We present a review of available tools for solving mixed integer nonlinear programming problems. Our aim is to give the reader a flavor of the difficulties one could face and to discuss the tools one could use to try ...
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We present a review of available tools for solving mixed integer nonlinear programming problems. Our aim is to give the reader a flavor of the difficulties one could face and to discuss the tools one could use to try to overcome such difficulties.
The maneuvers of aircraft conflict avoidance are studied for air traffic management systems. In the scenario, aircraft are considered to operate flight within a shared airspace and cannot violate the minimum safe sepa...
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The maneuvers of aircraft conflict avoidance are studied for air traffic management systems. In the scenario, aircraft are considered to operate flight within a shared airspace and cannot violate the minimum safe separation that they must keep in flight in order to avoid various possible conflicts. This paper proposes a formulation of the conflict avoidance problem as a mixed integer nonlinear programming (MINLP) with the maneuver that aircraft are allowed to change velocity and altitude to maintain the separation. Numerical experiments are performed to demonstrate the validity of the proposed MINLP model by comparison with the previous conflict avoidance model with only velocity change, and the illustration indicated a significant improvement in the efficiency of the conflict resolution as well as the magnitude of velocity variation. The optimal solutions of the problem are easily obtained by using global optimization solver in a shorter computational time even for large-scale aircraft.
The joint coordination of plug-in electric vehicles (PEVs) charging and grid power control is to minimize both PEVs' charging cost and energy generation cost in meeting both PEVs' power demands and power grid ...
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ISBN:
(纸本)9781538680995
The joint coordination of plug-in electric vehicles (PEVs) charging and grid power control is to minimize both PEVs' charging cost and energy generation cost in meeting both PEVs' power demands and power grid operational constraints. A bang-bang PEV charging strategy is adopted to exploit its simple online implementation, which requires computation of a mixed integer nonlinear programming problem (MINP) in binary variables of the PEV charging and continuous variables of the grid voltages. A novel solver for this challenging MINP is proposed. Its efficiency is shown by numerical simulations.
In this paper, the problem of aircraft conflict avoidance is studied arising in Air Traffic Management systems. The initial configuration of all aircraft including position, velocities, heading angles, altitude and fl...
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ISBN:
(纸本)9781665440899
In this paper, the problem of aircraft conflict avoidance is studied arising in Air Traffic Management systems. The initial configuration of all aircraft including position, velocities, heading angles, altitude and flight trajectories are known, and they are assumed to fly within a shared three-dimensional airspace. The aim of the problem is to find an optimal conflict avoidance strategy for the aircraft so that various conflicts situations can be avoided. A conflict occurs when the relative distance between any pairs of aircraft is less than the minimal safe separation during their flights. In order to ensure the safety of aircraft flight, a mixed integer nonlinear programming model (MINLP) for solving the three-dimensional conflict avoidance problem involving multiple aircrafts is proposed in this paper, where the aircraft are allowed to change simultaneously heading angle and velocity to achieve the separation. The illustration verifies the effectiveness of the method. The optimal solution of the problem can be obtained easily in a small computational time by using a standard global optimization solver to solve the proposed MINLP model.
Line-up competition algorithm (LCA), a global optimization algorithm proposed recently, is applied to the solution of mixed integer nonlinear programming (MINLP) problems. Through using alternative schemes to handle i...
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Line-up competition algorithm (LCA), a global optimization algorithm proposed recently, is applied to the solution of mixed integer nonlinear programming (MINLP) problems. Through using alternative schemes to handle integer variables, the algorithm reported previously for solving NLP problems can be extended expediently to the solution of MINLP problems. The performance of the LCA is tested with several non-convex MINLP problems published in the literature, including the optimal design of multi-product batch chemical processes and the location-allocation problem. Testing shows that the LCA algorithm is efficient and robust in the solution of MINLP problems. (C) 2004 Elsevier Ltd. All rights reserved.
In a heterogeneous parallel structure, two types of algorithms, Quesada Grossmann's (QG) algorithm and Tabu search (TS), are used to solve mixed integer nonlinear programming (MINLP) simultaneously. Communication ...
