# Population statistics for particle swarm optimization: Single-evaluation methods in noisy optimization problems

- 219 Downloads
- 9 Citations

## Abstract

Particle swarm optimization (PSO) is a metaheuristic whose quality of results deteriorates significantly in optimization problems subject to noise. The underlying reason to such a deterioration is that the effect of noise hinders the ability of particles to distinguish good from bad solutions, leading them to suffer from *deception*, *blindness* and *disorientation*. A deceived particle is not partially attracted to the true best solution in its neighborhood, a blinded particle misses an opportunity to improve upon its personal best solution, and a disoriented particle mistakenly prefers a worse solution. These conditions need to be addressed via noise mitigation mechanisms to prevent (or at least reduce) such a deterioration. Single-evaluation methods are the name by which we refer to PSO algorithms that address the effect of noise without performing additional function evaluations. The first of these algorithms was PSO with evaporation (PSO-E), which was proposed to reduce blindness in the swarms, and reports have suggested that it succeeds at finding better solutions than the regular PSO in different stochastic and dynamic optimization problems. However, PSO-E depends on an evaporation factor whose value is determined empirically, and the swarm is always at risk of exhibiting divergent behaviour. In this article, we propose a method to determine a priori the evaporation factor for PSO-E, and we also propose a new PSO with probabilistic updates (PSO-PU) to prevent the risk of divergence. Additionally, we take a different approach and develop a new PSO with average neighborhoods (PSO-AN) to blur the effect of noise and thereby reduce deception. Experiments on 20 large-scale benchmark functions subject to different levels of noise show that the regular PSO (lacking a noise mitigation mechanism) generally finds better solutions than PSO-E and PSO-PU because their approaches cause too much disorientation. However, PSO-AN finds better solutions than the regular PSO thanks to the improved quality of its neighborhood best solutions that partially attract the swarm towards better regions of the search space.

## Keywords

Particle swarm optimization Population statistics Noisy optimization problems Single-evaluation methods Evaporation mechanism## References

