Mario A. Muñoz

A meta-learning prediction model of algorithm performance for continuous optimization problems

Algorithm selection and configuration is a challenging problem in the continuous optimization domain. An approach to tackle this problem is to develop a model that links landscape analysis measures and algorithm parameters to performance. This model can be then used to predict algorithm performance when a new optimization problem is presented. In this paper, we investigate the use of a machine learning framework to build such a model. We demonstrate the effectiveness of our technique using CMA-ES as a representative algorithm and a feed-forward backpropagation neural network as the learning strategy. Our experimental results show that we can build sufficiently accurate predictions of an algorithms expected performance. This information is used to rank the algorithm parameter settings based on the current problem instance, hence increasing the probability of selecting the best configuration for a new problem.

Algorithm selection for black-box continuous optimization problems

Selecting the most appropriate algorithm to use when attempting to solve a black-box continuous optimization problem is a challenging task. Such problems typically lack algebraic expressions, it is not possible to calculate derivative information, and the problem may exhibit uncertainty or noise. In many cases, the input and output variables are analyzed without considering the internal details of the problem. Algorithm selection requires expert knowledge of search algorithm efficacy and skills in algorithm engineering and statistics. Even with the necessary knowledge and skills, success is not guaranteed.In this paper, we present a survey of methods for algorithm selection in the black-box continuous optimization domain. We start the review by presenting Rices (1976) selection framework. We describe each of the four component spaces - problem, algorithm, performance and characteristic - in terms of requirements for black-box continuous optimization problems. This is followed by an examination of exploratory landscape analysis methods that can be used to effectively extract the problem characteristics. Subsequently, we propose a classification of the landscape analysis methods based on their order, neighborhood structure and computational complexity. We then discuss applications of the algorithm selection framework and the relationship between it and algorithm portfolios, hybrid meta-heuristics, and hyper-heuristics. The paper concludes with the identification of key challenges and proposes future research directions.

Exploratory Landscape Analysis of Continuous Space Optimization Problems Using Information Content

Data-driven analysis methods, such as the information content of a fitness sequence, characterize a discrete fitness landscape by quantifying its smoothness, ruggedness, or neutrality. However, enhancements to the information content method are required when dealing with continuous fitness landscapes. One typically employed adaptation is to sample the fitness landscape using random walks with variable step size. However, this adaptation has significant limitations: random walks may produce biased samples, and uncertainty is added because the distance between observations is not accounted for. In this paper, we introduce a robust information content-based method for continuous fitness landscapes, which addresses these limitations. Our method generates four measures related to the landscape features. Numerical simulations are used to evaluate the efficacy of the proposed method. We calculate the Pearson correlation coefficient between the new measures and other well-known exploratory landscape analysis measures. Significant differences on the measures between benchmark functions are subsequently identified. We then demonstrate the practical relevance of the new measures using them as class predictors on a machine learning model, which classifies the benchmark functions into five groups. Classification accuracy greater than 90% was obtained, with computational costs bounded between 1% and 10% of the maximum function evaluation budget. The results demonstrate that our method provides relevant information, at a low cost in terms of function evaluations.

Simplifying the Bacteria Foraging Optimization Algorithm

The Bacterial Foraging Optimization Algorithm is a swarm intelligence technique which models the individual and group foraging policies of the E. Coli bacteria as a distributed optimization process. The algorithm is structurally complex due to its nested loop architecture and includes several parameters whose selection deeply influences the result. This paper presents some modifications to the original algorithm that simplifies the algorithm structure, and the inclusion of best member information into the search strategy, which improves the performance. The results on several benchmarks show reasonable performance in most tests and a considerable improvement in some complex functions. Also, with the use of the T-Test we were able to confirm that the performance enhancement is statistically significant.

A comparison of optimisation methods and knee joint degrees of freedom on muscle force predictions during single-leg hop landings.

