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The protein structure prediction (PSP) problem is concerned with the prediction of the folded, native, tertiary structure of a protein given its sequence of amino acids. It is a challenging and computationally open problem, as proven by the numerous methodological attempts and the research effort applied to it in the last few years. The potential energy functions used in the literature to evaluate the conformation of a protein are based on the calculations of two different interaction energies: local (bond atoms) and non-local (non-bond atoms). In this paper, we show experimentally that those types of interactions are in conflict, and do so by using the potential energy function Chemistry at HARvard Macromolecular Mechanics. A multi-objective formulation of the PSP problem is introduced and its applicability studied. We use a multi-objective evolutionary algorithm as a search procedure for exploring the conformational space of the PSP problem.

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Numerical optimization of given objective functions is a crucial task in many real-life problems. This paper introduces a new immunological algorithm for continuous global optimization problems, called opt-IMMALG; it is an improved version of a previously proposed clonal selection algorithm, using a real-code representation and a new Inversely Proportional Hypermutation operator.We evaluate and assess the performance of opt-IMMALG and several others algorithms, namely opt-IA, PSO, arPSO, DE, and SEA with respect to their general applicability as numerical optimization algorithms. The experiments have been performed on 23 widely used benchmark problems.The experimental results show that opt-IMMALG is a suitable numerical optimization technique that, in terms of accuracy, outperforms the analyzed algorithms in this comparative study. In addition it is shown that opt-IMMALG is also suitable for solving large-scale problems. Categories and Subject Descriptors General TermsAlgorithms. KeywordsArtificial Immune Systems, Immune Algorithms, Clonal Selection Algorithms, Hypermutation Operator, Aging Operator, Global Optimization. CLONAL SELECTION ALGORITHMPermission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Clonal Selection Algorithms are a special class of Immune algorithms (IA) which are inspired by the Clonal Selection Principle [1] to produce effective mechanisms for search and optimization [2,3]. In this paper we present an improved version of the immune algorithm, proposed in [4], which is inspired by the clonal selection principle, and use it for unconstrained global numerical optimization. We call this new algorithm opt-IMMALG (optimization IMMune ALG).The algorithm is population based, like any typical evolutionary algorithm. Each individual of the population is a candidate solution belonging to the fitness landscape of a given computational problem. Using the cloning operator, an immune algorithm produces individuals with higher affinities (higher fitness function values), introducing blind perturbation (by means of a hypermutation operator) and selecting their improved mature progenies. opt-IMMALG considers only two entities: antigens (Ag's) and B cells. The Ags are the problem to tackle or the function to optimize, whereas the B cells (or B cell receptors in immunological terminology), are the candidate solutions that have solved/approximated the problem, i.e. a population of points of the search space. At each time step t, we have a population P (t) of size d. The initial population of candidate solutions at time t = 0 is randomly generated using uniform distribution in the relative domains of each function. All genes of each B cell receptor x = (x...