The computational utility of inductive linearizations for binary quadratic programs when combined with a mixed-integer programming solver is investigated for several combinatorial optimization problems and established...
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The computational utility of inductive linearizations for binary quadratic programs when combined with a mixed-integer programming solver is investigated for several combinatorial optimization problems and established benchmark instances.
In this paper, we study the efficacy of several mathematical programming formulations for the single-source shortest path problem, the negative cost cycle detection problem, and the shortest negative cost cycle proble...
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In this paper, we study the efficacy of several mathematical programming formulations for the single-source shortest path problem, the negative cost cycle detection problem, and the shortest negative cost cycle problem in arc-dependent networks. In an arc-dependent network, the cost of an arc a depends upon the arc preceding a. These networks differ from traditional networks in which the cost associated with an arc is a fixed constant and part of the input. Arc-dependent networks are useful for modeling a number of real-world problems, such as the turn-penalty shortest path problem, which cannot be captured in the traditional network setting. We present new integer and non-linear programming formulations for each problem. We also perform the first known empirical study for arc-dependent networks to contrast the execution times of the two formulations on a set of graphs with varying families and sizes. Our experiments indicate that although non-linear programming formulations are more compact, integer programming formulations are more efficient for the problems studied in this paper. Additionally, we introduce a number of cuts for each integer programming formulation and examine their effectiveness.
Heat pump can be used to recover abundant thermal energy contained in the discharge of municipal wastewater treatment plants. While there are some design standards for common heat pump systems, the design of a sewage ...
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Heat pump can be used to recover abundant thermal energy contained in the discharge of municipal wastewater treatment plants. While there are some design standards for common heat pump systems, the design of a sewage source heat pump (SSHP) system is still often based on a fixed heat load and neglects the interdependencies between the equipment sizing and operating parameters. To address the issue that previous design methods have not balanced investment and operational costs well from a global optimisation perspective, this work formulates the simultaneous optimisation of SSHP design and operation as a non-linear programming problem. The proposed model features the consideration of multiple working conditions caused by the impact of ambient temperature variation on the heat load of the SSHP system. The feasibility and potential benefits of the optimised SSHP system are also evaluated by incorporating techno-economic performances and environmental impact analyses into the mathematical framework. A case study is carried out to demonstrate the effectiveness of the proposed methodology. The results show that the total annual cost of the optimally designed and operated SSHP in Harbin could be 9% lower than in Beijing and 39% lower than in Shanghai, suggesting that constructing and running the SSHP system in severe cold regions with great heating demands might be more economical than in less cold regions. The CO2, SO2, and NOx emissions of the SSHP could be approximately 50% less than that of coal-fired boiler heating, and 80% less than that of direct electric heating with coal-fired electricity. [GRAPHICS] .
Electric Solar Wind Sails (E -Sails) are a new type of spacecraft propellantless propulsion system that gathers its energy from solar wind protons and is potentially useful for interplanetary missions. Although optima...
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Electric Solar Wind Sails (E -Sails) are a new type of spacecraft propellantless propulsion system that gathers its energy from solar wind protons and is potentially useful for interplanetary missions. Although optimal interplanetary trajectories have been the subject of thorough research, the substantial variability of the solar wind necessitates the adoption of active guidance strategies, an area that has received significantly less scholarly attention. This paper proposes guidance algorithms for E -Sails based on Model Predictive Control (MPC), a modern control methodology based on online re -planning of the trajectory. To this end, first, properties of E -sail time -optimal orbits are studied applying Pontryagin's Minimum Principle, and then timeoptimal orbits for missions to Mars and Jupiter are computed via direct transcription methods. Next, solar wind perturbations are modeled, posing a challenging saturation problem due to their high variability. Guidance strategies based on Shrinking Horizon and Receding Horizon Model Predictive Control (RHMPC) are developed, analyzed and compared using Monte Carlo simulations, successfully implementing MPC to E -sail guidance. Lastly, the RHMPC strategy is successfully tested with accurate historical solar wind data from the WSA-Enlil model.
Small and medium enterprises (SMEs) play a critical role in supply chains and social stability. Unfortunately, SMEs often lack access to traditional bank financing. To develop SME suppliers, some creditworthy companie...
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Small and medium enterprises (SMEs) play a critical role in supply chains and social stability. Unfortunately, SMEs often lack access to traditional bank financing. To develop SME suppliers, some creditworthy companies have built platforms to coordinate banks and suppliers by employing purchase order financing (POF). After noting that SMEs differ in terms of their operational flexibility and uncertainty, this research examines optimal purchasing portfolios on such platforms. Specifically, we construct a Stackelberg model involving one buyer and two suppliers and analyse the Karush-Kuhn-Tucker necessary conditions for a buyer's strategy upon which the optimal portfolio can be achieved. According to the experiments that we design to simulate about 200,000 various scenarios, the large buyer only needs to consider the top five strategies. The choice of strategy mainly depends on cost differences of suppliers, and flexibility can be used as an identifier of the purchase quantity.
A wide range of real world optimization problems involves continuous decisions and non-linearities. Each nonlinear component of such problems can be modeled either linearly or non -linearly, considering or not additio...