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In a heterogeneous parallel structure, two types of algorithms, Quesada Grossmann's (QG) algorithm and Tabu search (TS), are used to solve mixed integer nonlinear programming (MINLP) simultaneously. Communication is well designed between two threads running the two algorithms individually by exchanging three kinds of information during iterations. First, the best feasible solution in TS can become a valid upper bound for QG. Second, new linearization which can further tighten the lower bound of QG can be generated at the node provided by the TS. Third, additional integer variables can be fixed in QG, thus reducing the search space of TS. Numerical results show that good performance can be achieved by using the proposed method. Further analysis reveals that the heterogeneous method has the potential for superlinear speedup, which may surpass that of the traditional homogeneous parallel method for solving MINLPs. (c) 2013 Elsevier Ltd. All rights reserved.
Optimising crop planning in conjunction with intra-seasonal water allocation necessitates the use of daily water budget calculations to determine the timing and amount of irrigation events, which complicates the solut...
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Optimising crop planning in conjunction with intra-seasonal water allocation necessitates the use of daily water budget calculations to determine the timing and amount of irrigation events, which complicates the solution of the problem to global optimality. The main objective of this research was to compare the intra-seasonal water allocation of a mixed integer nonlinear programming (MINLP) model with that of differential evolution (DE), to allocate a limited amount of water while considering irrigable area and the irrigation schedule that will maximise the total gross margin. Results show that both solution procedures adhere to economic theory of water allocation under limited water supply. The conclusion is that the MINLP model most likely achieved very near global optimality as the solutions of the two models were very close to each other. DE holds promise to solve more complex models involving risk and multiple crops.
The mixed integer nonlinear programming (MINLP) problem as an optimization problem involves both continuous and discrete variables. Moreover, at least one of the functions defining the objective function or the constr...
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The mixed integer nonlinear programming (MINLP) problem as an optimization problem involves both continuous and discrete variables. Moreover, at least one of the functions defining the objective function or the constraints must be nonlinear. Because of its complexity, it is very difficult to obtain the exact optimal solution. Therefore, the heuristic methods for getting a feasible solution of MINLPs are very important in practice. The feasibility pump is one of the famous heuristic methods, which alternates between solving nonlinearprogramming (NLP) problems and mixedinteger linear programming (MILP) relaxed master problems. In this paper, we will extend the feasibility pump to the case where the NLP problems are solved inexactly and propose the convergence of this method under some conditions. Moreover, we present the study of inexactness of the Lagrange multipliers (which are returned negative) of the NLP subproblems. (C) 2016 Elsevier B.V. All rights reserved.
This paper considers the solution of mixed integer nonlinear programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer p...
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This paper considers the solution of mixed integer nonlinear programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving nonlinearprogramming (NLP) and mixedinteger Linear programming problems. In contrast, an integrated approach to solving MINLP problems is considered here. This new algorithm is based on branch-and-bound, but does not require the NLP problem at each node to be solved to optimality. Instead, branching is allowed after each iteration of the NLP solver. In this way, the nonlinear part of the MINLP problem is solved whilst searching the tree. The nonlinear solver that is considered in this paper is a Sequential Quadratic programming solver. A numerical comparison of the new method with nonlinear branch-and-bound is presented and a factor of up to 3 improvement over branch-and-bound is observed.
The rendezvous and docking mission is usually divided into several phases, and the mission planning is performed phase by phase. A new planning method using mixed integer nonlinear programming, which investigates sing...
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The rendezvous and docking mission is usually divided into several phases, and the mission planning is performed phase by phase. A new planning method using mixed integer nonlinear programming, which investigates single phase parameters and phase connecting parameters simultaneously, is proposed to improve the rendezvous mission's overall performance. The design variables are composed of integers and continuous-valued numbers. The integer part consists of the parameters for station-keeping and sensor-switching, the number of maneuvers in each rendezvous phase and the number of repeating periods to start the rendezvous mission. The continuous part consists of the orbital transfer time and the station-keeping duration. The objective function is a combination of the propellant consumed, the sun angle which represents the power available, and the terminal precision of each rendezvous phase. The operational requirements for the spacecraft-ground communication, sun illumination and the sensor transition are considered. The simple genetic algorithm, which is a combination of the integer-coded and real-coded genetic algorithm, is chosen to obtain the optimal solution. A practical rendezvous mission planning problem is solved by the proposed method. The results show that the method proposed can solve the integral rendezvous mission planning problem effectively, and the solution obtained can satisfy the operational constraints and has a good overall performance. (C) 2010 Elsevier Ltd. All rights reserved.
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