Abstract:
Efficiency enhancement techniques—such as parallelization and hybridization—are among the most important ingredients of practical applications of genetic and evolutionary algorithms and that is why this research area represents an important niche of evolutionary computation. This paper describes and analyzes sporadic model building, which can be used to enhance the efficiency of the hierarchical Bayesian optimization algorithm (hBOA) and other estimation of distribution algorithms (EDAs) that use complex multivariate probabilistic models. With sporadic model building, the structure of the probabilistic model is updated once in every few iterations (generations), whereas in the remaining iterations, only model parameters (conditional and marginal probabilities) are updated. Since the time complexity of updating model parameters is much lower than the time complexity of learning the model structure, sporadic model building decreases the overall time complexity of model building. The paper shows that for boundedly difficult nearly decomposable and hierarchical optimization problems, sporadic model building leads to a significant model-building speedup, which decreases the asymptotic time complexity of model building in hBOA by a factor of O(n^0.26) to O(n^0.5), where n is the problem size. On the other hand, sporadic model building also increases the number of evaluations until convergence; nonetheless, if model building is the bottleneck, the evaluation slowdown is insignificant compared to the gains in the asymptotic complexity of model building. The paper also presents a dimensional model to provide a heuristic for scaling the structure-building period, which is the only parameter of the proposed sporadic model-building approach. The paper then tests the proposed method and the rule for setting the structure-building period on the problem of finding ground states of 2D and 3D Ising spin glasses.

Abstract:
Excited-state photodynamics is important in numerous varieties of important materials applications (e.g., liquid crystal display, light emitting diode), pharmaceuticals, and chemical manufacturing processing. We study the effectiveness of multiobjective genetic and evolutionary algorithms in multiscaling excited-state direct photodynamics via rapid reparameterization of semiempirical methods. Using a very limited set of ab initio and experimental data, semiempirical parameters are reoptimized to provide globally accurate potential energy surfaces, thereby eliminating the need for expensive ab initio dynamics simulations. Through reoptimization, excited-state energetics are predicted accurately via semiempirical methods, while retaining accurate ground-state predictions. In our initial study of small photo-excited molecules, our results show that the multiobjective evolutionary algorithm consistently yields solutions that are significantly better – up to 384% lower error in the energy and 87% lower error in the energy-gradient – than those reported previously. As verified with direct quantum dynamical calculations, multiple high-quality parameter sets obtained via genetic algorithms show near-ideal behavior on critical and untested excited-state geometries. The results demonstrate that the reparameterization via evolutionary algorithms is a promising way to extend direct dynamics simulations of photochemistry to multi-picosecond time scales and to larger molecules, with promise in more application beyond simple molecular chemistry.

Abstract:
We analyze the utility and scalability of extended compact genetic algorithm (eCGA) – a genetic algorithm (GA) that automatically and adaptively mines the regularities of the fitness landscape using machine learning methods and information theoretic measures – for ground state optimization of clusters. In order to reduce the computational time requirements while retaining the high reliability of predicting near-optimal structures, we employ two efficiency-enhancement techniques: (1) hybridizing eCGA with a local search method, and (2) seeding the initial population with lowest energy structures of a smaller cluster. The proposed method is exemplified by optimizing silicon clusters with 4-20 atoms. The results indicate that the population size required to obtain near-optimal solutions with 98% probability scales sub linearly (as ?(n^0.83)) with the cluster size. The total number of function evaluations (cluster energy calculations) scales sub-cubically (as ?(n^2.45)), which is a significant improvement over exponential scaling of poorly designed evolutionary algorithms.

Abstract:
The push for better understanding and design of complex systems requires the solution of challenging optimization problems with large numbers of decision variables. This note presents principled results demonstrating the scalable solution of a difficult test function on instances over a billion variables using a parallel implementation of a genetic algorithm (GA). The problem addressed is a noisy, blind problem over a vector of binary decision variables. Noise is added equaling a tenth of the deterministic objective function variance of the problem, thereby making it difficult for simple hillclimbers to find the optimal solution. The genetic algorithm used – the compact GA – is able to find the optimum in the presence of noise quickly, reliably, and accurately, and the solution scalability follows known convergence theories. These results on noisy problem together with other results on problems involving varying modularity, hierarchy, and overlap foreshadow routine solution of billion-variable problems across the landscape of complexity science.

Abstract:
Michigan-style learning classifier systems iteratively evolve a distributed solution to a problem in the form of potentially overlapping subsolutions. Each problem niche is covered by subsolutions that are represented by a set of predictive rules, termed classifiers. The genetic algorithm is designed to evolve classifier structures that together cover the whole problem space and represent a complete problem solution. An obvious challenge for such an online evolving, distributed knowledge representation is to continuously sustain all problem subsolutions covering all problem niches, that is, to ensure niche support. Effective niche support depends both on the probability of reproduction and on the probability of deletion of classifiers in a niche. In XCS, reproduction is occurrence-based whereas deletion is support-based. In combination, niche support is assured effectively. In this paper we present a Markov chain analysis of the niche support in XCS, which we validate experimentally. Evaluations in diverse Boolean function settings, which require non-overlapping and overlapping solution structures, support the theoretical derivations. We also consider the effects of mutation and crossover on niche support. With respect to computational complexity, the paper shows that XCS is able to maintain (partially overlapping) niches with a computational effort that is linear in the inverse of the niche occurrence frequency.