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A wide range of real world optimization problems involves continuous decisions and non-linearities. Each nonlinear component of such problems can be modeled either linearly or non -linearly, considering or not additional integer variables. This results into different modeling choices that can drastically impact the solution time and quality. In this paper, we evaluate representative modeling alternatives, including common models from the literature as well as new models featuring less common functions. The single plant Hydro Unit Commitment problem (1-HUC) is the considered non-linear use case. Among the non-linearities of the 1-HUC, we focus on those involved in the power production, more precisely the head effect and the turbines efficiency. The power is defined as a two-dimensional non -convex and non -concave function of the water flow and head decision variables, the latter being itself a one-dimensional concave function of the turbined volume. We consider both the general problem and a common special case, assuming that the water head is fixed. Several available solvers are used for each non-linear model and the best virtual solver is retained to focus on the model capabilities rather than on the solver performance. Based on the numerical experiments, three models stand out as the most efficient in terms of computational time, solution quality and feasibility, sometimes in a counter -intuitive manner. For each of these models, a solver is highlighted as the most adequate.
Truss lattices are potential candidates for the design of innovative aerostructures, thanks to their high stiffness-to-weight ratio, modularity, and aeroelastic properties. However, when designing ultralight structure...
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Truss lattices are potential candidates for the design of innovative aerostructures, thanks to their high stiffness-to-weight ratio, modularity, and aeroelastic properties. However, when designing ultralight structures, multiple mechanical constraints, such as maximum internal stress or local buckling constraints, must be taken into account since the early design phase. In response to this, a volume minimization problem for 3D structures, subject to multiple load cases, maximum stress, and topological buckling constraints, is formulated in this work. The optimization is solved using a two-step optimization strategy. First, a relaxed formulation is solved by a Sequential linearprogramming algorithm and is used to explore the vast design space of the optimization. During this phase, a heuristic is proposed to reduce the influence of the starting point on the optimized structure. The solution is refined in a second optimization step in which the full non-linear problem is solved using IPOPT, making sure that all the mechanical constraints are respected. The proposed method is validated on multiple two-dimensional classical benchmarks, showing robust behavior with respect to random starting point initializations. Later, the three-dimensional wingbox of the Common Research Model subject to multiple load cases is optimized. The results show that the proposed method can deal with real-sized structures with thousands of candidate members, all while being computationally efficient, optimizing the structure in minutes on a consumer notebook.
Dynamic facility layout planning (DFLP) involves determining an appropriate arrangement scheme of the elements making up the production system for each time period into which the planning horizon is divided. When form...
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Dynamic facility layout planning (DFLP) involves determining an appropriate arrangement scheme of the elements making up the production system for each time period into which the planning horizon is divided. When formulating the problem as an optimisation model, using the traditional top-down approach is usual, which firstly determines the block layout (BL) and then the detailed layout (DL) of each work cell. However by this approach, the BL generates area constraints in the detailed phase, which sometimes limit its implementation. In this context, the present paper presents a multi-objective mixed integer non-linear programming (MOMINLP) model that allows the problem to be addressed by considering an alternative approach, known in the literature as the bottom-up approach. The proposed model, called bottom-up mDFLP, considers three objective functions: (1) minimise the total material handling cost (TMHC) and the total rearrangement cost (TRAC);(2) maximise the total closeness rating (TCR) between departments;(3) maximise the area utilisation ratio (AUR). The original MOMINLP is transformed into a more computationally efficient multi-objective mixed integer linearprogramming (MOMILP) model. The proposed model is applied and validated in a case study of a company in the metal-mechanic sector with 12 departments for three 4-month periods.
For wireless communications and the Internet of Things, edge computing has emerged as the potential solution to meet users' demand of fast communications and effective computation by allocating computing resources...
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For wireless communications and the Internet of Things, edge computing has emerged as the potential solution to meet users' demand of fast communications and effective computation by allocating computing resources closer to users and tasks, and then reducing the process time and avoiding the transmission of huge amount of data. However, to achieve the potential of edge computing, an effective computation offloading scheme is a key issue needed to be addressed, because it determines how efficient the computing resource allocation and the whole network performance are. Toward providing a solution to such an important issue, this paper formulates the offloading problem as a cooperation game problem about how to share the reasonably adjacent computing resource to users to form an efficient coalition network for the best performance, and then proposes a Shapley value-based computation offloading approach. The proposed approach includes three main steps: Firstly, following the principle of edge computing (users to be close to resources) and reducing the complexity, a clustering algorithm is proposed to divide the whole network into clusters and each cluster has one edge node. Then the non-linear programming is implemented in each cluster and neighboring two or three clusters respectively to obtain the delay values and task allocation results. Finally, to check whether cooperation and coalition among neighboring clusters can bring better network performance, Shapley value is used to evaluate whether combining neighboring clusters in edge computing for the first time. The objective values obtained from the non-linear programming are used to evaluate the profit of different coalitions, which are used to compute Shapley values to determine the final best coalitions between clusters. The numerical results show the effectiveness of the proposed method.
Air conditioning loads (ACLs) represent an increasing proportion of power system loads, offering significant potential for optimised scheduling and active participation in demand response (DR) programs. While many stu...
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Air conditioning loads (ACLs) represent an increasing proportion of power system loads, offering significant potential for optimised scheduling and active participation in demand response (DR) programs. While many studies have focused on ON/OFF control schemes that satisfy system requirements, few have addressed quantifying the life loss of ACLs from the user perspective. To address this gap, a quantitative model of ACL life loss is established and an optimal scheduling model is developed for ACLs participating in DR that incorporates the cost of life loss. The relationship between life loss and refrigeration power is a complex non-linear high-order fractional function that cannot be solved by commercial solvers. Therefore, a bi-objective multi-weight optimisation algorithm is proposed with a complex non-linear fraction based on the Dinkelbach algorithm and its feasibility through mathematical examples is verified. Finally, a numerical example based on the IEEE 39-bus test system is provided to demonstrate the feasibility of the model and the effectiveness of the proposed solution method.
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