Denoising Autoencoders for fast Combinatorial Black Box Optimization

Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Autoencoders (AE) are generative stochastic networks with these desired properties. We integrate a special type of AE, the Denoising Autoencoder (DAE), into an EDA and evaluate the performance of DAE-EDA on several combinatorial optimization problems with a single objective. We asses the number of fitness evaluations as well as the required CPU times. We compare the results to the performance to the Bayesian Optimization Algorithm (BOA) and RBM-EDA, another EDA which is based on a generative neural network which has proven competitive with BOA. For the considered problem instances, DAE-EDA is considerably faster than BOA and RBM-EDA, sometimes by orders of magnitude. The number of fitness evaluations is higher than for BOA, but competitive with RBM-EDA. These results show that DAEs can be useful tools for problems with low but non-negligible fitness evaluation costs.Comment: corrected typos and small inconsistencie

Using Prior Knowledge and Learning from Experience in Estimation of Distribution Algorithms

Estimation of distribution algorithms (EDAs) are stochastic optimization techniques that explore the space of potential solutions by building and sampling explicit probabilistic models of promising candidate solutions. One of the primary advantages of EDAs over many other stochastic optimization techniques is that after each run they leave behind a sequence of probabilistic models describing useful decompositions of the problem. This sequence of models can be seen as a roadmap of how the EDA solves the problem. While this roadmap holds a great deal of information about the problem, until recently this information has largely been ignored. My thesis is that it is possible to exploit this information to speed up problem solving in EDAs in a principled way. The main contribution of this dissertation will be to show that there are multiple ways to exploit this problem-specific knowledge. Most importantly, it can be done in a principled way such that these methods lead to substantial speedups without requiring parameter tuning or hand-inspection of models

In Search of Optimal Linkage Trees

Linkage-learning Evolutionary Algorithms (EAs) use linkage learning to construct a linkage model, which is exploited to solve problems efficiently by taking into account important linkages, i.e. dependencies between problem variables, during variation. It has been shown that when this linkage model is aligned correctly with the structure of the problem, these EAs are capable of solving problems efficiently by performing variation based on this linkage model [2]. The Linkage Tree Genetic Algorithm (LTGA) uses a Linkage Tree (LT) as a linkage model to identify the problem's structure hierarchically, enabling it to solve various problems very efficiently. Understanding the reasons for LTGA's excellent performance is highly valuable as LTGA is also able to efficiently solve problems for which a tree-like linkage model seems inappropriate. This brings us to ask what in fact makes a linkage model ideal for LTGA to be used

Geometric generalisation of surrogate model-based optimisation to combinatorial and program spaces

Open access journalSurrogate models (SMs) can profitably be employed, often in conjunction with evolutionary algorithms, in optimisation in which it is expensive to test candidate solutions. The spatial intuition behind SMs makes them naturally suited to continuous problems, and the only combinatorial problems that have been previously addressed are those with solutions that can be encoded as integer vectors. We show how radial basis functions can provide a generalised SM for combinatorial problems which have a geometric solution representation, through the conversion of that representation to a different metric space. This approach allows an SM to be cast in a natural way for the problem at hand, without ad hoc adaptation to a specific representation. We test this adaptation process on problems involving binary strings, permutations, and tree-based genetic programs. © 2014 Yong-Hyuk Kim et al

GAMBIT: A parameterless model-based evolutionary algorithm for mixed-integer problems

Learning and exploiting problem structure is one of the key challenges in optimization. This is especially important for black-box optimization (BBO) where prior structural knowledge of a problem is not available. Existing model-based Evolutionary Algorithms (EAs) are very efficient at learning structure in both the discrete, and in the continuous domain. In this article, discrete and continuous model-building mechanisms are integrated for the Mixed-Integer (MI) domain, comprising discrete and continuous variables. We revisit a recently introduced model-based evolutionary algorithm for the MI domain, the Genetic Algorithm for Model-Based mixed-Integer opTimization (GAMBIT). We extend GAMBIT with a parameterless scheme that allows for practical use of the algorithm without the need to explicitly specify any parameters. We furthermore contrast GAMBIT with other model-based alternatives. The ultimate goal of processing mixed dependences explicitly in GAMBIT is also addressed by introducing a new mechanism for the explicit exploitation of mixed dependences. We find that processing mixed dependences with this novel mechanism allows for more efficient optimization. We further contrast the parameterless GAMBIT with Mixed-Integer Evolution Strategies (MIES) and other state-of-the-art MI optimization algorithms from the General Algebraic Modeling System (GAMS) commercial algorithm suite on problems with and without constraints, and show that GAMBIT is capable of solving problems where variable dependences prevent many algorithms from successfully optimizing them