Carlos R. B. Azevedo

Generalized immigration schemes for dynamic evolutionary multiobjective optimization

The insertion of atypical solutions (immigrants) in Evolutionary Algorithms populations is a well studied and successful strategy to cope with the difficulties of tracking optima in dynamic environments in single-objective optimization. This paper studies a probabilistic model, suggesting that centroid-based diversity measures can mislead the search towards optima, and presents an extended taxonomy of immigration schemes, from which three immigrants strategies are generalized and integrated into NSGA2 for Dynamic Multiobjective Optimization (DMO). The correlation between two diversity indicators and hypervolume is analyzed in order to assess the influence of the diversity generated by the immigration schemes in the evolution of non-dominated solutions sets on distinct continuous DMO problems under different levels of severity and periodicity of change. Furthermore, the proposed immigration schemes are ranked in terms of the observed offline hypervolume indicator.

Correlation between diversity and hypervolume in evolutionary multiobjective optimization

This paper reports a study of the influence of diversity in the convergence dynamics of Multiobjective Evolutionary Algorithms (MOEAs) towards the Pareto Front (PF). By varying mutation and crossover parameters, several scenarios of exploration and exploitation are considered, in which each of them is analysed in order to assess the role of diversity levels on the evolution of high quality sets of non-dominated solutions, in terms of the Hypervolume indicator. For this task, the application of the NSGA2 algorithm for approximating the PF in five ZDT benchmark problems is considered. The results not only indicate that there are significant statistical correlations between several diversity metrics and the observed maximum Hypervolume levels on the evolved populations, but also suggest that there are predictable temporal patterns of correlation when the evolutionary process is portrayed generation wise.

Money in trees: How memes, trees, and isolation can optimize financial portfolios

In this paper, we propose the hybrid application of two nature inspired approaches to the problem of Portfolio Optimization. This problem consists of the selection and weighting of financial assets. Its goal is to form an investment strategy which maximizes a return measure and minimizes a risk measure. We perform a series of simulation experiments with historical data in the NASDAQ and S&P500 markets between 2006 and 2008. The results show that adding a terrain strategy to a previously successful Memetic Algorithm promoted niching and speciation of the population, which led to a significant improvement in the performance when compared to previous evolutionary methods. We also show that the use of Memetic Algorithms gives the evolved solutions a degree of adaptability to changes in a dynamic market.

Anticipatory Stochastic Multi-Objective Optimization for uncertainty handling in portfolio selection

An anticipatory stochastic multi-objective model based on S-Metric maximization is proposed. The environment is assumed to be noisy and time-varying. This raises the question of how to incorporate anticipation in metaheuristics such that the Pareto optimal solutions can reflect the uncertainty about the subsequent environments. A principled anticipatory learning method for tracking the dynamics of the objective vectors is then proposed so that the estimated S-Metric contributions of each solution can integrate the underlying stochastic uncertainty. The proposal is assessed for minimum holding, cardinality constrained portfolio selection, using real-world stock data. Preliminary results suggest that, by taking into account the underlying uncertainty in the predictive knowledge provided by a Kalman filter, we were able to reduce the sum of squared errors prediction of the portfolios ex-post return and risk estimation in out-of-sample investment environments.

Adaptive terrain-based memetic algorithms

The Terrain-Based Memetic Algorithm (TBMA) is a diffusion MA in which the local search (LS) behavior depends on the topological distribution of memetic material over a grid (terrain). In TBMA, the spreading of meme values -- such as LS step sizes -- emulates cultural differences which often arise in sparse populations. In this paper, adaptive capabilities of TBMAs are investigated by meme diffusion: individuals are allowed to move in the terrain and/or to affect their environment, by either following more effective memes or by transmitting successful meme values to nearby cells. In this regard, four TBMA versions are proposed and evaluated on three image vector quantizer design instances. The TBMAs are compared with K-Means and a Cellular MA. The results strongly indicate that utilizing dynamically adaptive meme evolution produces the best solutions using fewer fitness evaluations for this application.

Learning to Anticipate Flexible Choices in Multiple Criteria Decision-Making Under Uncertainty

In several applications, a solution must be selected from a set of tradeoff alternatives for operating in dynamic and noisy environments. In this paper, such multicriteria decision process is handled by anticipating flexible options predicted to improve the decision maker future freedom of action. A methodology is then proposed for predicting tradeoff sets of maximal hypervolume, where a multiobjective metaheuristic was augmented with a Kalman filter and a dynamical Dirichlet model for tracking and predicting flexible solutions. The method identified decisions that were shown to improve the future hypervolume of tradeoff investment portfolio sets for out-of-sample stock data, when compared to a myopic strategy. Anticipating flexible portfolios was a superior strategy for smoother changing artificial and real-world scenarios, when compared to always implementing the decision of median risk and to randomly selecting a portfolio from the evolved anticipatory stochastic Pareto frontier, whereas the median choice strategy performed better for abruptly changing markets. Correlations between the portfolio compositions and future hypervolume were also observed.

Regularized hypervolume selection for robust portfolio optimization in dynamic environments

This paper proposes a regularized hypervolume (SMetric) selection algorithm. The proposal is used for incorporating stability and diversification in financial portfolios obtained by solving a temporal sequence of multi-objective Mean Variance Problems (MVP) on real-world stock data, for short to longterm rebalancing periods. We also propose the usage of robust statistics for estimating the parameters of the assets returns distribution so that we are able to test two variants (with and without regularization) on dynamic environments under different levels of instability. The results suggest that the maximum attaining Sharpe Ratio portfolios obtained for the original MVP without regularization are unstable, yielding high turnover rates, whereas solving the robust MVP with regularization mitigated turnover, providing more stable solutions for unseen, dynamic environments. Finally, we report an apparent conflict between stability in the objective space and in the decision space.

TOPOLOGICAL AND MOTION STRATEGIES FOR CELLULAR MEMETIC TREE-BASED PORTFOLIO OPTIMIZATION

Portfolio Optimization (PO) is a resource allocation problem where real valued weights are assigned to multiple financial assets in order to maximize the return and minimize the risk. The Memetic Tree-based Algorithm (MTGA), employing a tree representation allied with local search (LS) has shown great performance compared to other weight balancing techniques. In this work, we hybridize MTGA with topological frameworks — Cellular Memetic Algorithms (CMA) — and study four implementations, varying whether the individuals move through the grid, and whether meta-parameters are spread along the axes for self-adaptation. The approaches are compared using a historical data simulation. A CMA which incorporates motion performs best, while parameter tuning was less successful. The results not only describe an improved method for PO, but also have broader implications for cellular models wherein the benefits of motion are shown to deserve further investigation.

The influence of supervised clustering for RBFNN centers definition: a comparative study

Several clustering algorithms have been considered to determine the centers and dispersions of the hidden layer neurons of Radial Basis Function Neural Networks (RBFNNs) when applied both to regression and classification tasks. Most of the proposed approaches use unsupervised clustering techniques. However, for data classification, by performing supervised clustering it is expected that the obtained clusters represent meaningful aspects of the dataset. We therefore compared the original versions of k-means, Neural-Gas (NG) and Adaptive Radius Immune Algorithm (ARIA) along with their variants that use labeled information. The first two had already supervised versions in the literature, and we extended ARIA toward a supervised version. Artificial and real-world datasets were considered in our experiments and the results showed that supervised clustering is better indicated in problems with unbalanced and overlapping classes, and also when the number of input features is high.