Mario Garza-Fabre

Ranking Methods for Many-Objective Optimization

An important issue with Evolutionary Algorithms (EAs) is the way to identify the best solutions in order to guide the search process. Fitness comparisons among solutions in single-objective optimization is straightforward, but when dealing with multiple objectives, it becomes a non-trivial task. Pareto dominance has been the most commonly adopted relation to compare solutions in a multiobjective optimization context. However, it has been shown that as the number of objectives increases, the convergence ability of approaches based on Pareto dominance decreases. In this paper, we propose three novel fitness assignment methods for many-objective optimization. We also perform a comparative study in order to investigate how effective are the proposed approaches to guide the search in high-dimensional objective spaces. Results indicate that our approaches behave better than six state-of-the-art fitness assignment methods.

Two novel approaches for many-objective optimization

In this paper, two novel evolutionary approaches for many-objective optimization are proposed. These algorithms integrate a fine-grained ranking of solutions to favor convergence, with explicit methodologies for diversity promotion in order to guide the search towards a representative approximation of the Pareto-optimal surface. In order to validate the proposed algorithms, we performed a comparative study where four state-of-the-art representative approaches were considered. In such a study, four well-known scalable test problems were adopted as well as six different problem sizes, ranging from 5 to 50 objectives. Our results indicate that our two proposed algorithms consistently provide good convergence as the number of objectives increases, outperforming the other approaches with respect to which they were compared.

Locality-based multiobjectivization for the HP model of protein structure prediction

Even under the rather simplified HP lattice model, protein structure prediction remains a challenging problem in combinatorial optimization. Recently, the multiobjectivization of this problem was proposed. By decomposing the original objective function, a two-objective formulation for the HP model was defined. Such an alternative formulation showed very promising results, leading to an increased search performance in most of the conducted experiments. This paper introduces a novel multiobjectivization for the HP model which is based on the locality notion of amino acid interactions. Using different evolutionary algorithms, this proposal was compared with respect to both the conventional single-objective formulation and the previously reported multiobjectivization. The new proposed formulation scored the best results in most of the cases. Statistical significance testing and a large set of test cases support the findings of this study. Results are provided for both the two-dimensional square lattice and the three-dimensional cubic lattice.

Effective ranking + speciation = Many-objective optimization

Multiobjective optimization problems have been widely addressed using evolutionary computation techniques. However, when dealing with more than three conflicting objectives (the so-called many-objective problems), the performance of such approaches deteriorates. The problem lies in the inability of Pareto dominance to provide an effective discrimination. Alternative ranking methods have been successfully used to cope with this issue. Nevertheless, the high selection pressure associated with these approaches usually leads to diversity loss. In this study, we focus on parallel genetic algorithms, where multiple partially isolated subpopulations are evolved concurrently. As in nature, isolation leads to speciation, the process by which new species arise. Thus, evolving multiple subpopulations can be seen as a potential source of diversity and it is known to improve the search performance of genetic algorithms. Our experimental results suggest that such a behavior, integrated with an effective ranking, constitutes a suitable approach for many-objective optimization.

Constraint-handling through multi-objective optimization

In the multi-objective approach to constraint-handling, a constrained problem is transformed into an unconstrained one by defining additional optimization criteria to account for the problem constraints. In this paper, this approach is explored in the context of the hydrophobic-polar model, a simplified yet challenging representation of the protein structure prediction problem. Although focused on such a particular case of study, this research work is intended to contribute to the general understanding of the multi-objective constraint-handling strategy. First, a detailed analysis was conducted to investigate the extent to which this strategy impacts on the characteristics of the fitness landscape. As a result, it was found that an important fraction of the infeasibility translates into neutrality. This neutrality defines potentially shorter paths to move through the landscape, which can also be exploited to escape from local optima. By studying different mechanisms, the second part of this work highlights the relevance of introducing a proper search bias when handling constraints by multi-objective optimization. Finally, the suitability of the multi-objective approach was further evaluated in terms of its ability to effectively guide the search process. This strategy significantly improved the performance of the considered search algorithms when compared with respect to commonly adopted techniques from the literature.

