To solve hierarchical problems, one must be able to learn the linkage, represent partial solutions efficiently, and assure effective niching. We propose the hierarchical ...

The paper discusses three major issues. First, it discusses why it makes sense to approach problems in a hierarchical fashion. It defines the class of hierarchically decomposable functions that can be used to test the algorithms that approach problems in this fashion. Finally, the Bayesian optimization algorithm (BOA) is extended in order to solve the proposed class of problems.

We propose a sub-structural niching method that fully exploits the problem decomposition capability of linkagelearning methods such as the estimation distribution algorithms and concentrate on maintaining diversity at the sub-structural level. The proposed method consists of three key components: (1) Problem decomposition and sub-structure identification, (2) sub-structure fitness estimation, and (3) sub-structural niche preservation. The substructural niching method is compared to restricted tournament selection (RTS)—a niching method used in hierarchical Bayesian optimization algorithm—with special emphasis on sustained preservation of multiple global solutions of a class of boundedly-difficult, additively-separable multimodal problems. The results show that sub-structural niching successfully maintains multiple global optima over large number of generations and does so with significantly less population than RTS. Additionally, the market share of each of the niche is much closer to the expected level in sub-structural niching when compared to RTS.

The aim of this paper is to identify Genetic Algorithms (GAs) which perform well over a range of continuous and smooth multimodal real-variable functions. In our study, we focus on testing GAs combining three classes of genetic operators: selection, crossover and replacement.

Evolutionary Algorithms (EAs) are a useful tool to tackle real-world optimisation problems. Two important features that make these problems hard are multimodality and high dimensionality of the search landscape.

In this paper, we propose a GA model called Adaptive Isolation Model(AIM), for multimodal optimization. It uses a data clustering algorithm to detect clusters in GA population, which identifies the attractors in the fitness landscape. Then, subpopulations which makes-up the clusters are isolated and optimized independently. Meanwhile, the region of the isolated subpopulations in the original landscape are suppressed. The isolation increases comprehensiveness, i.e., the probability of finding weaker attractors, and the overall efficiency of multimodal search. The advantage of the AIM is that it does not require distance between the optima as a presumed parameter, as it is estimated from the variance/covariance matrix of the subpopulation. Further, AIM’s behavior and efficiency is equivalent to basic GA in unimodal landscape, in terms of number of evaluation. Therefore, it is applied recursively to all subpopulations until they converge to a suboptima. This makes AIM suitable for locallymultimodal landscapes, which have closely located attractors that are difficult to distinguish in the initial run. The performance of AIM is evaluated in several benchmark problems and compared to iterated hillclimbing methods. 1 1

Abstract — In contrast to optimization techniques intended to find a single, global solution in a problem domain, niching (speciation) techniques have the ability to locate multiple solutions in multimodal domains. Numerous niching techniques have been proposed, broadly classified as temporal (locating solutions sequentially) and parallel (multiple solutions are found concurrently) techniques. Most research efforts to date have considered niching solutions through the eyes of genetic algorithms (GAs), studying simple multimodal problems. Little attention has been given to the possibilities associated with emergent swarm intelligence techniques. Particle swarm optimization (PSO) utilizes properties of swarm behaviour not present in evolutionary algorithms such as GAs, to rapidly solve optimization problems. This paper investigates the ability of two genetic algorithm niching techniques, sequential niching and deterministic crowding, to scale to higher dimensional domains with large numbers of solutions, and compare their performance to a PSO-based niching technique, NichePSO. I.

Introduction. Evolutionary methods are exceedingly popular with practitioners of many fields; more so than perhaps any optimization tool in existence. Historically Genetic Algorithms (GAs) led the way in practitioner popularity 10 . However, in the last ten years Evolutionary Strategies (ESs) have gained a significant foothold 5 . One partial explanation for this shift is the interest in using GAs to solve continuous optimization problems. The typical GA relies on a binary representation of the design variables which is cumbersome. This is not true for ESs which work with real-valued design variables. One of the earliest ES references is Schwefel 12 in which an ES with a population of size one was examined. Not until Schwefel 13 and Rechenberg 11 were populations of varying sizes considered. For detailed current references on evolutionary methods in general and ESs in specific see Back

In inverse problems, often there is no available analytical expression relating the physical quantities of interest and the available data. In these cases, one resorts to using a numerical model with a finite number of parameters, resulting in a discrete problem. Also, many discrete inverse problems involve a highly nonlinear mapping between the model parameters and the simulation of the data by the model. Algorithms exist for estimating the model parameters in nonlinear discrete inverse problems. However, one needs to investigate how these estimated models relate to the true structure of the studied system (i.e. the truth model). This is known as model appraisal and it is greatly a#ected by three sources of uncertainty: misleading search, non-uniqueness and errors.

In this paper, we propose a replacement strategy for steady-state genetic algorithms that considers two features of the candidate chromosome to be included into the population: a measure of the contribution of diversity to the population and the fitness function. In particular, the proposal tries to replace an individual in the population with worse values for these two features. In this way, the diversity of the population becomes increased and the quality of the solutions gets better, thus preserving high levels of useful diversity. Experimental results show the proposed replacement strategy achieved significant performance for problems with different difficulties, which regards to other replacement strategies presented in the literature.