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

Discrete flower pollination algorithm for resource constrained project scheduling problem

YesIn this paper, a new population-based and nature-inspired metaheuristic algorithm, Discrete Flower Pollination Algorithm (DFPA), is presented to solve the Resource Constrained Project Scheduling Problem (RCPSP). The DFPA is a modification of existing Flower Pollination Algorithm adapted for solving combinatorial optimization problems by changing some of the algorithm's core concepts, such as flower, global pollination, Lévy flight, local pollination. The proposed DFPA is then tested on sets of benchmark instances and its performance is compared against other existing metaheuristic algorithms. The numerical results have shown that the proposed algorithm is efficient and outperforms several other popular metaheuristic algorithms, both in terms of quality of the results and execution time. Being discrete, the proposed algorithm can be used to solve any other combinatorial optimization problems.Innovate UKAwarded 'Best paper of the Month

Modified flower pollination algorithm for global optimization

In this paper, a modified flower pollination algorithm (MFPA) is proposed to improve the performance of the classical algorithm and to tackle the nonlinear equation systems widely used in engineering and science fields. In addition, the differential evolution (DE) is integrated with MFPA to strengthen its exploration operator in a new variant called HFPA. Those two algorithms were assessed using 23 well-known mathematical unimodal and multimodal test functions and 27 well-known nonlinear equation systems, and the obtained outcomes were extensively compared with those of eight well-known metaheuristic algorithms under various statistical analyses and the convergence curve. The experimental findings show that both MFPA and HFPA are competitive together and, compared to the others, they could be superior and competitive for most test cases

OPTIMISASI FUNGSI RASTRIGIN MENGGUNAKAN FLOWER POLLINATION ALGORITHM

The Rastrigin function is a multimodal function. It is difficult to find a global minimum of the function because it has many local minimums. So, we need an effective and efficient algorithm to find a solution to the global minimum of the function without being trapped by the local minimum. The flower pollination algorithm is a metaheuristic algorithm, it is expected to be capable of solving multimodal function optimization problems. In this study flower pollination algorithm is used to find the global minimum of the Rastrigin function of two variables with MATLAB. The Rastrigin function of two variables is used as objective function for the flower pollination algorithm. The parameters are divided into three configurations based on the difference amount of pollen gamets, the probability switch, and the search domain, with two different iterations 300 and 1500. In order, to get the best results each configuration is running for 10 times. The best results from the flower pollination algorithm are obtained from the first configuration and 1500 iteration

Flower Pollination Inspired Algorithm on Exchange Rates Prediction Case

Flower pollination algorithm is a bio-inspired system that adapts a similar process to genetic algorithm, that aims for optimization problems. In this research, we examine the utilization of the flower pollination algorithm in linear regression for currency exchange cases. The solutions are represented as a set that contains regression coefficients. Population size for the candidate solutions and the switch probability between global pollination and local pollination have been experimented with in this research. Our result shows that the final solution is better when a higher size population and higher switch probability are employed. Furthermore, our result shows the higher size of the population leads to considerable running time, where the leaning probability of global pollination slightly increases the running time

FPOA Implementation for WSN Energy Efficient Routing

In this paper,a soft computing technique Flower Pollination optimization Algorithm(FPOA) for WSN is proposed.The Sensor Network is heterogeneous in nature. Proposed algorithm is designed and implemented in MATLAB.In this technique some nodes send data directly to base station as local pollination and some by Multihop Routing as global pollination. A routing scheme is process which helps in minimizing the energy consumption. We implemented FPOA and compared the results with techniques that are already developed.(Low Energy adaptive clustering hierarchy (LEACH), Stable Election Protocol (SEP) and Zonal-Stable Election Protocol (Z-SEP) Simulation results show that FPOA enhance first node dead time, throughput and overall energy consumes less than existing protocols like LEACH, SEP and Z-SE

A modified flower pollination algorithm and carnivorous plant algorithm for solving engineering optimization problem

Optimization in an essential element in mechanical engineering and has never been an easy task. Hence, using an effective optimiser to solve these problems with high complexity is important. In this study, two metaheuristic algorithms, namely, modified flower pollination algorithm (MFPA) and carnivorous plant algorithm (CPA), were proposed. Flower pollination algorithm (FPA) is a biomimicry optimisation algorithm inspired by natural pollination. Although FPA has shown better convergence than particle swarm optimisation and genetic algorithm in the pioneering study, improving the convergence characteristic of FPA still needs more work. To speed up the convergence, modifications of: (i) employing chaos theory in the initialisation of initial population to enhance the diversity of the initial population in the search space, (ii) replacing FPA’s local search strategy with frog leaping algorithm to improve intensification, and (iii) integrating inertia weight into FPA’s global search strategy to adjust the searching ability of the global strategy, were presented. CPA, on the other hand, was developed based on the inspiration from how carnivorous plants adapt to survive in harsh environments. Both MFPA and CPA were first evaluated using twenty-five well-known benchmark functions with different characteristics and seven Congress on Evolutionary Computation (CEC) 2017 test functions. Their convergence characteristic and computational efficiency were analysed and compared with eight widely used metaheuristic algorithms, with the superiority validated using the Wilcoxon signed-rank test. The applicability of MFPA and CPA were further examined on eighteen mechanical engineering design problems and two challenging real-world applications of controlling the orientation of a five-degrees-of-freedom robotic arm and moving-object tracking in a complicated environment. For the optimisation of classical benchmark functions, CPA was ranked first. It also obtained the first rank in CEC04 and CEC07 modern test functions. Both CPA and MFPA showed promising results on the mechanical engineering design problems. CPA improved over the particle swarm optimisation algorithm in terms of the best fitness value by 69.40-95.99% in the optimisation of the robotic arm. Meanwhile, MFPA demonstrated a better tracking performance in the considered case studies by at least 52.99% better fitness function evaluation and fewer number of function evaluations as compared with the competitors

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