In this paper, we present a method to exactly certify the computational complexity of standard suboptimal branch-and-bound (B&B) algorithms for computing suboptimal solutions to mixed-integer linear programming (M...
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ISBN:
(纸本)9781713872344
In this paper, we present a method to exactly certify the computational complexity of standard suboptimal branch-and-bound (B&B) algorithms for computing suboptimal solutions to mixed-integer linear programming (MILP) problems. Three well-known approaches for suboptimal B&B are considered. This work shows that it is possible to exactly certify the computational complexity also when these approaches are used. Moreover, it also enables to compute exact bounds on the level of suboptimality actually to be obtained online, also for methods previously without any such guarantees. It additionally provides a novel deeper insight into how they affect the performance of the B&B algorithm in terms of the required computation time and memory storage. The exact bounds on the online worst-case computational complexity (e.g., the accumulated number of LP solver iterations or size of the B&B tree) and the worst-case suboptimality computed with the proposed method are very relevant for real-time applications such as Model Predictive Control (MPC) for hybrid systems. The numerical experiments confirm the correctness of the proposed method, and they demonstrate the usefulness of the certification method for certification of a standard online B&B-based MILP solver employing the three considered suboptimal techniques. Copyright (c) 2023 The Authors.
In transmission networks, power flows and network topology are deeply intertwined due to power flow physics. Recent literature shows that a specific more hierarchical network structure can effectively inhibit the prop...
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A mixed-integer linear programming (MILP) model is proposed for solving a one dimension cutting stock problem (1D-CSP) in the steel industry. A case study of a metallurgical company is presented and the objective is t...
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ISBN:
(纸本)9783030867027;9783030867010
A mixed-integer linear programming (MILP) model is proposed for solving a one dimension cutting stock problem (1D-CSP) in the steel industry. A case study of a metallurgical company is presented and the objective is to minimize waste in the cutting process of steel bars, considering inventory constraints and the potential use of the resulting leftovers. The computational results showed that an optimal solution was always found with an average improvement in waste reduction of 80%. There was no significant difference when comparing results between the complete model and the model without inventory constraints.
This research proposes an optimization approach to enhance the stencil printing process (SPP) in surface mount printed circuit board (PCB) assembly. Stencil printing behavior is affected by many variables including st...
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This paper aims to investigate the capability of mixed-integer linear programming (MILP) method and genetic algorithm (GA) to solve binary problem (BP). A comparative study on the MILP method and GA with default and t...
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ISBN:
(纸本)9781538657485
This paper aims to investigate the capability of mixed-integer linear programming (MILP) method and genetic algorithm (GA) to solve binary problem (BP). A comparative study on the MILP method and GA with default and tuned setting to find out an optimal solution is presented. The mixed-integerprogramming library (MIPLIB 2010) is used to test and evaluate algorithms. The evaluation is shown in quality of the solution and the execution time of computation. The results show that GA is superior to MILP in execution time with inconsistent results. However, MILP is superior to GA in quality of the solution with more stable results.
Benders' decomposition (BD) algorithm constitutes a powerful mathematical programming method of solving mixed-integer linear programming (MILP) problems with a specific block structure. Nevertheless, BD still need...
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ISBN:
(纸本)9781728190549
Benders' decomposition (BD) algorithm constitutes a powerful mathematical programming method of solving mixed-integer linear programming (MILP) problems with a specific block structure. Nevertheless, BD still needs to solve an NP-hard quasi-integerprogramming master problem (MAP), which motivates us to harness the popular variational quantum algorithm (VQA) to assist BD. More specifically, we choose the popular quantum approximate optimization algorithm (QAOA) of the VQA family. We transfer the BD's MAP into a digital quantum circuit associated with a physically tangible problem-specific ansatz, and then solve it with the aid of a state-of-the-art digital quantum computer. Next, we evaluate the computational results and discuss the feasibility of the proposed algorithm. The hybrid approach advocated, which utilizes both classical and digital quantum computers, is capable of tackling many practical MILP problems in communication and networking, as demonstrated by a pair of case studies.
In this paper, we propose a new vehicle routing problem variant. The new problem is a type of selective vehicle routing model in which it is not necessary to visit all nodes, but to visit enough nodes in such a way th...
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ISBN:
(纸本)9783030003531;9783030003524
In this paper, we propose a new vehicle routing problem variant. The new problem is a type of selective vehicle routing model in which it is not necessary to visit all nodes, but to visit enough nodes in such a way that all clusters are visited and from which it is possible to cover all nodes. Here, a mixed-integer linear programming formulation (MILP) is proposed in order to model the problem. The MILP is tested by using adapted instances from the generalized vehicle routing problem (GVRP). The model is also tested on small size GVRP instances as a special case of our proposed model. The results allow to evaluate the impact of clusters configuration in solver efficacy.
With advancements in technology, commercial aircraft formation flying is becoming increasingly feasible as an efficient and environmentally friendly flight method. However, gaps remain in practical implementation, par...
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In a society where the demand for multimedia applications and data exchange is experiencing an unstoppable growth, multibeam systems have proven to be one of the most relevant solutions for satellite-based communicati...
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ISBN:
(纸本)9781467395205
In a society where the demand for multimedia applications and data exchange is experiencing an unstoppable growth, multibeam systems have proven to be one of the most relevant solutions for satellite-based communication systems. Though already well represented among the geostationary satellites today, there are still several unresolved design optimization challenges for these complex systems that could lead to improved performances and to better system costs. The satellite platform, the repeater, and the antennas are examples of subsystems that should be designed jointly in order to reach an optimized technical solution that fulfills the service requirements. Traditionally, such complex tasks are addressed through a decomposition of the overall system design into a sequence of smaller decision problems. In this article, we propose to rely on operations research techniques to, on the one hand, take into account explicitly the interdependencies of these decomposed problems, and on the other hand, to handle the own constraints of each subsystem and their interactions. In this paper, the focus is laid on the optimization of the beam layouts of the multibeam satellites. Indeed, in addition to being a perfect example of the aforementioned importance of dealing with subsystem constraints, this problem appears early in the chain of design of a multibeam satellite system and is therefore critical for the quality of the telecommunication system;the weaknesses of a beam layout cannot be made up for later on in the system design. For this crucial optimization phase, the strength of the methodology we propose in this paper is to use mixed-integer linear programming to incorporate explicitly technological feasibility constraints of the subsystems involved, while preparing at best the subsequent design problems. Most importantly, our approach allows to overcome several resisting flaws of the already existing algorithms.
A nodal clearing price model in day ahead market considering security constraints is established. First, the intra-region and inter-region transaction modes are explained, and the order types are shown. The clearing m...
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A nodal clearing price model in day ahead market considering security constraints is established. First, the intra-region and inter-region transaction modes are explained, and the order types are shown. The clearing model takes the total social welfare as the goal, considers the security constraints of the network, and specifies the market clearing price expressed by the Lagrangian multiplier. Then the mixedlinearprogramming algorithm is used to solve the model in this paper, and a verification method based on the N-1 criterion is performed. Finally, a numerical case is performed to calculate the clearing price of the network, which illustrates the effectiveness of the proposed method and model.
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