Using a geometric framework for the interpretation of crossover of recent introduction, we show an intimate connection between particle swarm optimisation (PSO) and evolutionary algorithms. This connection enables us to generalise PSO to virtually any solution representation in a natural and straightforward way. The new Geometric
PSO (GPSO) applies naturally to both continuous and combinatorial spaces. We demonstrate this for the cases of Euclidean, Manhattan and Hamming spaces and report extensive experimental results. We also demonstrate the applicability of GPSO to more challenging combinatorial spaces. The Sudoku puzzle is a perfect candidate to test new
algorithmic ideas because it is entertaining and instructive as well as being a nontrivial constrained combinatorial problem. We apply GPSO to solve the Sudoku puzzle.

Alberto  Moraglio

Cecilia  Di Chio

Julian  Togelius

Riccardo  Poli

Geometric Particle Swarm Optimization

Simplified forms of the particle swarm algorithm are very 
    beneficial in contributing to understanding how a particle 
    swarm optimization (PSO) swarm functions. One of these forms, 
    PSO with discrete recombination, is extended and analyzed, 
    demonstrating not just improvements in performance relative to 
    a standard PSO algorithm, but also significantly different 
    behavior, namely, a reduction in bursting patterns due to the 
    removal of stochastic components from the update 
    equations.

Dan  Bratton

Tim  Blackwell

A Simplified Recombinant PSO

Particle swarm optimisation (PSO) has been enormously successful. Within little more
than a decade hundreds of papers have reported successful applications of PSO. In fact, there
are so many of them, that it is difficult for PSO practitioners and researchers to have a clear
up-to-date vision of what has been done in the area of PSO applications. This brief paper
attempts to fill this gap, by categorising a large number of publications dealing with PSO
applications stored in the IEEE Xplore database at the time of writing.

Analysis of the Publications on the Applications of  Particle Swarm Optimisation

The tail of the particle swarm optimisation (PSO) position distribution at stagnation
is shown to be describable by a power law. This tail fattening is attributed to
particle bursting on all length scales. The origin of the power law is concluded to
lie in multiplicative randomness, previously encountered in the study of first-order
stochastic difference equations, and generalised here to second-order equations. It
is argued that recombinant PSO, a competitive PSO variant without multiplicative
randomness, does not experience tail fattening at stagnation.

Examination of Particle Tails

Characteristics of mobile ad hoc networks (MANETs) such as lack of central coordination, mobility of hosts, and limited availability of resources make quality of service (QoS) provisioning very challenging. Limited resource availability such as battery power and insecure medium is one of the major QoS issues to be dealt with. In this paper, we have proposed a new secure power-aware ant routing algorithm (SPA-ARA) for mobile ad hoc networks that is inspired from ant colony optimization (ACO) algorithms which are a swarm intelligent technique. In this algorithm, we have introduced a new metric, 
<em>next-hop availability</em>, which is a combination of two metrics. It maximizes path availability and minimizes travel time of packets, and therefore it offers a good balance between selection of fast paths and a better use of network resources. The protocol also incorporates a trust model which helps in detection of unauthorized and compromised nodes in MANETs.

Shabana  Mehfuz

M. N. Doja

Swarm Intelligent Power-Aware Detection of Unauthorized and Compromised Nodes in MANETs

Evolutionary algorithms (EAs) can be used in order to design particle swarm optimization (PSO) algorithms
that work, in some cases, considerably better than the human-designed ones. By analyzing the
evolutionary process of designing PSO algorithms, we can identify different swarm phenomena (such as patterns
or rules) that can give us deep insights about the swarm behavior. The rules that have been observed
can help us design better PSO algorithms for optimization. We investigate and analyze swarm phenomena
by looking into the process of evolving PSO algorithms. Several test problems have been analyzed in the
experiments and interesting facts can be inferred from the strategy evolution process (the particle quality
could influence the update order, some particles are updated more frequently than others, the initial swarm
size is not always optimal).

Laura  Dio&#x015F;an

Mihai  Oltean

What Else Is the Evolution of PSO Telling Us?

A dynamic system is represented as a set of equations that specify how variables
change over time. The equations in the system specify how to compute the
new values of the state variables as a function of their current values and the values
of the control parameters. If those parameters change beyond certain values,
the system exhibits qualitative changes in its behavior. Those qualitative changes
are called bifurcations, and the values for the parameters where those changes occur
are called bifurcation points. In this contribution, we present an application
of particle swarm optimization methods for dynamic environments for plotting bifurcation
diagrams used in the analysis of dynamical systems. The use of particle
swarm optimization methods presents various advantages over traditional methods.

Julio  Barrera

Juan J. Flores

Claudio  Fuerte-Esquivel

Generating Complete Bifurcation Diagrams Using a Dynamic Environment Particle Swarm Optimization Algorithm

Reservoir modeling is a critical step in the planning and development of oil fields. Before 
a reservoir model can be accepted for forecasting future production, the model has to be updated with 
historical production data. This process is called history matching. History matching requires computer flow 
simulation, which is very time-consuming. As a result, only a small number of simulation runs are conducted 
and the history-matching results are normally unsatisfactory. This is particularly evident when the reservoir
 has a long production history and the quality of production data is poor. The inadequacy of the history-matching
  results frequently leads to high uncertainty of production forecasting. To enhance the quality of the 
  history-matching results and improve the confidence of production forecasts, we introduce a methodology 
  using genetic programming (GP) to construct proxies for reservoir simulators. Acting as surrogates for the
   computer simulators, the &#8220;cheap&#8221; GP proxies can evaluate a large number (millions) of reservoir
    models within a very short time frame. With such a large sampling size, the reservoir history-matching results
     are more informative and the production forecasts are more reliable than those based on a small number of
      simulation models. We have developed a workflow which incorporates the two GP proxies into the history 
      matching and production forecast process. Additionally, we conducted a case study to demonstrate the 
      effectiveness of this approach. The study has revealed useful reservoir information and delivered more
       reliable production forecasts. All of these were accomplished without introducing new computer simulation
        runs.

Tina  Yu

Dave  Wilkinson

Alexandre  Castellini

Constructing Reservoir Flow Simulator Proxies Using Genetic Programming for History Matching and Production Forecast Uncertainty Analysis

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