International Journal of Computing Science and Mathematics http://www.inderscience.com/browse/index.php?journalID=224&year=2010&vol=3&issue=3 Inderscience Publishers Ltd en-uk International Journal of Computing Science and Mathematics 1752-5055 1752-5063 © 2010 Inderscience Publishers Ltd editor@inderscience.com https://www.inderscience.com/images/files/coverImgs/ijcsm_scoverijcsm.jpg http://www.inderscience.com/browse/index.php?journalID=224&year=2010&vol=3&issue=3 http://www.inderscience.com/link.php?id=37444 This paper introduces a paradigm for the resolution of a particular class of games (K) within Game Theory and develops mathematical methods for the analysis of conflicting situations in which the contenders share a finite series of measurable information. Classical equilibria schemes do not contemplate the presence of a symmetric and incomplete perturbative element in the games, leaving out a study case of enormous interest. The main result is the demonstration of the existence of the temporised equilibrium for every K-game and, in particular, the solution properties in symmetric games, with references to the geometrical structure of the proposed argumentation. Temporised equilibria: a rational concept of fairness into game theory
Riccardo Alberti
International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 196 - 210
This paper introduces a paradigm for the resolution of a particular class of games (K) within Game Theory and develops mathematical methods for the analysis of conflicting situations in which the contenders share a finite series of measurable information. Classical equilibria schemes do not contemplate the presence of a symmetric and incomplete perturbative element in the games, leaving out a study case of enormous interest. The main result is the demonstration of the existence of the temporised equilibrium for every K-game and, in particular, the solution properties in symmetric games, with references to the geometrical structure of the proposed argumentation.

]]> 10.1504/IJCSM.2010.037444 International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 196 - 210 Riccardo Alberti Itatel S.p.a., Via Reiss Romoli – Localita Castelletto, 20019 Settimo Milanese (MI), Italy temporised equilibria fairness game theory K-game judge deterrent mathematics scalar parametric function Nash equilibria prisoner's dilemma non-zero-sum games mobile ad-hoc networks MANETs mobile networks symmetric games. 2010-12-13T23:20:50-05:00 3 3 196 210 2010-12-13T23:20:50-05:00 http://www.inderscience.com/link.php?id=37445 In this paper, an algorithm is proposed to solve a tri-level integer programming problem in which the objective function for the first level is an indefinite quadratic, the second one is linear and the third one is linear fractional. The feasible space of the decision variable is reduced at each level until a satisfactory point is obtained at the last level. The higher level decision-maker reduces the feasible space for the lower level decision maker to search for his optimum. A satisfactory solution of the bilevel decentralised programming problem can also be obtained by the method proposed above. This method is illustrated with the help of examples. An algorithm for non-linear multi-level integer programming problems
Ritu Arora, S.R. Arora
International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 211 - 225
In this paper, an algorithm is proposed to solve a tri-level integer programming problem in which the objective function for the first level is an indefinite quadratic, the second one is linear and the third one is linear fractional. The feasible space of the decision variable is reduced at each level until a satisfactory point is obtained at the last level. The higher level decision-maker reduces the feasible space for the lower level decision maker to search for his optimum. A satisfactory solution of the bilevel decentralised programming problem can also be obtained by the method proposed above. This method is illustrated with the help of examples.

]]> 10.1504/IJCSM.2010.037445 International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 211 - 225 Ritu Arora S.R. Arora Department of Mathematics, Keshav Mahavidyalaya, University of Delhi, India. ' Department of Mathematics, Hans Raj College, University of Delhi, India multi-level programming indefinite quadratic programming fractional programming integer programming satisfactory solutions nonlinear programming. 2010-12-13T23:20:50-05:00 3 3 211 225 2010-12-13T23:20:50-05:00 http://www.inderscience.com/link.php?id=37446 Stochastic programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are captured by scenario generation and so are crucial to the quality of solutions obtained. Presently there do not exist many literature reviews on scenario generation; this paper surveys them. We introduce the main concepts behind scenario generation, which are not just concerned with discretising methods. We review the main scenario generation classes and analyse the advantages and disadvantages. We also review new and less commonly known scenario generation methods, such as 'hybrid' methods. A review of scenario generation methods
Sovan Mitra, Nico Di Domenica
International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 226 - 244
Stochastic programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are captured by scenario generation and so are crucial to the quality of solutions obtained. Presently there do not exist many literature reviews on scenario generation; this paper surveys them. We introduce the main concepts behind scenario generation, which are not just concerned with discretising methods. We review the main scenario generation classes and analyse the advantages and disadvantages. We also review new and less commonly known scenario generation methods, such as 'hybrid' methods.

