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21.
Zelda B. Zabinsky David Bulger Charoenchai Khompatraporn 《Journal of Global Optimization》2010,46(2):273-286
Two common questions when one uses a stochastic global optimization algorithm, e.g., simulated annealing, are when to stop
a single run of the algorithm, and whether to restart with a new run or terminate the entire algorithm. In this paper, we
develop a stopping and restarting strategy that considers tradeoffs between the computational effort and the probability of
obtaining the global optimum. The analysis is based on a stochastic process called Hesitant Adaptive Search with Power-Law
Improvement Distribution (HASPLID). HASPLID models the behavior of stochastic optimization algorithms, and motivates an implementable
framework, Dynamic Multistart Sequential Search (DMSS). We demonstrate here the practicality of DMSS by using it to govern
the application of a simple local search heuristic on three test problems from the global optimization literature. 相似文献
22.
Mirjam Dür Charoenchai Khompatraporn Zelda B. Zabinsky 《Annals of Operations Research》2007,156(1):25-44
Fractional programming has numerous applications in economy and engineering. While some fractional problems are easy in the
sense that they are equivalent to an ordinary linear program, other problems like maximizing a sum or product of several ratios
are known to be hard, as these functions are highly nonconvex and multimodal. In contrast to the standard Branch-and-Bound
type algorithms proposed for specific types of fractional problems, we treat general fractional problems with stochastic algorithms
developed for multimodal global optimization. Specifically, we propose Improving Hit-and-Run with restarts, based on a theoretical
analysis of Multistart Pure Adaptive Search (cf. the dissertation of Khompatraporn (2004)) which prescribes a way to utilize problem specific information to sample until a certain level α of confidence is achieved. For this purpose, we analyze the Lipschitz properties of fractional functions, and then utilize
a unified method to solve general fractional problems. The paper ends with a report on numerical experiments.
This work was initiated while Mirjam Dür was spending a three-month research visit at the University of Washington. She would
like to thank the Fulbright Commission for financial support and the optimization group at UW for their warm hospitality.
The work of C. Khompatraporn and Z.B. Zabinsky was partially supported by the NSF grant DMI-0244286. 相似文献
23.
This paper addresses the issue of the optimal flow allocation in general supply chains. Our basic observation is that a distribution channel involving several reselling steps for a particular product can be viewed as a route in a supply chain network. The flow of goods or services along each route is influenced by the customer's demand, described by the corresponding utility functions, and prices charged at each node. We develop an optimization algorithm based on the primal-dual framework and the Newton's step that computes optimal prices at each node (dual problem) and then computes the optimal flow allocation (primal problem) based on these prices. Our main contribution is a discovery that the Newton's step leads to a partially decentralized algorithm which is a first step toward a decentralization schema for computing optimal prices. 相似文献
24.
Romeijn H. E. Zabinsky Z. B. Graesser D. L. Neogi S. 《Journal of Optimization Theory and Applications》1999,101(2):403-427
To reduce the well-known jamming problem in global optimization algorithms, we propose a new generator for the simulated annealing algorithm based on the idea of reflection. Furthermore, we give conditions under which the sequence of points generated by this simulated annealing algorithm converges in probability to the global optimum for mixed-integer/continuous global optimization problems. Finally, we present numerical results on some artificial test problems as well as on a composite structural design problem. 相似文献
25.
26.
Shabnam Zangeneh-Khamooshi Zelda B. Zabinsky Joseph A. Heim 《Optimization Letters》2013,7(6):1215-1225
In many applications of the vehicle routing problem with time windows (VRPTW), goods must be picked up within desired time frames. In addition, they have some limitations on their arrival time to the central depot. In this paper, we present a new version of VRPTW that minimizes the total cycle time of the goods. In order to meet the time windows and also minimize the cycle time, the courier’s schedule is allowed to vary. An algorithm, named VeRSA, is proposed to solve this problem. VeRSA employs concepts of scheduling theorems and algorithms to determine feasible routes and schedules of the available couriers. We prove a theoretical lower bound that provides a useful bound on the optimality gap. We also conduct a set of numerical experiments. VeRSA obtains a feasible solution faster than solving the MIP. The optimality gap using our proposed lower bound is smaller than the gap found with the standard LP relaxation. 相似文献
27.
Optimization algorithms usually rely on the setting of parameters, such as barrier coefficients. We have developed a generic
meta-control procedure to optimize the behavior of given iterative optimization algorithms. In this procedure, an optimal
continuous control problem is defined to compute the parameters of an iterative algorithm as control variables to achieve
a desired behavior of the algorithm (e.g., convergence time, memory resources, and quality of solution). The procedure is
illustrated with an interior point algorithm to control barrier coefficients for constrained nonlinear optimization. Three
numerical examples are included to demonstrate the enhanced performance of this method.
This work was primarily done when Z. Zabinsky was visiting Clearsight Systems Inc. 相似文献
28.
A common issue for stochastic global optimization algorithms is how to set the parameters of the sampling distribution (e.g. temperature, mutation/cross-over rates, selection rate, etc.) so that the samplings converge to the optimum effectively and efficiently. We consider an interacting-particle algorithm and develop a meta-control methodology which analytically guides the inverse temperature parameter of the algorithm to achieve desired performance characteristics (e.g. quality of the final outcome, algorithm running time, etc.). The main aspect of our meta-control methodology is to formulate an optimal control problem where the fractional change in the inverse temperature parameter is the control variable. The objectives of the optimal control problem are set according to the desired behavior of the interacting-particle algorithm. The control problem considers particles’ average behavior, rather than treating the behavior of individual particles. The solution to the control problem provides feedback on the inverse temperature parameter of the algorithm. 相似文献
29.
A meta-control algorithm for generating approximate solutions to binary integer programming problems
Kathrine von Haartman Wolf Kohn Zelda B. Zabinsky 《Nonlinear Analysis: Hybrid Systems》2008,2(4):1232-1244
Binary integer program problems, which are known to be difficult to solve, have long been an important research area. We use a new approach with continualization techniques to find approximate solutions to binary integer programming problems. The algorithm constructs a sequence of approximations to a solution using a meta-control approach that has low polynomial time complexity. The algorithm is illustrated with a BIP example. 相似文献
30.
Cherry Y. Wakayama Wolf Kohn Zelda B. Zabinsky C.J. Richard Shi 《Nonlinear Analysis: Hybrid Systems》2008,2(4):1098-1112
Efficient solar-energy harvesting is fundamental to solar cell technology. Much research effort has been devoted to the construction of new light-harvesting structures, including the use of semiconductor quantum dots (QDs), to improve the widespread availability of solar cells. In this research, a new light-harvesting architecture is developed, which utilizes quantum dots. The proposed architecture is composed of quantum phase-locked loops (QPLLs) to enhance the harvesting efficiency of QD solar cells by utilizing feedback control principles. The purpose of QPLL is to synchronize the phases of monochromatic light harvested by the antenna systems. This paper addresses deterministic modeling and control formulation of the QPLL within our conceptual framework. The QPLL consists of a tracking controller and a proportional–integral (PI) regulator. The QPLLs are simulated with external fluctuations to evaluate the performance of the controllers. Simulation results show that the tracking controller achieves robust and satisfactory performance. The PI regulator is more sensitive to external fluctuations and the nominal operating point. Our results demonstrate the possibility of improving light-harvesting efficiency by utilizing feedback control principles. 相似文献