Edwin D. de Jong

Reconstruction of a Functional Human Gene Network, with an Application for Prioritizing Positional Candidate Genes

Most common genetic disorders have a complex inheritance and may result from variants in many genes, each contributing only weak effects to the disease. Pinpointing these disease genes within the myriad of susceptibility loci identified in linkage studies is difficult because these loci may contain hundreds of genes. However, in any disorder, most of the disease genes will be involved in only a few different molecular pathways. If we know something about the relationships between the genes, we can assess whether some genes (which may reside in different loci) functionally interact with each other, indicating a joint basis for the disease etiology. There are various repositories of information on pathway relationships. To consolidate this information, we developed a functional human gene network that integrates information on genes and the functional relationships between genes, based on data from the Kyoto Encyclopedia of Genes and Genomes, the Biomolecular Interaction Network Database, Reactome, the Human Protein Reference Database, the Gene Ontology database, predicted protein-protein interactions, human yeast two-hybrid interactions, and microarray co-expressions. We applied this network to interrelate positional candidate genes from different disease loci and then tested 96 heritable disorders for which the Online Mendelian Inheritance in Man database reported at least three disease genes. Artificial susceptibility loci, each containing 100 genes, were constructed around each disease gene, and we used the network to rank these genes on the basis of their functional interactions. By following up the top five genes per artificial locus, we were able to detect at least one known disease gene in 54% of the loci studied, representing a 2.8-fold increase over random selection. This suggests that our method can significantly reduce the cost and effort of pinpointing true disease genes in analyses of disorders for which numerous loci have been reported but for which most of the genes are unknown.

Ideal Evaluation from Coevolution

In many problems of interest, performance can be evaluated using tests, such as examples in concept learning, test points in function approximation, and opponents in game-playing. Evaluation on all tests is often infeasible. Identification of an accurate evaluation or fitness function is a difficult problem in itself, and approximations are likely to introduce human biases into the search process. Coevolution evolves the set of tests used for evaluation, but has so far often led to inaccurate evaluation. We show that for any set of learners, a Complete Evaluation Set can be determined that provides ideal evaluation as specified by Evolutionary Multi-Objective Optimization. This provides a principled approach to evaluation in coevolution, and thereby brings automatic ideal evaluation within reach. The Complete Evaluation Set is of manageable size, and progress towards it can be accurately measured. Based on this observation, an algorithm named DELPHI is developed. The algorithm is tested on problems likely to permit progress on only a subset of the underlying objectives. Where all comparison methods result in overspecialization, the proposed method and a variant achieve sustained progress in all underlying objectives. These findings demonstrate that ideal evaluation may be approximated by practical algorithms, and that accurate evaluation for test-based problems is possible even when the underlying objectives of a problem are unknown.

Exploiting gradient information in numerical multi--objective evolutionary optimization

Various multi--objective evolutionary algorithms (MOEAs) have obtained promising results on various numerical multi--objective optimization problems. The combination with gradient--based local search operators has however been limited to only a few studies. In the single--objective case it is known that the additional use of gradient information can be beneficial. In this paper we provide an analytical parametric description of the set of all non--dominated (i.e. most promising) directions in which a solution can be moved such that its objectives either improve or remain the same. Moreover, the parameters describing this set can be computed efficiently using only the gradients of the individual objectives. We use this result to hybridize an existing MOEA with a local search operator that moves a solution in a randomly chosen non--dominated improving direction. We test the resulting algorithm on a few well--known benchmark problems and compare the results with the same MOEA without local search and the same MOEA with gradient--based techniques that use only one objective at a time. The results indicate that exploiting gradient information based on the non--dominated improving directions is superior to using the gradients of the objectives separately and that it can furthermore improve the result of MOEAs in which no local search is used, given enough evaluations.

Multi-Objective Methods for Tree Size Control

Variable length methods for evolutionary computation can lead to a progressive and mainly unnecessary growth of individuals, known as bloat. First, we propose to measure performance in genetic programming as a function of the number of nodes, rather than trees, that have been evaluated. Evolutionary Multi-Objective Optimization (EMOO) constitutes a principled way to optimize both size and fitness and may provide parameterless size control. Reportedly, its use can also lead to minimization of size at the expense of fitness. We replicate this problem, and an empirical analysis suggests that multi-objective size control particularly requires diversity maintenance. Experiments support this explanation.The multi-objective approach is compared to genetic programming without size control on the 11-multiplexer, 6-parity, and a symbolic regression problem. On all three test problems, the method greatly reduces bloat and significantly improves fitness as a function of computational expense. Using the FOCUS algorithm, multi-objective size control is combined with active pursuit of diversity, and hypothesized minimum-size solutions to 3-, 4- and 5-parity are found. The solutions thus found are furthermore easily interpretable. When combined with diversity maintenance, EMOO can provide an adequate and parameterless approach to size control in variable length evolution.

