Real coded clonal selection algorithm for unconstrained global optimization using a hybrid inversely proportional hypermutation operator

Abstract

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...

Enhancing the learning capacity of immunological algorithms: a comprehensive study of learning operators

“…In order to evaluate the performance of the proposed L sd learning operator, it is validated using some well-known benchmark numerical optimization problems obtained from the literatures (Yao et al, 1999;Cutello et al, 2006;Gong et al, 2010). Table 1 lists the details of the benchmark functions.…”

“…1, we can notice that the learning mechanisms used in (1)-(6) on the antibody Ab only utilize random perturbation on the antibody itself, while those in (7)- (8) make use of information in the environment. As reported in (Cutello et al, 2006;Gong et al, 2010), learning from the environment provides an encouraging alternative method, probably a more easy way to achieve better search performance. In details, the mechanism in (7) uses the information of a randomly selected antibodies in the population to Artificial Immune Systems -ICARIS guide the current search.…”

“…• Inversely proportional hypermutation L h3 (Cutello et al, 2004(Cutello et al, , 2005(Cutello et al, , 2006: the number of mutations is inversely proportional to the normalized affinity value, i.e., the higher affinity of an antibody, the less times of mutations will be carried out on it. It is reasonable to make such an inverse choice, since better antibodies usually contain more useful information for evolution.…”

“…• Lateral interaction mutation L li (Cutello et al, 2006;Pavone et al, 2011): in addition to hypermutation and receptor editing, the lateral interaction during different antibodies also takes place according to the idiotypic network theory (Gao et al, 2008). In other words, each paratope on an antibody can not only recognize a foreign antigen, but also can be recognized by external idiotopes.…”

New coupled EM and circuit simulation flow for integrated spiral inductor by introducing symbolic simplified expressions

“…The efficiency of the optimization algorithm is thus fundamental for the success of the simulation flow. In our research work five different optimization methods, both deterministic (POWELL [6], [7] and DIRECT [8]) and stochastic (CRS [9], CRS ENHANCED [10], OPTIA [11], [12]) have been tested, in combination with symbolic analysis and simplification techniques, for the fitting of inductor Y parameters. Symbolic analysis and simplification techniques have been introduced in an industrial flow [13] in order to reduce the running time necessary to evaluate the inductor model.…”