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19
Global Optimization of Statistical Functions with Simulated Annealing
 Journal of Econometrics
, 1994
"... Many statistical methods rely on numerical optimization to estimate a model’s parameters. Unfortunately, conventional algorithms sometimes fail. Even when they do converge, there is no assurance that they have found the global, rather than a local, optimum. We test a new optimization algorithm, simu ..."
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Cited by 126 (1 self)
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Many statistical methods rely on numerical optimization to estimate a model’s parameters. Unfortunately, conventional algorithms sometimes fail. Even when they do converge, there is no assurance that they have found the global, rather than a local, optimum. We test a new optimization algorithm, simulated annealing, on four econometric problems and compare it to three common conventional algorithms. Not only can simulated annealing find the global optimum, it is also less likely to fail on difficult functions because it is a very robust algorithm. The promise of simulated annealing is demonstrated on the four econometric problems.
Global Continuation For Distance Geometry Problems
 SIAM J. OPTIMIZATION
, 1995
"... Distance geometry problems arise in the interpretation of NMR data and in the determination of protein structure. We formulate the distance geometry problem as a global minimization problem with special structure, and show that global smoothing techniques and a continuation approach for global optim ..."
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Cited by 70 (7 self)
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Distance geometry problems arise in the interpretation of NMR data and in the determination of protein structure. We formulate the distance geometry problem as a global minimization problem with special structure, and show that global smoothing techniques and a continuation approach for global optimization can be used to determine solutions of distance geometry problems with a nearly 100% probability of success.
A Fluid Heuristic for Minimizing Makespan in JobShops
 Oper. Res
, 2001
"... We describe a simple online heuristic for scheduling jobshops. We assume there is a fixed set of routes for the jobs, and many jobs, say N , on each route. The heuristic uses safety stocks and keeps the bottleneck machine busy at almost all times, while the other machines are paced by the bottlene ..."
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Cited by 17 (1 self)
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We describe a simple online heuristic for scheduling jobshops. We assume there is a fixed set of routes for the jobs, and many jobs, say N , on each route. The heuristic uses safety stocks and keeps the bottleneck machine busy at almost all times, while the other machines are paced by the bottleneck machine. We perform a probabilistic analysis of the heuristic, under some assumptions on the distributions of the processing times. We show that our heuristic produces makespan which exceeds the optimal makespan by no more than c log N with a probability which exceeds 1  1/N for all N # 1, where c is some constant independent of N . 1 The JobShop Scheduling Problem with Fixed Routes A jobshop consists of machines i = 1, . . . , I, and routes r = 1, . . . , R. Route r consists of steps (r, k) where k = 1, . . . , K r indicate the steps along route r, in their required order of execution, and step (r, k) is carried out by machine #(r, k). We let C i denote the set of steps performed on machine i. In the standard jobshop formulation [23] there is one job on each route, and the objective is to schedule all the jobs so as to minimize the makespan, the earliest time by which all the jobs are completed. In our formulation of the job shop problem we assume that there are many jobs on each of the routes. In practice, in particular in factories, routes may correspond to various production processes, or to various types of products manufactured in the factory. In that case the jobs may correspond to parts or lots and there will indeed be many such jobs for each route. # School of Industrial and Systems Engineering and School of Mathematics, Georgia Institute of Technology, Atlanta, GA 303320205, USA; Research supported in part by NSF grants DMI9457336 and DMI9813345, US...
spot: An R Package For Automatic and Interactive Tuning of Optimization Algorithms by Sequential Parameter Optimization
, 2010
"... The sequential parameter optimization (spot) package for R (R Development Core Team, 2008) is a toolbox for tuning and understanding simulation and optimization algorithms. Modelbased investigations are common approaches in simulation and optimization. Sequential parameter optimization has been dev ..."
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Cited by 8 (7 self)
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The sequential parameter optimization (spot) package for R (R Development Core Team, 2008) is a toolbox for tuning and understanding simulation and optimization algorithms. Modelbased investigations are common approaches in simulation and optimization. Sequential parameter optimization has been developed, because there is a strong need for sound statistical analysis of simulation and optimization algorithms. spot includes methods for tuning based on classical regression and analysis of variance techniques; treebased models such as CART and random forest; Gaussian process models (Kriging) and combinations of different metamodeling approaches. This article exemplifies how spot can be used for automatic and interactive tuning. 1
A Simple Multistart Algorithm for Global Optimization
, 1997
"... this article is an extension of the multistart method. Having drawn a quasirandom sample of N points from the feasible set, p iterations of an inexpensive local search are applied to concentrate the sample. The q points with the smallest function values are retained, while the other N \Gamma q point ..."