Comparative Analysis of Different Evaluation Functions for Protein Structure Prediction Under the HP Model

The HP model for protein structure prediction abstracts the fact that hydrophobicity is a dominant force in the protein folding process. This challenging combinatorial optimization problem has been widely addressed through metaheuristics. The evaluation function is a key component for the success of metaheuristics; the poor discrimination of the conventional evaluation function of the HP model has motivated the proposal of alternative formulations for this component. This comparative analysis inquires into the effectiveness of seven different evaluation functions for the HP model. The degree of discrimination provided by each of the studied functions, their capability to preserve a rank ordering among potential solutions which is consistent with the original objective of the HP model, as well as their effect on the performance of local search methods are analyzed. The obtained results indicate that studying alternative evaluation schemes for the HP model represents a highly valuable direction which merits more attention.

Multi-objectivization, Fitness Landscape Transformation and Search Performance: A Case of Study on the HP model for Protein Structure Prediction

Multi-objectivization represents a current and promising research direction which has led to the development of more competitive search mechanisms. This concept involves the restatement of a single-objective problem in an alternative multi-objective form, which can facilitate the process of finding a solution to the original problem. Recently, this transformation was applied with success to the HP model, a simplified yet challenging representation of the protein structure prediction problem. The use of alternative multi-objective formulations, based on the decomposition of the original objective function of the problem, has significantly increased the performance of search algorithms. The present study goes further on this topic. With the primary aim of understanding and quantifying the potential effects of multi-objectivization, a detailed analysis is first conducted to evaluate the extent to which this problem transformation impacts on an important characteristic of the fitness landscape, neutrality. To the authors’ knowledge, the effects of multi-objectivization have not been previously investigated by explicitly sampling and evaluating the neutrality of the fitness landscape. Although focused on the HP model, most of the findings of such an analysis can be extrapolated to other problem domains, contributing thus to the general understanding of multi-objectivization. Finally, this study presents a comparative analysis where the advantages of multi-objectivization are evaluated in terms of the performance of a basic evolutionary algorithm. Both the two- and three-dimensional variants of the HP model (based on the square and cubic lattices, respectively) are considered.

An improved multiobjectivization strategy for HP model-based protein structure prediction

Through multiobjectivization, a single-objective problem is restated in multiobjective form with the aim of enabling a more efficient search process. Recently, this transformation was applied with success to the hydrophobic-polar (HP) lattice model, which is an abstract representation of the protein structure prediction problem. The use of alternative multiobjective formulations of the problem has led to significantly better results. In this paper, an improved multiobjectivization for the HP model is proposed. By decomposing the HP models energy function, a two-objective formulation for the problem is defined. A comparative analysis reveals that the new proposed multiobjectivization evaluates favorably with respect to both the conventional single-objective and the previously reported multiobjective formulations. Statistical significance testing and the use of a large set of test cases support the findings of this study. Both two-dimensional and three-dimensional lattices are considered.

Comparing alternative energy functions for the HP model of protein structure prediction

Protein structure prediction is the problem of finding the functional conformation of a protein given only its amino acid sequence. The HP lattice model is an abstract formulation of this problem, which captures the fact that hydrophobicity is one of the major driving forces in the protein folding process. This model represents a hard combinatorial optimization problem and has been widely addressed through metaheuristics such as evolutionary algorithms. However, the conventional energy (evaluation) function of the HP model does not provide an adequate discrimination among potential solutions, which is an essential requirement for metaheuristics in order to perform an effective search. Therefore, alternative energy functions have been proposed in the literature to cope with this issue. In this study, we inquire into the effectiveness of several of such alternative approaches. We analyzed the degree of discrimination provided by each of the studied functions as well as their impact on the behavior of a basic memetic algorithm. The obtained results support the relevance of following this research direction. To our knowledge, this is the first work reported in this regard.