The aim of this paper was to compare the effect of different optimisation methods and different knee joint degrees of freedom (DOF) on muscle force predictions during a single legged hop. Nineteen subjects performed single-legged hopping manoeuvres and subject-specific musculoskeletal models were developed to predict muscle forces during the movement. Muscle forces were predicted using static optimisation (SO) and computed muscle control (CMC) methods using either 1 or 3 DOF knee joint models. All sagittal and transverse plane joint angles calculated using inverse kinematics or CMC in a 1 DOF or 3 DOF knee were well-matched (RMS error<3°). Biarticular muscles (hamstrings, rectus femoris and gastrocnemius) showed more differences in muscle force profiles when comparing between the different muscle prediction approaches where these muscles showed larger time delays for many of the comparisons. The muscle force magnitudes of vasti, gluteus maximus and gluteus medius were not greatly influenced by the choice of muscle force prediction method with low normalised root mean squared errors (<48%) observed in most comparisons. We conclude that SO and CMC can be used to predict lower-limb muscle co-contraction during hopping movements. However, care must be taken in interpreting the magnitude of force predicted in the biarticular muscles and the soleus, especially when using a 1 DOF knee. Despite this limitation, given that SO is a more robust and computationally efficient method for predicting muscle forces than CMC, we suggest that SO can be used in conjunction with musculoskeletal models that have a 1 or 3 DOF knee joint to study the relative differences and the role of muscles during hopping activities in future studies.

The Algorithm Selection Problem on the Continuous Optimization Domain

The problem of algorithm selection, that is identifying the most efficient algorithm for a given computational task, is non-trivial. Meta-learning techniques have been used successfully for this problem in particular domains, including pattern recognition and constraint satisfaction. However, there has been a paucity of studies focused specifically on algorithm selection for continuous optimization problems. This may be attributed to some extent to the difficulties associated with quantifying problem “hardness” in terms of the underlying cost function. In this paper, we provide a survey of the related literature in the continuous optimization domain. We discuss alternative approaches for landscape analysis, algorithm modeling and portfolio development. Finally, we propose a meta-learning framework for the algorithm selection problem in the continuous optimization domain.

Landscape characterization of numerical optimization problems using biased scattered data

The characterization of optimization problems over continuous parameter spaces plays an important role in optimization. A form of “fitness landscape” analysis is often carried out to describe the problem space in terms of modality, smoothness and variable separability. The outcomes of this analysis can then be used as a measure of problem difficulty and to predict the behaviour of a given algorithm. However, the metric value estimates of the landscape characterization are dependent upon the representation scheme adopted and the sampling method used. Consequently, the development of a complete classification of problem structure and complexity has proven to be challenging. In this paper, we continue this line of research. We present a methodology for the characterization of two dimensional numerical optimization problems. In our approach, data extracted during the search process is analyzed and the dependency of the results to the nominated sampling method are corrected. We show via computational simulations that the calculated metric values using our approach are consistent with the results from random experiments. As such, this study provides a first step towards the on-line calculation of fitness landscape characterization metrics and the development of empirical performance models of search algorithms. Advances in these areas would provide answers to the algorithm selection and portfolio configuration problems.

On the selection of fitness landscape analysis metrics for continuous optimization problems

Selecting the best algorithm for a given optimization problem is non-trivial due to large number of existing algorithms and high complexity of problems. A possible way to tackle this challenge is to attempt to understand the problem complexity. Fitness Landscape Analysis (FLA) metrics are widely used techniques to extract characteristics from problems. Based on the extracted characteristics, machine learning methods are employed to select the optimal algorithm for a given problem. Therefore, the accuracy of the algorithm selection framework heavily relies on the choice of FLA metrics. Although researchers have paid great attention to designing FLA metrics to quantify the problem characteristics, there is still no agreement on which combination of FLA metrics should be employed. In this paper, we present some well-performed FLA metrics, discuss their contributions and limitations in detail, and map each FLA metric to the captured problem characteristics. Moreover, computational complexity of each FLA metric is carefully analysed. We propose two criteria to follow when selecting FLA metrics. We hope our work can help researchers identify the best combination of FLA metrics.

Bacteria Swarm Foraging Optimization for Dynamical Resource Allocation in a Multizone Temperature Experimentation Platform

In this work, an algorithm based on the Bacteria Swarm Foraging Optimization was used for the dynamical resource allocation in a multiple input/output experimentation platform. This platform, which mimics a temperature grid plant, is composed of multiple sensors and actuators organized in zones. The use of the bacteria based algorithm in this application allows the search the best actuators in each sample time. This allowed us to obtain a uniform temperature over the platform. Good behavior of the implemented algorithm in the experimentation platform was observed.

Implementation of a distributed control experimentation platform

In this work, we present the implementation of a planar temperature grid plant. This plant emulates the working of a control system that is designed to maintain a constant temperature over a surface. The behavior of the implemented plant presents characteristics difficult to describe in mathematical terms like disturbances, interferences, deviations, and temperature gradients. We describe the functional characteristics of the system and its application in the study of distributed control systems in an educational environment. To test the working of the plant we present the obtained results with two resource allocation strategies such as control algorithms