- Andradóttir S (1998) A review of simulation optimization techniques. In: Proceedings of the 2003 winter simulation conference, vol 1, pp 151–158Google Scholar
- April J, Glover F, Kelly J, Laguna M (2003) Practical introduction to simulation optimization. In: Proceedings of the 2003 winter simulation conference, vol 1, pp 71–78Google Scholar
- April J, Better M, Glover F, Kelly J, Laguna M (2006) Enhancing business process management with simulation optimization. In: Proceedings of the Winter Simulation Conference, pp 642–649Google Scholar
- Branke J (1999) Memory enhanced evolutionary algorithms for changing optimization problems. In: Proceedings of the 1999 congress on evolutionary computation, vol 3, pp 1875–1882Google Scholar
- Carlisle A, Dozier G (2002) Tracking changing extrema with adaptive particle swarm optimizer. In: Proceedings of the 5th biannual world automation congress, vol 13, pp 265–270Google Scholar
- Cui X, Potok TE (2007) Distributed adaptive particle swarm optimizer in dynamic environment. In: Proceedings of the IEEE international parallel and distributed processing symposium, pp 1–7Google Scholar
- Cui X, Hardin CT, Ragade RK, Potok TE, Elmaghraby AS (2005) Tracking non-stationary optimal solution by particle swarm optimizer. In: Proceedings of the 6th international conference on software engineering. Artificial intelligence, networking and parallel/distributed computing, pp 133–138Google Scholar
- Cui X, Charles JS, Potok TE (2009) A simple distributed particle swarm optimization for dynamic and noisy environments. In: Nature inspired cooperative strategies for optimization, studies in computational intelligence, vol 236. Springer, Berlin, pp 89–102Google Scholar
- Deng G (2007) Simulation-based optimization. PhD thesis, University of Wisconsin, MadisonGoogle Scholar
- Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the 6th international symposium on micro machine and human science, pp 39–43Google Scholar
- Eberhart RC, Shi Y (2001) Tracking and optimizing dynamic systems with particle swarms. In: Proceedings of the IEEE congress on evolutionary computation, pp 94–100Google Scholar
- Engelbrecht AP (2006) Fundamentals of computational swarm intelligence. Wiley, New YorkGoogle Scholar
- Fernandez-Marquez JL, Arcos JL (2009) An evaporation mechanism for dynamic and noisy multimodal optimization. In: Proceedings of the genetic and evolutionary computation conference, pp 17–24Google Scholar
- Fernandez-Marquez JL, Arcos JL (2010) Adapting particle swarm optimization in dynamic and noisy environments. In: Proceedings of the IEEE congress on evolutionary computation, pp 1–8Google Scholar
- Fu MC (2002) Optimization for simulation: theory vs. practice. INFORMS J Comput 14(3):192–215MathSciNetCrossRefGoogle Scholar
- Fu MC, Andradóttir S, II JSC, Glover F, Harrell CR, Ho YC, Kelly JP, Robinson SM (2000) Integrating optimization and simulation: research and practice. In: Proceedings of the winter simulation conference, pp 610–616Google Scholar
- Fu M, Glover F, April J (2005) Simulation optimization: a review, new developments, and applications. In: Proceedings of the winter simulation conference, pp 83–95Google Scholar
- Jin Y, Branke J (2005) Evolutionary optimization in uncertain environments—a survey. IEEE Trans Evol Comput 9(3):303–317CrossRefGoogle Scholar
- Mendes R (2004) Population topologies and their influence in particle swarm performance. PhD thesis, Universidade do Minho, PortugalGoogle Scholar
- Mendes R, Kennedy J, Neves J (2004) The fully informed particle swarm: simpler, maybe better. IEEE Trans Evol Comput 8(3):204–210CrossRefGoogle Scholar
- Morrison RW, De Jong KA (1999) A test problem generator for non-stationary environments. In: Proceedings of the 1999 congress on evolutionary computation, vol 3, pp 1875–1882Google Scholar
- Ólafsson S, Kim J (2002) Simulation optimization. In: Proceedings of the winter simulation conference, pp 79–84Google Scholar
- Pietro AD (2007) Optimising evolutionary strategies for problems with varying noise strength. PhD thesis, The University of Western AustraliaGoogle Scholar
- Poli R (2008) Analysis of the publications on the applications of particle swarm optimisation. J Artif Evol Appl 2008(4):1–10MathSciNetGoogle Scholar
- Pugh J, Martinoli A, Zhang Y (2005) Particle swarm optimization for unsupervised robotic learning. In: Proceedings of the IEEE swarm intelligence symposium, pp 92–99Google Scholar
- Rada-Vilela J, Zhang M, Seah W (2011) Random asynchronous PSO. In: Proceedings of the 5th international conference on automation, robotics and applications, pp 220–225Google Scholar
- Rada-Vilela J, Zhang M, Seah W (2012a) Evaporation mechanisms for particle swarm optimization. In: Proceedings of the international conference on simulated evolution and learning, pp 238–247Google Scholar
- Rada-Vilela J, Zhang M, Seah W (2012b) A performance study on the effects of noise and evaporation in particle swarm optimization. In: Proceedings of the IEEE congress on evolutionary computation, pp 873–880Google Scholar
- Rada-Vilela J, Johnston M, Zhang M (2014) Population statistics for particle swarm optimization: deception, blindness and disorientation in noisy problems. In: Technical report 14-01, Victoria University of Wellington. http://ecs.victoria.ac.nz/Main/TechnicalReportSeries
- Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: Proceedings of the IEEE world congress on computational intelligence, pp 69–73Google Scholar
- Syberfeldt A (2009) A multi-objective evolutionary approach to simulation-based optimisation of real-world problems. PhD thesis, De Montfort University, UKGoogle Scholar
- Tang K, Li X, Suganthan PN, Yang Z, Weise T (2009) Benchmark functions for the CEC’2010 special session and competition on large-scale global optimization. In: Technical report. Nature Inspired Computation and Applications Laboratory, USTC, ChinaGoogle Scholar
- van den Bergh F (2002) An analysis of particle swarm optimizers. PhD thesis, University of Pretoria, South AfricaGoogle Scholar