Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Investigation of Simulated Trading — A multi agent based trading system for optimization purposes
2010
Abstract Some years ago, Bachem, Hochstattler, and Malich proposed a heuristic algorithm called Simulated Trading for the optimization of vehicle routing problems. Computational agents place buy-orders and sell-orders for customers to be handled at a virtual financial market, the prices of the orders depending on the costs of inserting the customer in the tour or for his removal. According to a proposed rule set, the financial market creates a buy-and-sell graph for the various orders in the order book, intending to optimize the overall system. Here I present a thorough investigation for the application of this algorithm to the traveling salesman problem.
A tabu search algorithm for assigning teachers to courses
2002
In this paper we deal with the problem of assigning teachers to courses in a secondary school. The problem appears when a timetable is to be built and the teaching assignments are not fixed. We have developed a tabu search algorithm to solve the problem. The parameters involved in the algorithm have been estimated by using multiple regression techniques. The computational results, obtained on a set of Spanish secondary schools, show that the solutions obtained by this automatic procedure can be favourably compared with the solutions proposed by the experts.
A decision support system methodology for forecasting of time series based on soft computing
2006
Exponential procedures are widely used as forecasting techniques for inventory control and business planning. A number of modifications to the generalized exponential smoothing (Holt-Winters) approach to forecasting univariate time series is presented, which have been adapted into a tool for decision support systems. This methodology unifies the phases of estimation and model selection into just one optimization framework which permits the identification of robust solutions. This procedure may provide forecasts from different versions of exponential smoothing by fitting the updated formulas of Holt-Winters and selects the best method using a fuzzy multicriteria approach. The elements of the…
Adaptive Modifications of Hypotheses After an Interim Analysis
2001
It is investigated how one can modify hypotheses in a trial after an interim analysis such that the type I error rate is controlled. If only a global statement is desired, a solution was given by Bauer (1989). For a general multiple testing problem, Kieser, Bauer and Lehmacher (1999) and Bauer and Kieser (1999) gave solutions, by means of which the initial set of hypotheses can be reduced after the interim analysis. The same techniques can be applied to obtain more flexible strategies, as changing weights of hypotheses, changing an a priori order, or even including new hypotheses. It is emphasized that the application of these methods requires very careful planning of a trial as well as a c…
Misinterpretation risks of global stochastic optimisation of kinetic models revealed by multiple optimisation runs
2016
Abstract One of use cases for metabolic network optimisation of biotechnologically applied microorganisms is the in silico design of new strains with an improved distribution of metabolic fluxes. Global stochastic optimisation methods (genetic algorithms, evolutionary programing, particle swarm and others) can optimise complicated nonlinear kinetic models and are friendly for unexperienced user: they can return optimisation results with default method settings (population size, number of generations and others) and without adaptation of the model. Drawbacks of these methods (stochastic behaviour, undefined duration of optimisation, possible stagnation and no guaranty of reaching optima) cau…
Portfolio optimisation with strictly positive transaction costs and impulse control
1998
One crucial assumption in modern portfolio theory of continuous-time models is the no transaction cost assumption. This assumption normally leads to trading strategies with infinite variation. However, following such a strategy in the presence of transaction costs will lead to immediate ruin. We present an impulse control approach where the investor can change his portfolio only finitely often in finite time intervals. Further, we consider transaction costs including a fixed and a proportional cost component. For the solution of the resulting control problems we present a formal optimal stopping approach and an approach using quasi-variational inequalities. As an application we derive a non…
Robust Mean Field Games
2015
Recently there has been renewed interest in large-scale games in several research disciplines, with diverse application domains as in the smart grid, cloud computing, financial markets, biochemical reaction networks, transportation science, and molecular biology. Prior works have provided rich mathematical foundations and equilibrium concepts but relatively little in terms of robustness in the presence of uncertainties. In this paper, we study mean field games with uncertainty in both states and payoffs. We consider a population of players with individual states driven by a standard Brownian motion and a disturbance term. The contribution is threefold: First, we establish a mean field syste…
Robust linear quadratic mean-field games in crowd-seeking social networks.
2013
We consider a social network where opinions evolve following a stochastic averaging process under the influence of adversarial disturbances. We provide a robust mean-field game model in the spirit of H∞-optimal control, establish existence of a mean-field equilibrium, and analyze its stochastic stability.
Stochastic acceleration in generalized squared Bessel processes
2015
We analyze the time behavior of generalized squared Bessel processes, which are useful for modeling the relevant scales of stochastic acceleration problems. These nonstationary stochastic processes obey a Langevin equation with a non-Gaussian multiplicative noise. We obtain the long-time asymptotic behavior of the probability density function for non-Gaussian white and colored noise sources. We find that the functional form of the probability density functions is independent of the statistics of the noise source considered. Theoretical results are in good agreement with those obtained by numerical simulations of the Langevin equation with pulse noise sources.
A Fokker–Planck control framework for multidimensional stochastic processes
2013
AbstractAn efficient framework for the optimal control of probability density functions (PDFs) of multidimensional stochastic processes is presented. This framework is based on the Fokker–Planck equation that governs the time evolution of the PDF of stochastic processes and on tracking objectives of terminal configuration of the desired PDF. The corresponding optimization problems are formulated as a sequence of open-loop optimality systems in a receding-horizon control strategy. Many theoretical results concerning the forward and the optimal control problem are provided. In particular, it is shown that under appropriate assumptions the open-loop bilinear control function is unique. The res…