this paper "ergodic" is used in a very weak sense, as it is not proposed, theoretically or practically, that all states of the system are actually to be visited

INTRODUCTION In this paper we consider Simulated Annealing algorithms (SA in what follows) applied to continuous global optimization problems, i.e. problems with the following form f = min x2X f(x); (1.1) where X ` ! n is a continuous domain, often assumed to be compact, which, combined with the continuity or lower semicontinuity of f , guarantees the existence of the minimum value f . SA algorithms are based on an analogy with a physical phenomenon: while at high temperatures the molecules in a liquid move freely, if the temperature is slowly decreased the thermal mobility of the molecules is lost and they form a pure crystal which also corresponds to a state of minimum energy. If the temperature is decreased too quickly (the so called quenching) a liquid metal rather ends up in a polycrystalline or amorphous state with

Simulated Annealing (SA) is a powerful stochastic search method applicable to a wide range of problems for which little prior knowledge is available. It can produce very high quality solutions for hard combinatorial optimization problems. However, the computation time required by SA is very large. Various methods have been proposed to reduce the computation time, but they mainly deal with the careful tuning of SA's control parameters. This paper first analyzes the impact of SA's neighbourhood on SA's performance and shows that SA with a larger neighbourhood is better than SA with a smaller one. The paper also gives a general model of SA, which has both dynamic generation probability and acceptance probability, and proves its convergence. All variants of SA can be unified under such a generalization. Finally, a method of extending SA's neighbourhood is proposed, which uses a discrete approximation to some continuous probability function as the generation function in SA, and several impo...

Simulated annealing and and single trial versions of evolution strategies possess a close relationship when they are designed for optimization over continuous variables. Analytical investigations of their differences and similarities lead to a cross-fertilization of both approaches, resulting in new theoretical results, new parallel population based algorithms, and a better understanding of the interrelationships.

. In this paper we present a method called NOVEL (Nonlinear Optimization via External Lead) for solving continuous and discrete global optimization problems. NOVEL addresses the balance between global search and local search, using a trace to aid in identifying promising regions before committing to local searches. We discuss NOVEL for solving continuous constrained optimization problems and show how it can be extended to solve constrained satisfaction and discrete satisfiability problems. We first transform the problem using Lagrange multipliers into an unconstrained version. Since a stable solution in a Lagrangian formulation only guarantees a local optimum satisfying the constraints, we propose a global search phase in which an aperiodic and bounded trace function is added to the search to first identify promising regions for local search. The trace generates an information-bearing trajectory from which good starting points are identified for further local searches. Taking only a sm...

... these new methods, we develop a prototype, called Novel (Nonlinear Optimization Via External Lead), that solves nonlinear constrained and unconstrained problems in a unified framework. We show experimental results in applying Novel to solve nonlinear optimization problems, including (a) the learning of feedforward neural networks, (b) the design of quadrature-mirror-filter digital filter banks, (c) the satisfiability problem, (d) the maximum satisfiability problem, and (e) the design of multiplierless quadrature-mirror-filter digital filter banks. Our method achieves better solutions than existing methods, or achieves solutions of the same quality but at a lower cost.

An overview is given of the current status of inverse methods and data assimilation for nonlinear ocean models. The inverse theory for time dependent dynamical models is formulated and the most promising solution methods like simulated annealing, the representer method, and sequential methods based on Monte Carlo simulations, are discussed with special focus on applications with nonlinear dynamics. A rather general "model independent" presentation has been used to make the methodology more accessible for different scientific areas dealing with dynamical models and data.

A multidisciplinary design optimization framework suitable for application to mixed continuous/discrete systems has been developed. This framework, called Concurrent Subspace Design, employs artificial neural networks to provide response surface approximations. A concise metric indicating how accurately a neural network is able to approximate the design space was defined and used to assess different networks, which were obtained by varying the amount of data considered in their construction and the means by which discrete design variables are represented in them. Results demonstrate that this framework is able to locate optimal designs and that its computational requirements are related to some degree to the database used in formulating the neural network approximations.

This thesis addresses the problem of estimating the surface reflection model of objects observed in a terrestrial scene, illuminated by natural illumination; that is, a scene which is illuminated by sun and sky light alone. This is a departure from the traditional analysis of laboratory scenes, which are illuminated by idealised light sources with positions and radiance distributions that are precisely controlled. Natural illumination presents a complex hemispherical light source which changes in both spatial and spectral distribution with time, terrestrial location, and atmospheric conditions. An image-based approach to the measurement of surface reflection is presented. The use of a sequence of images, taken over a period of time, allows the varying reflection from the scene due to the changing natural illumination to be measured. It is shown that the temporal change in image pixel values is suitable for the parameters of a reflection model to be estimated. These parameters are estim...

Experimental design and response surface methodology is applied to tuning the parameters of an optimization program employing genetic algorithms. Attention is directed to the combinatorially challenging DNA sequence assembly problem. Fine tuning of a 10K size test problem leads to a considerably improved solution to a 35K problem of sequence assembly that is of significant biological interest. Key Words and Phrases: genetic algorithms; design of experiments; response surface methods; DNA sequence assembly. R.J. PARSONS & M.E. JOHNSON 1. Introduction Design and analysis of experiments and response surface methods have prospered in this century through successful applications in agriculture initially and in industry in more recent decades. Great strides in the development of these methods have taken place owing to improvements in computing capability. Although the semiconductor industry upon which our computing platforms depend has particularly benefited from design of experiments and ...