A novel numerical optimization algorithm inspired from weed colonization
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):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.
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