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Abstract. 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.

Difficulty in sampling large and complex conformational spaces remains a key limitation in fragment-based de novo prediction of protein structure. Our previous work has shown that even for small-to-medium-sized proteins, some current methods inadequately sample alternative structures. We have developed two new conformational sampling techniques, one employing a bilevel optimisation framework and the other employing iterated local search. We combine strategies of forced structural perturbation (where some fragment insertions are accepted regardless of their impact on scores) and greedy local optimisation, allowing greater exploration of the available conformational space. Comparisons against the Rosetta Abinitio method indicate that our protocols more frequently generate native-like predictions for many targets, even following the low-resolution phase, using a given set of fragment libraries. By contrasting results across two different fragment sets, we show that our methods are able to better take advantage of high-quality fragments. These improvements can also translate into more reliable identification of near-native structures in a simple clustering-based model selection procedure. We show that when fragment libraries are sufficiently well-constructed, improved breadth of exploration within runs improves prediction accuracy. Our results also suggest that in benchmarking scenarios, a total exclusion of fragments drawn from homologous templates can make performance differences between methods appear less pronounced.

Computational approaches to de novo protein tertiary structure prediction, including those based on the preeminent “fragment-assembly” technique, have failed to scale up fully to larger proteins (on the order of 100 residues and above). A number of limiting factors are thought to contribute to the scaling problem over and above the simple combinatorial explosion, but the key ones relate to the lack of exploration of properly diverse protein folds, and to an acute form of “deception” in the energy function, whereby low-energy conformations do not reliably equate with native structures. In this article, solutions to both of these problems are investigated through a multistage memetic algorithm incorporating the successful Rosetta method as a local search routine. We found that specialised genetic operators significantly add to structural diversity and that this translates well to reaching low energies. The use of a generalised stochastic ranking procedure for selection enables the memetic algorithm to handle and traverse deep energy wells that can be considered deceptive, which further adds to the ability of the algorithm to obtain a much-improved diversity of folds. The results should translate to a tangible improvement in the performance of protein structure prediction algorithms in blind experiments such as CASP, and potentially to a further step towards the more challenging problem of predicting the three-dimensional shape of large proteins.

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.978-1-4244-8126-2/10/$26.00 ©2010 IEEE