]]> 10.1504/IJCSM.2010.037446 International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 226 - 244 Sovan Mitra Nico Di Domenica Glasgow Caledonian University, Caledonian Business School, Cowcaddens Road, Glasgow, G4 0BA, Scotland, UK. ' Value Lab, Via Durini, Milano, Italy stochastic programming stochastic optimisation scenario generation scenarios decision making uncertainty. 2010-12-13T23:20:50-05:00 3 3 226 244 2010-12-13T23:20:50-05:00 http://www.inderscience.com/link.php?id=37447 The paper addresses the issues of parameter selection of a Particle Swarm Optimisation (PSO) algorithm by a thorough stability analysis of the swarm dynamics. The effectiveness of the work lies in considering the dynamic behaviour of the local best position of a given particle. The behaviour of an individual particle here is modelled as a closed loop control system, where the forward path describes the particle dynamics, and the feedback path adapts the local best position of the particle over the iterations of the algorithm. The stability analysis of the closed loop system is undertaken using Jury's test, and optimal parameter setting of the dynamics is performed by the root locus technique of the classical control theory. Parameter selection of a Particle Swarm Optimisation dynamics by closed loop stability analysis
Nayan R. Samal, Amit Konar, Swagatam Das, Atulya K. Nagar
International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 245 - 274
The paper addresses the issues of parameter selection of a Particle Swarm Optimisation (PSO) algorithm by a thorough stability analysis of the swarm dynamics. The effectiveness of the work lies in considering the dynamic behaviour of the local best position of a given particle. The behaviour of an individual particle here is modelled as a closed loop control system, where the forward path describes the particle dynamics, and the feedback path adapts the local best position of the particle over the iterations of the algorithm. The stability analysis of the closed loop system is undertaken using Jury's test, and optimal parameter setting of the dynamics is performed by the root locus technique of the classical control theory.

]]> 10.1504/IJCSM.2010.037447 International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 245 - 274 Nayan R. Samal Amit Konar Swagatam Das Atulya K. Nagar Department of Electronics and Telecommunication Engineering, Jadavpur University, Calcutta 32, India. ' Department of Electronics and Telecommunication Engineering, Jadavpur University, Calcutta 32, India. ' Department of Electronics and Telecommunication Engineering, Jadavpur University, Calcutta 32, India. ' Intelligence and Distributed Systems Lab, Department of Computer Science, Liverpool Hope University, Hope Park Liverpool, L16 9JD, UK PSO dynamics convergence Jury's test root locus dominant poles dominant roots particle swarm optimisation parameter selection stability analysis swarm dynamics closed loop control control theory. 2010-12-13T23:20:50-05:00 3 3 245 274 2010-12-13T23:20:50-05:00 http://www.inderscience.com/link.php?id=37448 In a competitive electric power market, the knowledge of Available Transfer Capability (ATC) can help power marketers, sellers and buyers in planning, operation and reserving transmission services. Capacity Benefit Margin (CBM) is an important factor in the calculation of ATC, without which ATC may be overestimated and this will lead to the risk of having generation unreliability. In this paper, a new algorithm using Differential Evolution along with Monte Carlo is proposed to evaluate CBM. The superiority of the proposed algorithm is tested on modified IEEE 30 bus system, over PSO. Computation of Capacity Benefit Margin using Differential Evolution
R. Rajathy, R. Gnanadass, K. Manivannan, Harish Kumar
International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 275 - 287
In a competitive electric power market, the knowledge of Available Transfer Capability (ATC) can help power marketers, sellers and buyers in planning, operation and reserving transmission services. Capacity Benefit Margin (CBM) is an important factor in the calculation of ATC, without which ATC may be overestimated and this will lead to the risk of having generation unreliability. In this paper, a new algorithm using Differential Evolution along with Monte Carlo is proposed to evaluate CBM. The superiority of the proposed algorithm is tested on modified IEEE 30 bus system, over PSO.