The Incremental Pareto-Coevolution Archive

Coevolution can in principle provide progress for problems where no accurate evaluation function is available. An important open question however is how coevolution can be set up such that progress can be ensured. Previous work has provided progress guarantees either for limited cases or using strict acceptance conditions that can result in stalling. We present a monotonically improving archive for the gen- eral asymmetric case of coevolution where learners and tests may be of distinct types, for which any detectable improvement can be accepted into the archive. The Incremental Pareto-Coevolution Archive is demon- strated in experiments.

A Monotonic Archive for Pareto-Coevolution

Coevolution has already produced promising results, but its dynamic evaluation can lead to a variety of problems that preventmost algorithms from progressing monotonically. An important open question therefore is how progress towards a chosen solution concept can be achieved. A general solution concept for coevolution is obtained by viewing opponents or tests as objectives. In this setup known as Pareto-coevolution, the desired solution is the Pareto-optimal set. We present an archive that guarantees monotonicity for this solution concept. The algorithm is called the Incremental Pareto-Coevolution Archive (IPCA), and is based on Evolutionary Multi-Objective Optimization (EMOO). By virtue of its monotonicity, IPCA avoids regress even when combined with a highly explorative generator. This capacity is demonstrated on a challenging test problem requiring both exploration and reliability. IPCA maintains a highly specific selection of tests, but the size of the test archive nonetheless grows unboundedly. We therefore furthermore investigate how archive sizes may be limited while still providing approximate reliability. The LAyered Pareto-Coevolution Archive (LAPCA) maintains a limited number of layers of candidate solutions and tests, and thereby permits a trade-off between archive size and reliability. The algorithm is compared in experiments, and found to be more efficient than IPCA. The work demonstrates how the approximation of amonotonic algorithm can lead to algorithms that are sufficiently reliable in practice while offering better efficiency.

The MaxSolve algorithm for coevolution

Coevolution can be used to adaptively choose the tests used for evaluating candidate solutions. A long-standing question is how this dynamic setup may be organized to yield reliable search methods. Reliability can only be considered in connection with a particular solution concept specifying what constitutes a solution. Recently, monotonic coevolution algorithms have been proposed for several solution concepts. Here, we introduce a new algorithm that guarantees monotonicity for the solution concept of maximizing the expected utility of a candidate solution. The method, called MaxSolve, is compared to the IPCA algorithm and found to perform more efficiently for a range of parameter values on an abstract test problem.

Automated Extraction of Problem Structure

Most problems studied in artificial intelligence possess some form of structure, but a precise way to define such structure is so far lacking. We investigate how the notion of problem structure can be made precise, and propose a formal definition of problem structure. The definition is applicable to problems in which the quality of candidate solutions is evaluated by means of a series of tests. This specifies a wide range of problems: tests can be examples in classification, test sequences for a sorting network, or opponents for board games. Based on our definition of problem structure, we provide an automatic procedure for problem structure extraction, and results of proof-of-concept experiments. The definition of problem structure assigns a precise meaning to the notion of the underlying objectives of a problem, a concept which has been used to explain how one can evaluate individuals in a coevolutionary setting. The ability to analyze and represent problem structure may yield new insight into existing problems, and benefit the design of algorithms for learning and search.

On the complexity of hierarchical problem solving

Competent Genetic Algorithms can efficiently address problems in which the linkage between variables is limited to a small order k. Problems with higher order dependencies can only be addressed efficiently if further problem properties exist that can be exploited. An important class of problems for which this occurs is that of hierarchical problems. Hierarchical problems can contain dependencies between all variables (k=n) while being solvable in polynomial time.An open question so far is what precise properties a hierarchical problem must possess in order to be solvable efficiently. We study this question by investigating several features of hierarchical problems and determining their effect on computational complexity, both analytically and empirically. The analyses are based on the Hierarchical Genetic Algorithm (HGA), which is developed as part of this work. The HGA is tested on ranges of hierarchical problems, produced by a generator for hierarchical problems.

Combining gradient techniques for numerical multi-objective evolutionary optimization

Recently, gradient techniques for solving numerical multi-objective optimization problems have appeared in the literature. Although promising results have already been obtained when combined with multi-objective evolutionary algorithms (MOEAs), an important question remains: what is the best way to integrate the use of gradient techniques in the evolutionary cycle of a MOEA. In this paper, we present an adaptive resource-allocation scheme that uses three gradient techniques in addition to the variation operator in a MOEA. During optimization, the effectivity of the gradient techniques is monitored and the available computational resources are redistributed to allow the (currently) most effective operator to spend the most resources. In addition, we indicate how the multi-objective search can be stimulated to also search