Heuristic methods for evolutionary computation techniques

Evolutionary computation techniques, which are based on a powerful principle of evolution—survival of the fittest, constitute an interesting category of heuristic search. In other words, evolutionary techniques are stochastic algorithms whose search methods model some natural phenomena: genetic inheritance and Darwinian strife for survival.Any evolutionary algorithm applied to a particular problem must address the issue of genetic representation of solutions to the problem and genetic operators that would alter the genetic composition of offspring during the reproduction process. However, additional heuristics should be incorporated in the algorithm as well; some of these heuristic rules provide guidelines for evaluating (feasible and infeasible) individuals in the population. This paper surveys such heuristics and discusses their merits and drawbacks.An abridged version of this paper appears in the volume entitled META-HEURISTICS: Theory & Application, edited by Ibrahim H. Osman and James P. Kelly, to be published by Kluwer Academic Publishers in March 1996.     

Core molecular orbital contribution to N2O isomerization as studied using theoretical electron momentum spectroscopy

Core molecular orbital contribution to the electronic structure of N2O isomers has been studied using quantum mechanical density functional theory combined with a plane wave impulse approximation method. Momentum distributions of wave functions for inner shell molecular orbitals of the linear NNO, cyclic and linear NON isomers of N2O are calculated through the (e, 2e) differential cross sections in momentum space. This is possible because this momentum distribution is directly proportional to the modulus squared of the momentum space wave function for the molecular orbital in question. While the momentum distributions of the NNO and cyclic N2O isomers demonstrate strong atomic orbital characteristics in their core space, the outer core molecular orbitals of the linear NON isomer exhibit configuration interactions between them and the valence molecular orbitals. It is suggested that the frozen core approximation breaks down in the prediction of the electronic structure of such an isomer. Core molecular orbital contributions to the electronic structure can alter the order of total energies of the isomers and lead to incorrect conclusions of the stability among the isomers. As a result, full electron calculations should be employed in the study of N2O isomerization.     

An analysis of the velocity updating rule of the particle swarm optimization algorithm

The particle swarm optimization algorithm includes three vectors associated with each particle: inertia, personal, and social influence vectors. The personal and social influence vectors are typically multiplied by random diagonal matrices (often referred to as random vectors) resulting in changes in their lengths and directions. This multiplication, in turn, influences the variation of the particles in the swarm. In this paper we examine several issues associated with the multiplication of personal and social influence vectors by such random matrices, these include: (1) Uncontrollable changes in the length and direction of these vectors resulting in delay in convergence or attraction to locations far from quality solutions in some situations (2) Weak direction alternation for the vectors that are aligned closely to coordinate axes resulting in preventing the swarm from further improvement in some situations, and (3) limitation in particle movement to one orthant resulting in premature convergence in some situations. To overcome these issues, we use randomly generated rotation matrices (rather than the random diagonal matrices) in the velocity updating rule of the particle swarm optimizer. This approach makes it possible to control the impact of the random components (i.e. the random matrices) on the direction and length of personal and social influence vectors separately. As a result, all the above mentioned issues are effectively addressed. We propose to use the Euclidean rotation matrices for rotation because it preserves the length of the vectors during rotation, which makes it easier to control the effects of the randomness on the direction and length of vectors. The direction of the Euclidean matrices is generated randomly by a normal distribution. The mean and variance of the distribution are investigated in detail for different algorithms and different numbers of dimensions. Also, an adaptive approach for the variance of the normal distribution is proposed which is independent from the algorithm and the number of dimensions. The method is adjoined to several particle swarm optimization variants. It is tested on 18 standard optimization benchmark functions in 10, 30 and 60 dimensional spaces. Experimental results show that the proposed method can significantly improve the performance of several types of particle swarm optimization algorithms in terms of convergence speed and solution quality.     

The use of genetic algorithms to solve the economic lot size scheduling problem

The purpose of this paper is to investigate the use genetic algorithms (GAs) for solving the Economic Lot Size Scheduling Problem (ELSP). The ELSP is formulated using the Basic Period (BP) approach which results in a problem having one continuous decision variable and a number of integer decision variables equal to the number of products being produced. This formulation is ideally suited for using GAs. The GA is tested on Bomberger's classical problem. The resulting solutions were better than those obtained using an iterative dynamic programming (DP) approach. The total cost of GA solutions to the problem with utilization up to 65% were within 3.4% of the lower bound. The GA also performed well for higher utilization yielding solutions within 13.87% of the lower bound for utilization up to 86%. The GA was tested on a 30-item problem and good solutions were obtained. The results of the GA under different binary representations, crossover methods, and initialization methods are compared to identify the best settings. The results indicate that for this particular problem, binary representation works better than Gray coding, 2-point crossover is best, and an infeasible starting population is better than feasible.