Convergence analysis of the plant propagation algorithm for continuous global optimization

2018 ◽  
Vol 52 (2) ◽  
pp. 429-438 ◽  
Author(s):  
Nassim Brahimi ◽  
Abdellah Salhi ◽  
Megdouda Ourbih-Tari
Keyword(s):  
Global Optimization ◽  
Convergence Analysis ◽  
Convergence Theorem ◽  
Optimization Problems ◽  
Stochastic Algorithm ◽  
Strawberry Plant ◽  
Plant Propagation ◽  
Propagation Algorithm ◽  
Continuous Global Optimization ◽  
General Convergence

The Plant Propagation Algorithm (PPA) is a Nature-Inspired stochastic algorithm, which emulates the way plants, in particular the strawberry plant, propagate using runners. It has been experimentally tested both on unconstrained and constrained continuous global optimization problems and was found to be competitive against well established algorithms. This paper is concerned with its convergence analysis. It first puts forward a general convergence theorem for a large class of random algorithms, before the PPA convergence theorem is derived and proved. It then illustrates the results on simple problems.

scholarly journals Fresa: A Plant Propagation Algorithm for Black-Box Single and Multiple Objective Optimization

2021 ◽  
Vol 2 (4) ◽  
Keyword(s):  
Mathematical Programming ◽  
Objective Function ◽  
Optimization Problems ◽  
Population Based ◽  
Black Box ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Plant Propagation ◽  
Propagation Algorithm ◽  
Multiple Dispatch

Fresa implements a nature inspired plant propagation algorithm for the solution of single and multiple objective optimization problems. The method is population based and evolutionary. Treating the objective function as a black box, the implementation is able to solve problems exhibiting behaviour that is challenging for mathematical programming methods. Fresa is easily adapted to new problems which may benefit from bespoke representations of solutions by taking advantage of the dynamic typing and multiple dispatch capabilities of the Julia language. Further, the support for threads in Julia enables an efficient implementation on multi-core computers.

scholarly journals A DE-Based Scatter Search for Global Optimization Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Kun Li ◽  
Huixin Tian
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Scatter Search ◽  
Benchmark Problems ◽  
Local Optimum ◽  
Candidate Mutation ◽  
Mutation Operators ◽  
Reference Set ◽  
Solution Generation ◽  
Continuous Global Optimization

This paper proposes a hybrid scatter search (SS) algorithm for continuous global optimization problems by incorporating the evolution mechanism of differential evolution (DE) into the reference set updated procedure of SS to act as the new solution generation method. This hybrid algorithm is called a DE-based SS (SSDE) algorithm. Since different kinds of mutation operators of DE have been proposed in the literature and they have shown different search abilities for different kinds of problems, four traditional mutation operators are adopted in the hybrid SSDE algorithm. To adaptively select the mutation operator that is most appropriate to the current problem, an adaptive mechanism for the candidate mutation operators is developed. In addition, to enhance the exploration ability of SSDE, a reinitialization method is adopted to create a new population and subsequently construct a new reference set whenever the search process of SSDE is trapped in local optimum. Computational experiments on benchmark problems show that the proposed SSDE is competitive or superior to some state-of-the-art algorithms in the literature.

scholarly journals A Novel Optimization Algorithm Combing Gbest-Guided Artificial Bee Colony Algorithm with Variable Gradients

2020 ◽  
Vol 10 (10) ◽  
pp. 3352
Author(s):  
Xiaodong Ruan ◽  
Jiaming Wang ◽  
Xu Zhang ◽  
Weiting Liu ◽  
Xin Fu
Keyword(s):  
Global Optimization ◽  
Optimization Algorithm ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Optimization Problems ◽  
Numerical Test ◽  
Stochastic Algorithm ◽  
Abc Algorithm ◽  
Bee Colony ◽  
Novel Algorithm

