Spider monkey optimization (SMO) algorithm, which simulates the food searching behavior of a swarm of spider monkeys, is a new addition to the class of swarm intelligent techniques for solving unconstrained optimization problems. The purpose of this article is to study the performance of SMO after incorporating quadratic approximation (QA) operator in it. The proposed version is named as QA-based spider monkey optimization (QASMO). An experimental study has been carried out to check the validity and applicability of QASMO. For validation purpose, the performance of QASMO is tested over a benchmark set of 46 scalable and nonscalable problems, and results are compared with the original SMO algorithm. In order to test the applicability of the proposed algorithm in solving real-life optimization problems, one of the most challenging optimization problems, namely, Lennard-Jones (LJ) problem is considered. LJ clusters containing atoms from three to ten have been taken into consideration, and results are presented. To the best of our knowledge, this is the first attempt to apply SMO and its proposed variant on a real-life problem. The results demonstrate that incorporation of QA in SMO has positive effects on its performance in terms of reliability, efficiency, and accuracy.
NOMENCLATUREN swarm size D no. of dimensions U.a; b/ uniformly generated random number between a and b NG number of groups in the current swarm MG maximum number of groups allowed in the swarm Pr perturbation rate GS [k] number of members in the kth group G[k] [0] index of the first member of the kth group in the swarm G[k] [1] index of the last member of the kth group in the swarm SM i position vector of the ith spider monkey in the swarm SM new a trial vector for creating a new position of a spider monkey SM newlocal a trial vector for creating a new position of a spider monkey in local leader phase SM newglobal a trial vector for creating a new position of a spider monkey in global leader phase SM r position vector of randomly selected member of the group SM worstglobal position vector of worst member of the swarm in global leader learning phase SM worstlocal position vector of worst member of a group in local leader learning phase
The present paper discusses enhanced flow in a capacitated indefinite
quadratic transportation problem. Sometimes, situations arise where either
reserve stocks have to be kept at the supply points say, for emergencies, or
there may be extra demand in the markets. In such situations, the total flow
needs to be controlled or enhanced. In this paper, a special class of
transportation problems is studied, where the total transportation flow is
enhanced to a known specified level. A related indefinite quadratic
transportation problem is formulated, and it is shown that to each basic
feasible solution called corner feasible solution to related transportation
problem, there is a corresponding feasible solution to this enhanced flow
problem. The optimal solution to enhanced flow problem may be obtained from
the optimal solution to the related transportation problem. An algorithm is
presented to solve a capacitated indefinite quadratic transportation problem
with enhanced flow. Numerical illustrations are also included in support of
the theory. Computational software GAMS is also used.
Multi-choice programming problems arise due to diverse needs of people. In this paper, multi-choice optimisation is applied to bilevel transportation problem. This problem deals with transportation at both the levels, upper as well as lower. There are multiple choices for demand and supply parameters. The multi-choice parameters at the respective levels are converted into polynomials which transmute the defined problem into a mixed integer programming problem. The objective of the paper is to determine a solution methodology for the transformed problem. The significance of the formulated model is exhibited through an example by applying it to a hotel industry. The fuzzy programing approach is employed to obtain the satisfactory solution for the decision makers at the two levels. A comparative analysis is presented in the paper by solving bilevel multi-choice transportation problem with goal programming mode as well as by the linear transformation technique proposed in the paper by Khalil et al. The example is solved using computing software.
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