No abstract

This paper proposes an estimation of distribution algorithm (EDA) aiming at addressing globally multimodal problems, i.e., problems that present several global optima. It can be recognized that many real-world problems are of this nature, and this property generally degrades the efficiency and effectiveness of evolutionary algorithms. To overcome this source of difficulty, we designed an EDA that builds and samples multiple probabilistic models at each generation. Different from previous studies of globally multimodal problems that also use multiple models, we adopt multivariate probabilistic models. Furthermore, we have also devised a mechanism to automatically estimate the number of models that should be employed. The empirical results demonstrate that our approach obtains more global optima per run compared to the well-known EDA that employs the same class of probabilistic models but builds a single model at each generation. Moreover, the experiments also suggest that using multiple models reduces the generations spent to reach convergence.

The probabilistic model building performed by estimation of distribution algorithms (EDAs) enables these methods to use advanced techniques of statistics and machine learning for automatic discovery of problem structures. However, in some situations, it may not be possible to completely and accurately identify the whole problem structure by probabilistic modeling due to certain inherent properties of the given problem. In this work, we illustrate one possible cause of such situations with problems consisting of structures with unequal fitness contributions. Based on the illustrative example, we introduce a notion that the estimated probabilistic models should be inspected to reveal the effective search directions and further propose a general approach which utilizes a reserved set of solutions to examine the built model for likely inaccurate fragments. Furthermore, the proposed approach is implemented on the extended compact genetic algorithm (ECGA) and experiments are performed on several sets of additively separable problems with different scaling setups. The results indicate that the proposed method can significantly assist ECGA to handle problems comprising structures of disparate fitness contributions and therefore may potentially help EDAs in general to overcome those situations in which the entire problem structure cannot be recognized properly due to the temporal delay of emergence of some promising partial solutions.

The goal of linkage identification is to obtain the dependencies among decision variables. Such information or knowledge can be applied to design crossover operators and/or the encoding schemes in genetic and evolutionary methods. Thus, promising sub-solutions to the problem will be disrupted less likely, and successful convergence may be achieved more likely. To obtain linkage information, a linkage identification technique, called Inductive Linkage Identification (ILI), was proposed recently. ILI was established upon the mechanism of perturbation and the idea of decision tree learning. By constructing a decision tree according to decision variables and fitness difference values, the interdependent variables will be determined by the adopted decision tree learning algorithm. In this article, we aim to acquire a better understanding on the characteristics of ILI, especially its behaviour under problems composed of different-sized and different-type building blocks (BBs) which are not overlapped. Experiments showed that ILI can efficiently handle BBs of different sizes and is insensitive to BB types. Our experimental observations indicate the flexibility and the applicability of ILI on various elementary BB types that are commonly adopted in related experiments.

Estimation of distribution algorithms (EDAs) are a class of evolutionary algorithms that capture the likely structure of promising solutions by explicitly building a probabilistic model and utilize the built model to guide the further search. It is presumed that EDAs can detect the structure of the problem by recognizing the regularities of the promising solutions. However, in certain situations, EDAs are unable to discover the entire structure of the problem because the set of promising solutions on which the model is built contains insufficient information regrading some parts of the problem and renders EDAs incapable of processing those parts accurately. In this work, we firstly propose a general concept that the estimated probabilistic models should be inspected to reveal the effective search directions. Based on that concept, we design a practical approach which utilizes a reserved set of solutions to examine the built model for the fragments that may be inconsistent with the actual problem structure. Furthermore, we provide an implementation of the designed approach on the extended compact genetic algorithm (ECGA) and conduct numerical experiments. The experimental results indicate that the proposed method can significantly assist ECGA to handle problems comprising building blocks of disparate scalings.