Global convergence analysis of the flower pollination algorithm: a Discrete-Time Markov Chain Approach

Flower pollination algorithm is a recent metaheuristic algorithm for solving nonlinear global optimization problems. The algorithm has also been extended to solve multiobjective optimization with promising results. In this work, we analyze this algorithm mathematically and prove its convergence properties by using Markov chain theory. By constructing the appropriate transition probability for a population of flower pollen and using the homogeneity property, it can be shown that the constructed stochastic sequences can converge to the optimal set. Under the two proper conditions for convergence, it is proved that the simplified flower pollination algorithm can indeed satisfy these convergence conditions and thus the global convergence of this algorithm can be guaranteed. Numerical experiments are used to demonstrate that the flower pollination algorithm can converge quickly in practice and can thus achieve global optimality efficiently

Global convergence analysis of the flower pollination algorithm: a Discrete-Time Markov Chain Approach

Flower pollination algorithm is a recent metaheuristic algorithm for solving nonlinear global optimization problems. The algorithm has also been extended to solve multiobjective optimization with promising results. In this work, we analyze this algorithm mathematically and prove its convergence properties by using Markov chain theory. By constructing the appropriate transition probability for a population of flower pollen and using the homogeneity property, it can be shown that the constructed stochastic sequences can converge to the optimal set. Under the two proper conditions for convergence, it is proved that the simplified flower pollination algorithm can indeed satisfy these convergence conditions and thus the global convergence of this algorithm can be guaranteed. Numerical experiments are used to demonstrate that the flower pollination algorithm can converge quickly in practice and can thus achieve global optimality efficiently

Flower pollination algorithm: a novel approach for multiobjective optimization

Multiobjective design optimization problems require multiobjective optimization techniques to solve, and it is often very challenging to obtain high-quality Pareto fronts accurately. In this article, the recently developed flower pollination algorithm (FPA) is extended to solve multiobjective optimization problems. The proposed method is used to solve a set of multiobjective test functions and two bi-objective design benchmarks, and a comparison of the proposed algorithm with other algorithms has been made, which shows that the FPA is efficient with a good convergence rate. Finally, the importance for further parametric studies and theoretical analysis is highlighted and discussed

Maximum power point tracking for brushless DC motor-driven photovoltaic pumping systems using a hybrid ANFIS-FLOWER pollination optimization algorithm

In this research paper, a hybrid Artificial Neural Network (ANN)-Fuzzy Logic Control (FLC) tuned Flower Pollination Algorithm (FPA) as a Maximum Power Point Tracker (MPPT) is employed to amend root mean square error (RMSE) of photovoltaic (PV) modeling. Moreover, Gaussian membership functions have been considered for fuzzy controller design. This paper interprets the Luo converter occupied brushless DC motor (BLDC)-directed PV water pump application. Experimental responses certify the effectiveness of the suggested motor-pump system supporting diverse operating states. The Luo converter, a newly developed DC-DC converter, has high power density, better voltage gain transfer and superior output waveform and can track optimal power from PV modules. For BLDC speed control there is no extra circuitry, and phase current sensors are enforced for this scheme. The most recent attempt using adaptive neuro-fuzzy inference system (ANFIS)-FPA-operated BLDC directed PV pump with advanced Luo converter, has not been formerly conferred

Comparison of constraint-handling techniques for metaheuristic optimization

Many design problems in engineering have highly nonlinear constraints and the proper handling of such constraints can be important to ensure solution quality. There are many different ways of handling constraints and different algorithms for optimization problems, which makes it difficult to choose for users. This paper compares six different constraint-handling techniques such as penalty methods, barrier functions, epsilon-constrained method, feasibility criteria and stochastic ranking. The pressure vessel design problem is solved by the flower pollination algorithm, and results show that stochastic ranking and epsilon-constrained method are most effective for this type of design optimization

A Brief Survey on Intelligent Swarm-Based Algorithms for Solving Optimization Problems

This chapter presents an overview of optimization techniques followed by a brief survey on several swarm-based natural inspired algorithms which were introduced in the last decade. These techniques were inspired by the natural processes of plants, foraging behaviors of insects and social behaviors of animals. These swam intelligent methods have been tested on various standard benchmark problems and are capable in solving a wide range of optimization issues including stochastic, robust and dynamic problems

An improved optimization technique for estimation of solar photovoltaic parameters

The nonlinear current vs voltage (I-V) characteristics of solar PV make its modelling difficult. Optimization techniques are the best tool for identifying the parameters of nonlinear models. Even though, there are different optimization techniques used for parameter estimation of solar PV, still the best optimized results are not achieved to date. In this paper, Wind Driven Optimization (WDO) technique is proposed as the new method for identifying the parameters of solar PV. The accuracy and convergence time of the proposed method is compared with results of Pattern Search (PS), Genetic Algorithm (GA), and Simulated Annealing (SA) for single diode and double diode models of solar PV. Furthermore, for performance validation, the parameters obtained through WDO are compared with hybrid Bee Pollinator Flower Pollination Algorithm (BPFPA), Flower Pollination Algorithm (FPA), Generalized Oppositional Teaching Learning Based Optimization (GOTLBO), Artificial Bee Swarm Optimization (ABSO), and Harmony Search (HS). The obtained results clearly reveal that WDO algorithm can provide accurate optimized values with less number of iterations at different environmental conditions. Therefore, the WDO can be recommended as the best optimization algorithm for parameter estimation of solar PV