A Collection of Challenging Optimization Problems in Science, Engineering and Economics

Function optimization and finding simultaneous solutions of a system of nonlinear equations (SNE) are two closely related and important optimization problems. However, unlike in the case of function optimization in which one is required to find the global minimum and sometimes local minima, a database of challenging SNEs where one is required to find stationary points (extrama and saddle points) is not readily available. In this article, we initiate building such a database of important SNE (which also includes related function optimization problems), arising from Science, Engineering and Economics. After providing a short review of the most commonly used mathematical and computational approaches to find solutions of such systems, we provide a preliminary list of challenging problems by writing the Mathematical formulation down, briefly explaning the origin and importance of the problem and giving a short account on the currently known results, for each of the problems. We anticipate that this database will not only help benchmarking novel numerical methods for solving SNEs and function optimization problems but also will help advancing the corresponding research areas.Comment: Accepted as an invited contribution to the special session on Evolutionary Computation for Nonlinear Equation Systems at the 2015 IEEE Congress on Evolutionary Computation (at Sendai International Center, Sendai, Japan, from 25th to 28th May, 2015.

Approximating Pareto frontier using a hybrid line search approach

This is the post-print version of the final paper published in Information Sciences. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.The aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach. But it is well known that this technique sometimes fail in different aspects for determining the Pareto frontier. This paper proposes a new approach for multicriteria optimization, which aggregates the objective functions and uses a line search method in order to locate an approximate efficient point. Once the first Pareto solution is obtained, a simplified version of the former one is used in the context of Pareto dominance to obtain a set of efficient points, which will assure a thorough distribution of solutions on the Pareto frontier. In the current form, the proposed technique is well suitable for problems having multiple objectives (it is not limited to bi-objective problems) and require the functions to be continuous twice differentiable. In order to assess the effectiveness of this approach, some experiments were performed and compared with two recent well known population-based metaheuristics namely ParEGO and NSGA II. When compared to ParEGO and NSGA II, the proposed approach not only assures a better convergence to the Pareto frontier but also illustrates a good distribution of solutions. From a computational point of view, both stages of the line search converge within a short time (average about 150 ms for the first stage and about 20 ms for the second stage). Apart from this, the proposed technique is very simple, easy to implement and use to solve multiobjective problems.CNCSIS IDEI 2412, Romani

Meta-QSAR: a large-scale application of meta-learning to drug design and discovery.

We investigate the learning of quantitative structure activity relationships (QSARs) as a case-study of meta-learning. This application area is of the highest societal importance, as it is a key step in the development of new medicines. The standard QSAR learning problem is: given a target (usually a protein) and a set of chemical compounds (small molecules) with associated bioactivities (e.g. inhibition of the target), learn a predictive mapping from molecular representation to activity. Although almost every type of machine learning method has been applied to QSAR learning there is no agreed single best way of learning QSARs, and therefore the problem area is well-suited to meta-learning. We first carried out the most comprehensive ever comparison of machine learning methods for QSAR learning: 18 regression methods, 3 molecular representations, applied to more than 2700 QSAR problems. (These results have been made publicly available on OpenML and represent a valuable resource for testing novel meta-learning methods.) We then investigated the utility of algorithm selection for QSAR problems. We found that this meta-learning approach outperformed the best individual QSAR learning method (random forests using a molecular fingerprint representation) by up to 13%, on average. We conclude that meta-learning outperforms base-learning methods for QSAR learning, and as this investigation is one of the most extensive ever comparisons of base and meta-learning methods ever made, it provides evidence for the general effectiveness of meta-learning over base-learning

Computational models for inferring biochemical networks

Biochemical networks are of great practical importance. The interaction of biological compounds in cells has been enforced to a proper understanding by the numerous bioinformatics projects, which contributed to a vast amount of biological information. The construction of biochemical systems (systems of chemical reactions), which include both topology and kinetic constants of the chemical reactions, is NP-hard and is a well-studied system biology problem. In this paper, we propose a hybrid architecture, which combines genetic programming and simulated annealing in order to generate and optimize both the topology (the network) and the reaction rates of a biochemical system. Simulations and analysis of an artificial model and three real models (two models and the noisy version of one of them) show promising results for the proposed method.The Romanian National Authority for Scientific Research, CNDI–UEFISCDI, Project No. PN-II-PT-PCCA-2011-3.2-0917

Feature Selection via Chaotic Antlion Optimization

Selecting a subset of relevant properties from a large set of features that describe a dataset is a challenging machine learning task. In biology, for instance, the advances in the available technologies enable the generation of a very large number of biomarkers that describe the data. Choosing the more informative markers along with performing a high-accuracy classification over the data can be a daunting task, particularly if the data are high dimensional. An often adopted approach is to formulate the feature selection problem as a biobjective optimization problem, with the aim of maximizing the performance of the data analysis model (the quality of the data training fitting) while minimizing the number of features used.This work was partially supported by the IPROCOM Marie Curie initial training network, funded through the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA grants agreement No. 316555, and by the Romanian National Authority for Scientific Research, CNDIUEFISCDI, project number PN-II-PT-PCCA-2011-3.2- 0917. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Solving Nonlinear Equation Systems Using Evolutionary Algorithms ABSTRACT

This paper proposes a new perspective for solving systems of nonlinear equations. A system of equations can be viewed as a multiobjective optimization problem: every equation represents an objective function whose goal is to minimize difference between the right and left term of the corresponding equation in the system. We used an evolutionary computation technique to solve the problem obtained by transforming the system of nonlinear equations into a multiobjective problem. Results obtained are compared with a very new technique [10] and also some standard techniques used for solving nonlinear equation systems. Empirical results illustrate that the proposed method is efficient. 1

Automatic Programming Methodologies for Electronic Hardware Fault Monitoring

Abstract: This paper presents three variants of Genetic Programming (GP) approaches for intelligent online performance monitoring of electronic circuits and systems. Reliability modeling of electronic circuits can be best performed by the stressor – susceptibility interaction model. A circuit or a system is considered to be failed once the stressor has exceeded the susceptibility limits. For on-line prediction, validated stressor vectors may be obtained by direct measurements or sensors, which after pre-processing and standardization are fed into the GP models. Empirical results are compared with artificial neural networks trained using backpropagation algorithm and classification and regression trees. The performance of the proposed method is evaluated by comparing the experiment results with the actual failure model values. The developed model reveals that GP could play an important role for future fault monitoring systems