Elsevier

Ecological Informatics

Volume 1, Issue 4, December 2006, Pages 355-366
Ecological Informatics

A novel numerical optimization algorithm inspired from weed colonization

https://doi.org/10.1016/j.ecoinf.2006.07.003Get rights and content

Abstract

This paper introduces a novel numerical stochastic optimization algorithm inspired from colonizing weeds. Weeds are plants whose vigorous, invasive habits of growth pose a serious threat to desirable, cultivated plants making them a threat for agriculture. Weeds have shown to be very robust and adaptive to change in environment. Thus, capturing their properties would lead to a powerful optimization algorithm. It is tried to mimic robustness, adaptation and randomness of colonizing weeds in a simple but effective optimizing algorithm designated as Invasive Weed Optimization (IWO). The feasibility, the efficiency and the effectiveness of IWO are tested in details through a set of benchmark multi-dimensional functions, of which global and local minima are known. The reported results are compared with other recent evolutionary-based algorithms: genetic algorithms, memetic algorithms, particle swarm optimization, and shuffled frog leaping. The results are also compared with different versions of simulated annealing — a generic probabilistic meta-algorithm for the global optimization problem — which are simplex simulated annealing, and direct search simulated annealing. Additionally, IWO is employed for finding a solution for an engineering problem, which is optimization and tuning of a robust controller. The experimental results suggest that results from IWO are better than results from other methods. In conclusion, the performance of IWO has a reasonable performance for all the test functions.

Introduction

Engineering design problems and applications always involve optimization problems that must be solved efficiently and effectively. To solve a problem, an engineer must sketch a proper view from the problem in her hand. So, the design is the struggle of the designer for finding a solution which best suits the sketched view. In support of this need, there have been various optimization techniques proposed by scientists. In practice, many engineering problems do not have explicit presentation of control variables and/or do not have continuity, which are necessary for applying gradient-based optimization techniques. In order to overcome this difficulty, scientists proposed direct optimization methods that only use objective function and constrain values to steer towards the solution. Since derivative information is not used, the direct search methods are typically slow, requiring many function evaluations for convergence. For the same reason, they can also be applied to different problems without applying major changes in the algorithm.

Recently, in the literature, there has been a considerable attention paid for employing algorithms inspired from natural processes and/or events in order to solve optimization problems. For example, genetic algorithms (GAs) which was first introduced by Holland (1975) are now a standard optimization tool in engineering. There are also other numerical direct search optimization methods, e.g. simulated annealing (SA); tabu search (TS) (Pham and Karaboga, 2000); Ant colony optimization (ACO) (Dorigo et al., 1996); and particle swarm optimization (PSO) (Kennedy and Eberhart, 1995).

Recently, many studies were carried out with inspirations from ecological phenomena for developing optimization techniques. For instance, a novel evolutionary algorithm inspired by the nature of spatial interactions in ecological systems is introduced in (Kirley, 2002), where the author have examined the response of the evolving population to the process of fragmentation and disturbance cased by natural events (like fire, floods or climate changes). Another ecology-inspired EA is introduced in (Yuchi and Kim, 2005). In the mentioned research, in each generation, according to the feasibility of the individuals, the whole population is divided into two groups: feasible group and infeasible group. Evaluation and ranking of these two groups are performed in parallel and separately. The best individuals from feasible and infeasible groups are selected together as parents. The number of feasible parents has a sigmoid-type relation with that of feasible individuals, which is inspired by the natural ecological population growth in a confined space.

This work is motivated by a common phenomenon in agriculture that is colonization of invasive weeds. According to the common definition, a weed is any plant growing where it is not wanted. Any tree, vine, shrub, or herb may qualify as a weed, depending on the situation; generally, however, the term is reserved for those plants whose vigorous, invasive habits of growth pose a serious threat to desirable, cultivated plants. Weeds have shown very robust and adaptive nature which turns them to undesirable plants in agriculture. That's why many Journals (e.g. Weed Biology and Management Journal, Weed Research Journal, and Weed Science Journal) are being published world-wide focusing on the study of weed taxonomy, ecology and physiology, weed management and control methodologies, etc. In this paper it is tried to introduce a simple numerical general-purpose optimization algorithm that is inspired by weed colonization designated as Invasive Weed Optimization (IWO). The algorithm is simple but has shown to be effective in converging to optimal solution by employing basic properties, e.g. seeding, growth and competition, in a weed colony. Simulation studies are conducted to evaluate convergence and performance of the proposed algorithm.

Section snippets

Weed ecology1

In this section our goal is to provide the reader some sense of weed biology, ecology, and colonization.

Simulating weed colonizing behavior

To simulate colonizing behavior of weeds some basic properties of the process is considered:

  • 1)

    a finite number of seeds are being dispread over the search area (initializing a population),

  • 2)

    every seed grows to a flowering plant and produces seeds depending on its fitness (reproduction),

  • 3)

    the produced seeds are being randomly dispread over the search area and grow to new plants (spatial dispersal),

  • 4)

    this process continues until maximum number of plants is reached; now only the plants with lower fitness

Simulation studies

In this section several simulation studies are carried out to demonstrate merits of the proposed optimization algorithm. In the first step, the capability of the algorithm in finding global minimum of three benchmark functions, which are frequently employed in the literature, is demonstrated. These functions are ‘Sphere’, ‘Griewank’ and ‘Rastrigin’; to show that the algorithm converges to the global solution, the results are compared to a standard GA.

As the second step, IWO algorithm is applied

A practical example

An interesting application of optimization problems appears in dynamic and control systems theory. A system is considered an optimum control system when the system parameters are adjusted so that an index — a quantitative measure of the performance of the system — reaches an extreme value. For example, consider a dynamic model of a flexible structure is given by Eq. (5):G(s)=(1+kωn2)s2+2ζωns+ωn2s2(s2+2ζωns+ωn2)where ωn is natural frequency of the flexible mode and ζ is the corresponding

Conclusion

Invasive Weed Optimization (IWO) is a numerical stochastic search algorithm mimicking natural behavior of weed colonizing in opportunity spaces for function optimization. Adapting with their environments, invasive weed ride opportunity spaces left behind by improper tillage; followed by enduring occupation of the field. They reproduce rapidly by making seeds and raise their population. Their behavior changes with time as the colony become dense leaving lesser opportunity of life for the ones

Acknowledgements

Authors would like to sincerely thank the anonymous reviewers of the paper for their thoughtful suggestions which led to many improvements in the paper.

References (20)

  • E. Elbeltagi et al.

    Comparison among five evolutionary-based optimization algorithms

    Advanced Engineering Informatics

    (2005)
  • V. Cerny

    A thermodynamical approach to the travelling salesman problem: an efficient simulation algorithm

    Journal of Optimization Theory and Applications

    (1985)
  • Chatterjee, A., Siarry, P., 2006. Nonlinear inertia variation for dynamic adaptation in particle swarm optimization,...
  • R. Dawkins

    The extended phenotype: the long reach of the gene

  • Dekker, Jack, 2005. Course works of Agronomy 517: a course on the biology and evolutionary ecology of invasive weeds....
  • R.C. Dorf et al.

    Modern Control Systems

    (1995)
  • M. Dorigo et al.

    The ant system: optimization by a colony of cooperating agents

    IEEE Transactions on Systems, Man and Cybernetics. Part B. Cybernetics

    (1996)
  • M.M. Eusuff et al.

    Optimization of water distribution network design using the shuffled frog leaping algorithm

    Journal of Water Resources planning and management

    (2003)
  • Evolver

    Evolver Version 4.0.2

    (1998)
There are more references available in the full text version of this article.

Cited by (0)

View full text