construction management problem. Storage locations influence the delivery path and overall project efficiency. Lower floor...
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Material storage locations incurring minimum transportation costs in construction are a common construction management problem. Storage locations influence the delivery path and overall project efficiency. Lower floors of buildings after completion and developing sufficient structural strength will be utilized as storages and layout plans should be designed to achieve maximum construction efficiency in terms of total transportation and distribution costs. A mixed-integer programming is formulated to optimize the vertical hoisting and storage layout solvable by a branch-and-bound technique. Total transportation cost is derived as an objective for optimization. Material storage locations are defined as binary variables. Linear constraints are developed to satisfy design requirements. A numerical example storing 10 material types and delivering materials in a 30-storey building is given for illustration. Numerical results optimized by the MIP approach will be compared with those optimized by the genetic algorithms. The MIP solution shows better solution quality taking less computing time.
The paper presents a new mixed-integer programming formulation for the maximally diverse grouping problem (MDGP) with attribute values. The MDGP is the problem of assigning items to groups such that all groups are as ...
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The paper presents a new mixed-integer programming formulation for the maximally diverse grouping problem (MDGP) with attribute values. The MDGP is the problem of assigning items to groups such that all groups are as heterogeneous as possible. In the version with attribute values, the heterogeneity of groups is measured by the sum of pairwise absolute differences of the attribute values of the assigned items, i.e. by the Manhattan metric. The advantage of the version with attribute values is that the objective function can be reformulated such that it is linear instead of quadratic like in the standard MDGP formulation. We evaluate the new model formulation for the MDGP with attribute values in comparison with two different MDGP formulations from the literature. Our model formulation leads to substantially improved computation times and solves instances of realistic sizes (for example the assignment of students to seminars) with up to 70 items and three attributes, 50 items and five attributes, and 30 items and ten attributes to (near) optimality within half an hour.
The increased use of multi-vehicles raises concerns about safety and economic aspects in several applications. Therefore, this work proposes a moving horizon planning algorithm for covering unexplored regions using mu...
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Fenchel cutting planes are based on the dual relationship between separation and optimization and can be applied in many instances where alternative cutting planes cannot. They are deep in the sense of providing the m...
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Fenchel cutting planes are based on the dual relationship between separation and optimization and can be applied in many instances where alternative cutting planes cannot. They are deep in the sense of providing the maximum separation between a point ($) over cap x and a polyhedron P as measured by an arbitrary norm which is specified in the process of generating a Fenchel cut. This paper demonstrates a number of fundamental convergence properties of Fenchel cuts and addresses the question of which norms lead to the most desirable Fenchel cuts. The strengths and weaknesses of the related class of 1-polar cuts are also examined.
In this paper, an under development mixed-integer programming model is presented and used to solve the Production-Inventory-Distribution-Routing Problem (PIDRP), the main objective is to minimize the total cost of pro...
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ISBN:
(纸本)9781467380669
In this paper, an under development mixed-integer programming model is presented and used to solve the Production-Inventory-Distribution-Routing Problem (PIDRP), the main objective is to minimize the total cost of production, inventory, and transportation without violating the demand fulfillment policy. The proposed model deals with multiple products with different characteristics, split deliveries, a heterogeneous fleet of vehicles, and a route limitation for each vehicle. The main contribution of this work is the validation of the mathematical model and testing it for solving small-sized instances from literature.
The present authors consider the widely popular Argentine Turismo Carretera car racing series, which consists of 11 regular phase races followed by five playoff races. After the regular phase, the first 12 racers in t...
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The present authors consider the widely popular Argentine Turismo Carretera car racing series, which consists of 11 regular phase races followed by five playoff races. After the regular phase, the first 12 racers in the standings qualify for the playoffs, which determine the champion. The present authors address the problem of determining, at any point within the regular phase, the minimum number of points that each racer must earn in the remainder of the regular phase in order to secure a playoff spot. Two mixed-integer programming models for this problem are presented, their properties and practical performance are analysed, and the obtained results are discussed.
Dantzig-Wolfe decomposition can be used to solve the Lagrangian dual of a linear mixed-integer programming problem (MIP) if the dual structure of the (MIP) is exploited via Lagrangian relaxation with respect to the co...
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In recent years, load monitoring and analysis have played an increasingly important role in power system dispatch management. Although event-based non-intrusive load monitoring methods have made some progress in theor...
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ISBN:
(纸本)9798350386783;9798350386776
In recent years, load monitoring and analysis have played an increasingly important role in power system dispatch management. Although event-based non-intrusive load monitoring methods have made some progress in theory and practice, the increasing diversification and complexity of equipment types require enhanced recognition accuracy of existing methods. It is challenging to capture the power usage behavior of multi-state appliances. In this paper, a load matching method based on mixed-integer programming is proposed to assist in correcting the event detection identification results. This method involves constructing a matching matrix and solving it by considering event matching constraints, power matching constraints, and the number of matches constraints. The goal is to minimize the power error and the penalty terms associated with the number of matches constraints. Through arithmetic analysis of 546 real data in the public dataset PLAID, the method achieves an accuracy of 92.13%. This validates the effectiveness of mixed-integer programming modeling and demonstrates its potential as a supplementary tool for improving load identification results.
Piecewise regression is a versatile approach used in various disciplines to approximate complex functions from limited, potentially noisy data points. In control, piecewise regression is, e.g., used to approximate the...
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Piecewise regression is a versatile approach used in various disciplines to approximate complex functions from limited, potentially noisy data points. In control, piecewise regression is, e.g., used to approximate the optimal control law of model predictive control (MPC), the optimal value function, or unknown system dynamics. Neural networks are a common choice to solve the piecewise regression problem. However, due to their nonlinear structure, training is often based on gradient-based methods, which may fail to find a global optimum or even a solution that leads to a small approximation error. To overcome this problem and to find a global optimal solution, methods based on mixed-integer programming (MIP) can be used. However, the known MIP-based methods are either limited to a special class of functions, e.g., convex piecewise affine functions, or they lead to complex approximations in terms of the number of regions of the piecewise defined function. Both complicate a usage in the framework of control. We propose a new MIP-based method that is not restricted to a particular class of piecewise defined functions and leads to functions that are fast to evaluate and can be used within an optimization problem, making them well suited for use in control.
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