]]> 10.1504/IJCSM.2010.037448 International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 275 - 287 R. Rajathy R. Gnanadass K. Manivannan Harish Kumar Department of Electrical and Electronics Engineering, Pondicherry Engineering College, Puducherry – 605 014, India. ' Department of Electrical and Electronics Engineering, Pondicherry Engineering College, Puducherry – 605 014, India. ' Department of Electrical and Electronics Engineering, Pondicherry Engineering College, Puducherry – 605 014, India. ' Department of Physics, Pondicherry Engineering College, Puducherry – 605 014, India TTC total transfer capability differential evolution capacity benefit margin loss-of-load expected PSO particle swarm optimisation electric power markets electricity markets available transfer capability Monte Carlo simulation. 2010-12-13T23:20:50-05:00 3 3 275 287 2010-12-13T23:20:50-05:00 http://www.inderscience.com/link.php?id=37449 In this paper a class of first and second order differentiable generalised semi-E-invex functions are introduced. Duality results for a non-linear programming problem under second order generalised E-invexity are derived. Duality results using higher order generalised E-invex functions
Sangeeta Jaiswal, Geetanjali Panda
International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 288 - 297
In this paper a class of first and second order differentiable generalised semi-E-invex functions are introduced. Duality results for a non-linear programming problem under second order generalised E-invexity are derived.

]]> 10.1504/IJCSM.2010.037449 International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 288 - 297 Sangeeta Jaiswal Geetanjali Panda Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India. ' Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India E-invex set E-invex function semi-E-invex function duality results nonlinear programming. 2010-12-13T23:20:50-05:00 3 3 288 297 2010-12-13T23:20:50-05:00 http://www.inderscience.com/link.php?id=37450 Differential Evolution (DE) is a popular metaheuristics for global optimisation, but little research has been done on its initial population generation. The selection of the initial population is important, since it affects the search for several iterations and often has an influence on the final solution. In this study, quadratic interpolation is used in conjugation with pseudorandom numbers to generate initial population for DE. The proposed algorithm named Quadratic Interpolation DE (QIDE) is validated on a set of 20 benchmark problems. Numerical results show the competence of the proposed scheme in terms of convergence rate and average CPU time. Interpolated differential evolution for global optimisation problems
Musrrat Ali, Millie Pant, Atulya K. Nagar
International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 298 - 315
Differential Evolution (DE) is a popular metaheuristics for global optimisation, but little research has been done on its initial population generation. The selection of the initial population is important, since it affects the search for several iterations and often has an influence on the final solution. In this study, quadratic interpolation is used in conjugation with pseudorandom numbers to generate initial population for DE. The proposed algorithm named Quadratic Interpolation DE (QIDE) is validated on a set of 20 benchmark problems. Numerical results show the competence of the proposed scheme in terms of convergence rate and average CPU time.

]]> 10.1504/IJCSM.2010.037450 International Journal of Computing Science and Mathematics, Vol. 3, No. 3 (2010) pp. 298 - 315 Musrrat Ali Millie Pant Atulya K. Nagar Department of Paper Technology, Indian Institute of Technology Roorkee, Saharanpur campus, Uttrapradesh 247001, India. ' Department of Paper Technology, Indian Institute of Technology Roorkee, Saharanpur campus, Uttrapradesh 247001, India. ' Intelligence and Distributed Systems Lab, Department of Computer Science, Liverpool Hope University, Hope Park Liverpool, L16 9JD, UK metaheuristics differential evolution crossover initial population random numbers global optimisation quadratic interpolation. 2010-12-13T23:20:50-05:00 3 3 298 315 2010-12-13T23:20:50-05:00