The artificial bee colony (ABC) algorithm, which has been widely studied for years, is a stochastic algorithm for solving global optimization problems. Taking advantage of the information of a global best solution, the Gbest-guided artificial bee colony (GABC) algorithm goes further by modifying the solution search equation. However, the coefficient in its equation is based only on a numerical test and is not suitable for all problems. Therefore, we propose a novel algorithm named the Gbest-guided ABC algorithm with gradient information (GABCG) to make up for its weakness. Without coefficient factors, a new solution search equation based on variable gradients is established. Besides, the gradients are also applied to differentiate the priority of different variables and enhance the judgment of abandoned solutions. Extensive experiments are conducted on a set of benchmark functions with the GABCG algorithm. The results demonstrate that the GABCG algorithm is more effective than the traditional ABC algorithm and the GABC algorithm, especially in the latter stages of the evolution.

scholarly journals Influence of a neighborhood shape on the efficiency of continuous variable neighborhood search

2020 ◽  
Vol 30 (1) ◽  
pp. 3-17
Author(s):  
Milan Drazic
Keyword(s):  
Global Optimization ◽  
Variable Neighborhood Search ◽  
Optimization Problems ◽  
Continuous Variable ◽  
Efficient Algorithms ◽  
Geometric Shape ◽  
Neighborhood Search ◽  
High Dimensional ◽  
Neighborhood Structures ◽  
Continuous Global Optimization

The efficiency of a Variable neighborhood search metaheuristic for continuous global optimization problems greatly depends on geometric shape of neighborhood structures used by the algorithm. Among the neighborhoods defined by balls in ?p, 1 ?p ? ? metric, we tested the ?1, ?2, and ?? ball shape neighborhoods, for which there exist efficient algorithms for obtaining uniformly distributed points. On many challenging high-dimensional problems, our exhaustive testings showed that, popular and the easiest for implementation, ?? ball shape of neighborhoods performed the worst, and much better efficiency was obtained with ?1 and ?2.

scholarly journals Seed based plant propagation algorithm for multiple travelling salesman problem

2018 ◽  
Vol 7 (3.3) ◽  
pp. 515
Author(s):  
S Kalaiarasi ◽  
P Sriramya
Keyword(s):  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Routing Algorithm ◽  
Complex Problem ◽  
Travelling Salesman ◽  
Biologically Inspired ◽  
Plant Propagation ◽  
Propagation Algorithm ◽  
Biologically Inspired Algorithms ◽  
Multiple Travelling Salesman Problem

Multiple Travelling Salesman Problem is a complex problem in which route for a salesman is assigned to visit a city that has various hurdles such as congested road, damaged road, etc. In recent years biologically inspired algorithms are most widely used to solve many optimization problems. Here seed based plant propagation algorithm is applied for the multiple travelling salesman problem that is also a optimization problem, and the result is compared with a short-cut routing algorithm. The result shows that Seed based Propagation Algorithm is easy to implement since it has few parameters to be utilized and also time complexity is reduced when implemented in multiple travelling salesman problem.  

scholarly journals Adaptive Plant Propagation Algorithm for Solving Economic Load Dispatch Problem

2017 ◽  
Author(s):  
Sayan Nag
Keyword(s):  
Optimization Problems ◽  
State Of The Art ◽  
Economic Load Dispatch ◽  
Objective Functions ◽  
Plant Propagation ◽  
Propagation Algorithm ◽  
Highly Nonlinear ◽  
Plant Intelligence ◽  
Classical Optimization

Optimization problems in design engineering are complex by nature, often because of the involvement of critical objective functions accompanied by a number of rigid constraints associated with the products involved. One such problem is Economic Load Dispatch (ED) problem which focuses on the optimization of the fuel cost while satisfying some system constraints. Classical optimization algorithms are not sufficient and also inefficient for the ED problem involving highly nonlinear, and non-convex functions both in the objective and in the constraints. This led to the development of metaheuristic optimization approaches which can solve the ED problem almost efficiently. This paper presents a novel robust plant intelligence based Adaptive Plant Propagation Algorithm (APPA) which is used to solve the classical ED problem. The application of the proposed method to the 3-generator and 6-generator systems shows the efficiency and robustness of the proposed algorithm. A comparative study with another state-of-the-art algorithm (APSO) demonstrates the quality of the solution achieved by the proposed method along with the convergence characteristics of the proposed approach.

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