Abstract:

A bottleneck for multi-timescale thermally-activated dynamics is the computation of the potential energy surface (PES). We explore the use of genetic programming (GP) to symbolically regress a mapping of the saddle-point barriers from only a few calculated points via molecular dynamics, thereby avoiding explicit calculation of all barriers. The GP-regressed barrier function enables use of kinetic Monte Carlo (KMC) to simulate real-time kinetics (seconds to hours) based upon realistic atomic interactions. To illustrate the concept, we apply a GP regression to vacancy-assisted migration on a surface of a concentrated binary alloy (from both quantum and empirical potentials) and predict the diffusion barriers within ~0.1% error from 3% (or less) of the barriers. We discuss the significant reduction in CPU time (4 to 7 orders of magnitude), the efficacy of GP over standard regression, e.g., polynomial, and the independence of the method on the type of potential.

Recent analysis of the XCS classifier system have shown that successful genetic learning strongly depends on the amount of fitness pressure towards accurate classifiers. Since the traditionally used proportionate selection is dependent on fitness scaling and fitness distribution, the resulting evolutionary fitness pressure may be neither stable nor sufficiently strong. Thus, we apply tournament selection to XCS. In particular, we exhibit the weakness of proportionate selection and suggest tournament selection as a more reliable alternative. We show that tournament selection results in a learning classifier system that is more parameter independent, noise independent, and more efficient in exploiting fitness guidance in single-step problems as well as multistep problems. The evolving population is more focused on promising subregions of the problem space and thus finds the desired accurate, maximally general representation faster and more reliably.

We propose the use of genetic programming (GP)—a genetic algorithm that evolves computer programs—for bridging simulation methods across multiple scales of time and/or length. The effectiveness of genetic programming in multiscale simulation is demonstrated using two illustrative, non-trivial case studies in science and engineering. The first case is multi-timescale materials kinetics modeling, where genetic programming is used to symbolically regress a mapping of all diffusion barriers from only a few calculated ones, thereby avoiding explicit calculation of all the barriers. The GP-regressed barrier function enables use of kinetic Monte Carlo for realistic potentials and simulation of realistic experimental times (seconds). Specifically, a GP regression is applied to vacancy-assisted migration on a surface of a binary alloy and predict the diffusion barriers within 0.1–1\% error using 3\% (or less) of the barriers. The second case is the development of constitutive relation between macroscopic variables using measured data, where GP is used to evolve both the function form of the constitutive equation as well as the coefficient values. Specifically, GP regression is used for developing a constitutive relation between flow stress and temperature-compensated strain rate based on microstructural characterization for an aluminum alloy AA7055. We not only reproduce a constitutive relation proposed in literature, but also develop a new constitutive equation that fits both low-strain-rate and high-strain-rate data. We hope these disparate example applications exemplify the power of GP for multiscaling at the price, of course, of not knowing physical details at the intermediate scales.

To solve a wide range of different problems, the research in black-box optimization faces several important challenges. One of the most important challenges is the design of methods capable of automatically discovering the regularities in the problem and utilizing these to ensure efficient and reliable search. This paper discusses the Bayesian optimization algorithm (BOA) that uses Bayesian networks to model promising solutions and guide exploration of the search space. Using Bayesian networks in combination with population-based genetic and evolutionary search allows the algorithm to discover and utilize regularities in the form of problem decomposition. The paper analyzes the applicability of the methods for learning Bayesian networks in context of genetic and evolutionary search. In particular, the population sizing ensuring that BOA learns a proper decomposition of the problem is analyzed. The paper concludes that the combination of the two approaches in BOA yields a robust, efficient, and accurate search.

A new non-sequential technique is proposed for the estimation of effective heat transfer parameters using radial temperature profile measurements in a gas-liquid co-current downflow through packed bed reactors (often referred to as trickle bed reactors). Orthogonal collocation method combined with a new optimization technique, differential evolution (DE) is employed for estimation. DE is an exceptionally simple, fast and robust, population based search algorithm that is able to locate near-optimal solutions to difficult problems. The results obtained from this new technique are compared with that of radial temperature profile (RTP) method. Results indicate that orthogonal collocation augmented with DE offer a powerful alternative to other methods reported in the literature. The proposed technique takes less computational time to converge when compared to the existing techniques without compromising with the accuracy of the parameter estimates. This new technique takes on an average 10 s on a 90 MHz Pentium processor as compared to 30 s by the RTP method. This new technique also assures of convergence from any starting point and requires less number of function evaluations.