Repel the swarm to the optimum!

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Abstract

We improve the particle swarm optimization (PSO) by introducing the concept of the repellor. So far, the PSO algorithm is guided by the optimum of each particle and the optimum found by all the particles. We now add to the algorithm the location of the worst point found so far and location the worst point found by all the particles. These worst points have the property of repelling the particles to the local and the global optima, respectively. This way the PSO algorithm is improved in the sense that the swarm is able to locate the global optimum more rapidly. Empirical results are presented on archaeological data.

Introduction

The particle swarm optimization (PSO) is a recently introduced [1] optimization algorithm. At the same time is one of the most promising optimization algorithms with applications to many different fields of science and engineering (e.g. [2], [3], [4]). The main concept of the PSO is to mimic the behavior of a swarm (i.e. zero-dimensional particles) which search for food resources (i.e. the function minimum) on a field (i.e. the search space).

Even each member of the swarm bears minimal intelligence, the swarm as a whole shows a good amount of intelligence as if the intelligence of each member is added up. The PSO algorithm mimics this type of behavior. The search of each particle is guided by the minimum it has been found through its historical record of flights (i.e. iterations of the algorithm) and is also guided by the historical record of the flights of the whole swarm. These minima act as attractors for each particle. In this letter we improve the search by helping the swarm avoid the regions where the worst results were found.

The structure of this letter is the following. In Section 2 we introduce the concept of repellor. Section 3 presents empirical applications of the PSO algorithm applied on archaeological data. Finally, Section 4 concludes this work and proposes further developments.

Section snippets

The concept of the repellor

Imagine a swarm of bees searching for flowers on a field. They initially start at random locations. Through their memory they remember the location of the best flower they have found so far. An inherit form of communication they bear, helps them know where the best flower of the field is located. There are 2 equations that can describe this form of behavior.xi,d=xi-1,d+vi,d,vi,d=c1rand()(pd-xi,d)+c2rand()(Pd-xi,d),where xi is an m-dimensional vector (particle), d = 1, 2,  , m, i is the number of

Empirical application on archaeological data

An archaeological deposit may contain particles (artifacts and non-artifacts) of numerous materials and size classes derived from various sources. The particles and their arrangement typically reflect a complex depositional history of natural and cultural processes. The size distributions of these various materials can offer insights into their complex depositional histories, including their sources and transport agents and post-depositional processes [6]. However, complete analysis of an

Multiple repellors

As a possible extension of the repellor add-on about the PSO algorithm is to theorize multiple repellors. Large problems with a greater number of dimensions, may be very difficult (or even impossible) to be solved by few flights. Since none is able to guarantee that the initially distributed particles can easily locate the global minimum within 100 or even 1000 flights, the concept of the repellor may help on this problem.

In order to utilize the concept of the multiple repellors we may first

Conclusions

This study has revealed that the PSO algorithm can be considerably improved with a small computational cost. It introduced the concept of the repellor which acts complementary to the concept of the attractor used so far. A justification regarding observations of natural swarms was also provided.

This concept has to be tested further in future applications. Our experience has shown that this new concept can be considered as an essential part of the PSO algorithm. Further improvements can also be

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