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Low Discrepancy Initialized Particle Swarm Optimization for Solving Constrained Optimization Problems

Pant M., Thangaraj R., Abraham A.

Fundamenta Informaticae

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2009

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Vol. 95, nr 4

511-531

EN

Population based metaheuristics are commonly used for global optimization problems. These techniques depend largely on the generation of initial population. A good initial population may not only result in a better fitness function value but may also help in faster convergence. Although these techniques have been popular since more than three decades very little research has been done on the initialization of the population. In this paper, we propose a modified Particle Swarm Optimization (PSO) called Improved Constraint Particle Swarm Optimization (ICPSO) algorithm for solving constrained optimization. The proposed ICPSO algorithm is initialized using quasi random Vander Corput sequence and differs from unconstrained PSO algorithm in the phase of updating the position vectors and sorting every generation solutions. The performance of ICPSO algorithm is validated on eighteen constrained benchmark problems. The numerical results show that the proposed algorithm is a quite promising for solving constraint optimization problems.

2

An Improved Harmony Search Algorithm with Differential Mutation Operator

Chakraborty P., Roy G.G., Das S., Jain D., Abraham A.

Fundamenta Informaticae

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2009

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Vol. 95, nr 4

401-426

EN

Harmony Search (HS) is a recently developed stochastic algorithm which imitates the music improvisation process. In this process, the musicians improvise their instrument pitches searching for the perfect state of harmony. Practical experiences, however, suggest that the algorithm suffers from the problems of slow and/or premature convergence over multimodal and rough fitness landscapes. This paper presents an attempt to improve the search performance of HS by hybridizing it with Differential Evolution (DE) algorithm. The performance of the resulting hybrid algorithm has been compared with classical HS, the global best HS, and a very popular variant of DE over a test-suite of six well known benchmark functions and one interesting practical optimization problem. The comparison is based on the following performance indices - (i) accuracy of final result, (ii) computational speed, and (iii) frequency of hitting the optima.

3

A Multi-swarm Approach to Multi-objective Flexible Job-shop Scheduling Problems

Liu H., Abraham A., Wang Z.

Fundamenta Informaticae

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2009

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Vol. 95, nr 4

465-489

EN

Swarm Intelligence (SI) is an innovative distributed intelligent paradigm whereby the collective behaviors of unsophisticated individuals interacting locally with their environment cause coherent functional global patterns to emerge. In this paper, we model the scheduling problem for the multi-objective Flexible Job-shop Scheduling Problems (FJSP) and attempt to formulate and solve the problem using a Multi Particle Swarm Optimization (MPSO) approach. MPSO consists of multi-swarms of particles, which searches for the operation order update and machine selection. All the swarms search the optima synergistically and maintain the balance between diversity of particles and search space. We theoretically prove that the multi-swarm synergetic optimization algorithm converges with a probability of 1 towards the global optima. The details of the implementation for the multi-objective FJSP and the corresponding computational experiments are reported. The results indicate that the proposed algorithm is an efficient approach for the multi-objective FJSP, especially for large scale problems.

4

A very simple approach for 3-D to 2-D mapping

Dey S., Abraham A., Sanyal S.

Image Processing & Communications

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2006

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Vol. 11, no 2

75-82

EN

Many times we need to plot 3-D functions e.g., in many scientific experiments. To plot this 3-D functions on 2-D screen it requires some kind of mapping. Though OpenGL, DirectX etc 3-D rendering libraries have made this job very simple, still these libraries come with many complex pre-operations that are simply not intended, also to integrate these libraries with any kind of system is often a tough trial. This article presents a very simple method of mapping from 3-D to 2-D, that is free from any complex pre-operation, also it will work with any graphics system where we have some primitive 2-D graphics function. Also we discuss the inverse transform and how to do basic computer graphics transformations using our coordinate mapping system.