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Cited by 5 (1 self)
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this article is an extension of the multistart method. Having drawn a quasirandom sample of N points from the feasible set, p iterations of an inexpensive local search are applied to concentrate the sample. The q points with the smallest function values are retained, while the other N \Gamma q points are replaced by new quasirandom points. Then the concentration step is repeated. Any point that is retained for s iterations is used to start an efficient complete local search, provided that its function value is not significantly larger than the smallest function value obtained so far. The algorithm terminates when no new local minimum is found after several iterations. The next section describes our algorithm in detail. It is also recast in a form suitable for solving systems of nonlinear equations. Numerical results are reported in Section 3. 2. The Algorithm
Stochastic Limit Laws For Schedule Makespans
 Stochastic Models
, 1996
"... A basic multiprocessor version of the makespan scheduling problem requires that n tasks be scheduled on m identical processors so as to minimize the latest task finishing time. In the standard probability model considered here, the task durations are i.i.d. random variables with a general distributi ..."
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Cited by 2 (2 self)
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A basic multiprocessor version of the makespan scheduling problem requires that n tasks be scheduled on m identical processors so as to minimize the latest task finishing time. In the standard probability model considered here, the task durations are i.i.d. random variables with a general distribution F having finite mean. Our main objective is to estimate the distribution of the makespan as a function of m, n, and F , under the online greedy policy, i.e., where the tasks are put in sequence and assigned in order to processors whenever they become idle. Because of the difficulty of exact analysis, we concentrate on the asymptotic behavior as n ! 1 or as both m ! 1 and n !1 with m n. The focal point is the Markov chain giving the remaining processing times of the m \Gamma 1 tasks still running at task completion epochs. The theory of stationary marked point processes is used to show that the stationary distribution of this Markov chain coincides with the order statistics of m \Gamma ...
Parallel Global Optimization of Proteins
, 1994
"... The convention says that a foreword can be at most one page. One page? I think one should be able to write a foreword that is longer. First of all, if one has a lot to say, there should be room to do so. Second, I don't like conventions. Third and last, what's in a page? It would be left intentiona ..."
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Cited by 2 (1 self)
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The convention says that a foreword can be at most one page. One page? I think one should be able to write a foreword that is longer. First of all, if one has a lot to say, there should be room to do so. Second, I don't like conventions. Third and last, what's in a page? It would be left intentionally  blank anyway. However, convention is convention. So, despite all the words I have tosay, I will try not to ll more than one page. This thesis is the result of one of the most interesting experiences in my life: working full time as a Professional Research Assistant at the University of Colorado at Boulder, in the mean time being a student at the Erasmus University Rotterdam. It has been quite an adventure to nish classes in Rotterdam, while physically being located in Boulder. I thank Martin van Wijngaarden for our smooth cooperation in this (i.e., him staying up late). I will remember our pleasant talksessions, which were a recurring event onmyweekly schedule. Of course this experience would not have been possible without Bobby Schnabel giving me the opportunitytowork with him and Richard Byrd in the very interesting area of global optimization. Besides having learned a lot all of which Iamentitled to forget now, I will mostly remember the pleasant cooperation in our group. Thanks Betty Eskow and ChungShang Shao, you were
Sharing Demographic Risk – Who is Afraid of the Baby Bust?” Mannheim Research Institute for the Economics of Aging working paper
, 2008
"... We model the optimal reaction of a public PAYG pension system to demographic shocks. We compare the exante first best and second best solution of a Ramsey planner with full commitment to the outcome under simple third best rules that mimic the pension systems observed in the real world. The model, ..."
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Cited by 2 (0 self)
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We model the optimal reaction of a public PAYG pension system to demographic shocks. We compare the exante first best and second best solution of a Ramsey planner with full commitment to the outcome under simple third best rules that mimic the pension systems observed in the real world. The model, in particular the pension system, is calibrated to the German economy. The objective of the social planner is calibrated such that the size of the German pension system was optimal under the economic and demographic conditions of the 1960s. We find that the German system comes relatively close to the secondbest solution. Furthermore, the German system and a constant contribution rate lead to a lower variability of lifetime utility than does the second best policy. The recent babyboom/babybust cycle leads to welfare losses of about 5 % of lifetime consumption for some cohorts. We argue that it is crucial for these results to model correctly the labor market distortions arising from the pension system. JEL classification: E62, H3, H55
Modelling and estimation for random fields
 Laboratoryfor Information and Decision Systems, MIT
, 1992
"... ..."
A LargeScale StochasticPerturbation Global Optimization Method for Molecular Cluster problems
, 1999
"... this paper both involve the determination of the structure of clusters of atoms or molecules, but each application uses a di#erent potential energy function. The first potential is given by the sum of the pairwise interactions between atoms described by the LennardJones function, and the second is ..."
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Cited by 1 (0 self)
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this paper both involve the determination of the structure of clusters of atoms or molecules, but each application uses a di#erent potential energy function. The first potential is given by the sum of the pairwise interactions between atoms described by the LennardJones function, and the second is the empirical water dimer potential energy surface function (RWK2M) described in [10]. Problems in determining molecular structure lead to optimization problems because the naturally occurring structure usually minimizes the potential energy of the system. These problems become global optimization problems because typically such functions have very many local minimizers.