A novel integerlinearprogramming (ILP) formulation of deploying base stations and repeaters to meet a target coverage of traffic points (TPs) with minimum cost is presented, where the number of discrete variables ap...
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A novel integerlinearprogramming (ILP) formulation of deploying base stations and repeaters to meet a target coverage of traffic points (TPs) with minimum cost is presented, where the number of discrete variables approximately equals the sum between the number of TPs and the number of backhaul links. The ILP is proved equivalent to a mixed-ILP (MILP) where the number of discrete variables is reduced by the number of TPs. Our MILP approach always yields optimal deployment solutions. A case study is presented to demonstrate the benefits of using repeaters based on the optimal solutions of the MILP.
This paper addresses resource-constrained project scheduling problem with mixed uncertainty of randomness and fuzziness (FS-RCPSP). The activity durations are considered to be fuzzy random variables. A resource flow n...
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This paper addresses resource-constrained project scheduling problem with mixed uncertainty of randomness and fuzziness (FS-RCPSP). The activity durations are considered to be fuzzy random variables. A resource flow network based mathematical model with fuzzy random variables is presented. Then, this model is transformed into a mixed-integer linear programming model with crisp variables. The CPLEX 12.6.0.1 solver in AIMMS (2014) is employed for applying the proposed model to solve 960 benchmark instances generated from the well-known sets J30 and J60 in PSPLIB. The computational results are encouraging and indicate the ability of the proposed model to handle the FS-RCPSP.
Multi-objective optimization problems (MOOP) reflect the complexity of many real-world decision problems where objectives are conflicting. The presence of more than one criterion makes finding the non-dominated (ND) p...
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Multi-objective optimization problems (MOOP) reflect the complexity of many real-world decision problems where objectives are conflicting. The presence of more than one criterion makes finding the non-dominated (ND) points a crucial issue in the decision making process. Tri-objective mixed-integerlinear programs (TOMILP) are an important subclass of MOOPs that are applicable to many problems in economics, business, science, and engineering including sustainable systems that must consider economic, environmental, and social concerns simultaneously. The literature on finding the ND points of TOMILPs is limited;there are only a few algorithms published in the literature that do not guarantee generating the entire ND points of TOMILPs. We present a new method, the Slicing with Adaptive Steps Search (SASS), to generate the ND points of TOMILPs. The result of SASS is primarily a superset of the set of ND points in the form of (partially) ND faces. We then perform a post-processing to eliminate the dominated parts of the partially ND faces. We provide a theoretical analysis of SASS and illustrate its effectiveness on a large set of instances.
This paper addresses a fuel-constrained, multiple vehicle routing problem (FCMVRP) in the presence of multiple refueling stations. We are given a set of targets, a set of refueling stations, and a depot where m vehicl...
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This paper addresses a fuel-constrained, multiple vehicle routing problem (FCMVRP) in the presence of multiple refueling stations. We are given a set of targets, a set of refueling stations, and a depot where m vehicles are stationed. The vehicles are allowed to refuel at any refueling station, and the objective of the problem is to determine a route for each vehicle starting and terminating at the depot, such that each target is visited by at least one vehicle, the vehicles never run out of fuel while traversing their routes, and the total travel cost of all the routes is a minimum. We present four new mixed-integer linear programming (MILP) formulations for the problem. These formulations are compared both analytically and empirically, and a branch-and-cut algorithm is developed to compute an optimal solution. Extensive computational results on a large class of test instances that corroborate the effectiveness of the algorithm are also presented.
Extraction and development sequences must be scheduled strategically in order to maximize the life of mine. The complexities and computational difficulties associated with underground mine planning makes it challengin...
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Extraction and development sequences must be scheduled strategically in order to maximize the life of mine. The complexities and computational difficulties associated with underground mine planning makes it challenging and open to further research. This paper presents a mathematical programming framework based on mixed-integer linear programming (MILP) formulation for integrated open stope development and production scheduling. Additionally, the MILP model incorporates backfilling, operational levels control, and stope extraction duration control during production scheduling. The MILP model generated a net present value of $244.7 M and determined the capital, ventilation, operational, and ore pass development schedules as well as mining and processing schedules for a gold project with 25 years mine life. A total of 2.48 Mt of material was extracted and processed out of 2.88 Mt mineralized material.
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 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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The Benders' decomposition algorithm is a technique in mathematical programming for complex mixed-integer linear programming (MILP) problems with a particular block structure. The strategy of Benders' decompos...
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ISBN:
(纸本)9781665442664
The Benders' decomposition algorithm is a technique in mathematical programming for complex mixed-integer linear programming (MILP) problems with a particular block structure. The strategy of Benders' decomposition can be described as a strategy of divide and conquer. The Benders' decomposition algorithm has been employed in a variety of applications such as communication, networking, and machine learning. However, the master problem in Benders' decomposition is still NP-hard, which motivates us to employ quantum computing. In the paper, we propose a hybrid quantum-classical Benders' decomposition algorithm. We transfer the Benders' decomposition's master problem into the quadratic unconstrained binary optimization (QUBO) model and solve it by the state-of-the-art quantum annealer. Then, we analyze the computational results and discuss the feasibility of the proposed algorithm. Due to our reformulation in the master problem in Benders' decomposition, our hybrid algorithm, which takes advantage of both classical and quantum computers, can guarantee the solution quality for solving MILP problems.
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.
The use of EV batteries as secondary energy sources has recently been attracting great attention due to their large capacities. This paper is concerned with energy management of a workplace making use of the employees...
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ISBN:
(纸本)9798350379068;9798350379051
The use of EV batteries as secondary energy sources has recently been attracting great attention due to their large capacities. This paper is concerned with energy management of a workplace making use of the employees' EVs. We formulate such an energy management as a mixed-integer linear programming (MILP) problem by taking account of the arrival/departure status of the EVs and the benefits of the EV owners. Through a numerical simulation, we compare the effectiveness of the centralized algorithm and the distributed algorithm (Camisa et al. 2022) for finding a near-optimal solution to the MILP. The following points turn out from the simulation. If the number of EVs is small, the centralized algorithm can obtain a better solution to the MILP problem faster than the distributed algorithm without admitting the EV owners' decision-making. In contrast, in the case of a large number of EVs, the distributed algorithm can solve the problem faster than the centralized one taking account of the EV owners' decision-making at the price of the quality of its solution.
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