The cross entropy algorithm can provide a suboptimal solution in solving the static weapon target assignment problem. A further improvement of the quality of the solution costs a longer computational time, making it d...
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This article analyzes the stochastic runtime of a cross-entropyalgorithm mimicking an Max-MM Ant System with iteration-best reinforcement. It investigates the impact of magnitude of the sample size on the runtime to ...
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This article analyzes the stochastic runtime of a cross-entropyalgorithm mimicking an Max-MM Ant System with iteration-best reinforcement. It investigates the impact of magnitude of the sample size on the runtime to find optimal solutions for TSP instances. For simple TSP instances that have a {1,n}-valued distance function and a unique optimal solution, we show that sample size N is an element of omega(Inn) results in a stochastically polynomial runtime, and N is an element of O(In n) results in a stochastically exponential runtime, where "stochastically" means with a probability of 1 - n(-omega(1)), and n represents number of cities. In particular, for N is an element of omega(In n), we prove a stochastic runtime of O(N . n(6)) with the vertex-based random solution generation, and a stochastic runtime of O(N . n(3) Inn) with the edge-based random solution generation. These runtimes are very close to the best known expected runtime for variants of Max-Min Ant System with best-so-far reinforcement by choosing a small N is an element of omega(In n). They are obtained for the stronger notion of stochastic runtime, and analyze the runtime in most cases. We also inspect more complex instances with n vertices positioned on an m x m grid. When the n vertices span a convex polygon, we obtain a stochastic runtime of O(n(4)m(3+is an element of)) with the vertex-based random solution generation, and a stochastic runtime of O(n(3)m(3+is an element of)) for the edge-based random solution generation. When there are k is an element of O(1) many vertices inside a convex polygon spanned by the other n k vertices, we obtain a stochastic runtime of O(n(4)m(5+is an element of) + n(6k-1)m(is an element of)) with the vertex-based random solution generation, and a stochastic runtime of O(n(3)m(5+is an element of) + n(3k)m(is an element of)) with the edge-based random solution generation. These runtimes are better than the expected runtime for the so-called (mu+lambda) EA reported in a r
Studies on seaport operations emphasize the fact that the numbers of resources utilized at seaport terminals add a multitude of complexities to dynamic optimization problems. In such dynamic environments, there has be...
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Studies on seaport operations emphasize the fact that the numbers of resources utilized at seaport terminals add a multitude of complexities to dynamic optimization problems. In such dynamic environments, there has been a need for solving each complex operational problem to increase service efficiency and to improve seaport competitiveness. This paper states the key problems of seaport logistics and proposes an innovative cross-entropy (CE) algorithm for solving the complex problems of combinatorial seaport logistics. Computational results exhibit that the CE algorithm is an efficient, convenient and applicable stochastic method for solving the optimization problems of seaport logistics operations.
An emerging task in catering services for high-speed railways (CSHR) is to design a distribution system for the delivery of high-quality perishable food products to trains in need. This paper proposes a novel model fo...
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An emerging task in catering services for high-speed railways (CSHR) is to design a distribution system for the delivery of high-quality perishable food products to trains in need. This paper proposes a novel model for integrating location decision making with daily rail catering operations, which are affected by various aspects of rail planning, to meet time sensitive passenger demands. A three-echelon location routing problem with time windows and time budget constraints (3E-LRPTWTBC) is thus proposed toward formulating this integrated distribution system design problem. This model attempts to determine the capacities/locations of distribution centers and to optimize the number of meals delivered to stations. The model also attempts to generate a schedule for refrigerated cars traveling from distribution centers to rail stations for train loading whereby meals can be catered to trains within tight time windows and sold before a specified time deadline. By relaxing the time-window constraints, a relaxation model that can be solved using an off-the-shelf mixed integer programming (MIP) solver is obtained to provide a lower bound on the 3E-LRPTVVTBC. A hybrid cross entropy algorithm (HCEA) is proposed to solve the 3E-LRPTWTBC. A small-scale case study is implemented, which reveals a 9.3% gap between the solution obtained using the HCEA and that obtained using the relaxation model (RM). A comparative analysis of the HCEA and an exhaustive enumeration algorithm indicates that the HCEA shows good performance in terms of computation time. Finally, a case study considering 156 trains on the Beijing-Shanghai high-speed corridor and a large-scale case study considering 1130 trains on the Chinese railway network are addressed in a comprehensive study to demonstrate the applicability of the proposed models and algorithm. (C) 2016 Elsevier Ltd. All rights reserved.
The intermittency of renewable energy and load uncertainty in the combined cooling, heating, and power (CCHP) system operation is considered in this study. The authors propose a robust optimisation scheduling method t...
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The intermittency of renewable energy and load uncertainty in the combined cooling, heating, and power (CCHP) system operation is considered in this study. The authors propose a robust optimisation scheduling method to attenuate the disturbance of uncertainty, and derive the day-ahead scheduling decision under two strategies including electrical load tracking and thermal load tracking. Also, the budget of uncertainty is introduced to alleviate the conservatism of robust optimisation. Moreover, a minimax regret non-linear formulation is constructed to describe the performance of the system and different realisations of uncertainty. To solve the problem, the authors develop a hybrid solution method, which is composed of a two-stage Lagrangian relaxation iterative algorithm and an improved cross entropy algorithm. Simulation results demonstrate that the minimum of the maximum regret can be obtained, and the conservatism of robust optimisation is significantly reduced by properly setting the level of budget of uncertainty. As a result, the validity and effectiveness of the proposed robust optimisation model and algorithm are confirmed.
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