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: