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.

We describe a simple on-line heuristic for scheduling job-shops. 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 Job-Shop Scheduling Problem with Fixed Routes A job-shop 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 job-shop 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 30332-0205, USA; Research supported in part by NSF grants DMI-9457336 and DMI-9813345, US-...

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 on-line 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 ...

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 talk-sessions, 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 Chung-Shang Shao, you were

We model the optimal reaction of a public PAYG pension system to demographic shocks. We compare the ex-ante 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 second-best 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 baby-boom/baby-bust 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

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

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 Lennard-Jones function, and the second is the empirical water dimer potential energy surface function (RWK2-M) 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.

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In this report we describe a set of numerical experiments carried out in order to appreciate the merits of a new class of stochastic global optimisation algorithms developed by the authors. These methods are based upon a mixture of random sampling and local optimisation, and all possess the following theoretical properties: convergence to the global optimum with probability 1; detection of the global optimum in a finite number of iterations w.p.1; probability of starting a local search decreasing to 0; total number of local searches performed even if the algorithm is run forever, finite w.p.1. Introduction This technical report contains a detailed description of numerical experiments carried out by the authors on the stochastic global optimization methods introduced in (Locatelli & Schoen, 1998). Following a suggestion of the editor, the numerical experience was not included in that paper, so we include it in this report for sake of completeness. Numerical results. A set of numeric...

We consider a manufacturer, served by a single supplier, who has to quote due dates to arriving customers in a maketo-order production environment. The manufacturer is penalized for long lead times and for missing due dates. To meet due dates, the manufacturer has to obtain components from a supplier. We model this manufacturer and supplier as a two-machine flow shop, consider several variations of this problem, and design effective due-date quotation and scheduling algorithms for centralized and decentralized versions of the model. We perform extensive computational testing to assess the effectiveness of our algorithms and to compare the centralized and decentralized models to quantify the value of centralized control in a make-to-order supply chain. Since complete information exchange and centralized control is not always practical or cost-effective, we explore the value of partial