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

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 with pollinator attraction

The Flower Pollination Algorithm (FPA) is a highly efficient optimization algorithm that is inspired by the evolution process of flowering plants. In the present study, a modified version of FPA is proposed accounting for an additional feature of flower pollination in nature that is the so-called pollinator attraction. Pollinator attraction represents the natural tendency of flower species to evolve in order to attract pollinators by using their colour, shape and scent as well as nutritious rewards. To reflect this evolution mechanism, the proposed FPA variant with Pollinator Attraction (FPAPA) provides fitter flowers of the population with higher probabilities of achieving pollen transfer via biotic pollination than other flowers. FPAPA is tested against a set of 28 benchmark mathematical functions, defined in IEEE-CEC’13 for real-parameter single-objective optimization problems, as well as structural optimization problems. Numerical experiments show that the modified FPA represents a statistically significant improvement upon the original FPA and that it can outperform other state-of-the-art optimization algorithms offering better and more robust optimal solutions. Additional research is suggested to combine FPAPA with other modified and hybridized versions of FPA to further increase its performance in challenging optimization problems

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 parameters tuning

The flower pollination algorithm (FPA) is a highly efficient metaheuristic optimization algorithm that is inspired by the pollination process of flowering species. FPA is characterised by simplicity in its formulation and high computational performance. Previous studies on FPA assume fixed parameter values based on empirical observations or experimental comparisons of limited scale and scope. In this study, a comprehensive effort is made to identify appropriate values of the FPA parameters that maximize its computational performance. To serve this goal, a simple non-iterative, single-stage sampling tuning method is employed, oriented towards practical applications of FPA. The tuning method is applied to the set of 28 functions specified in IEEE-CEC'13 for real-parameter single-objective optimization problems. It is found that the optimal FPA parameters depend significantly on the objective functions, the problem dimensions and affordable computational cost. Furthermore, it is found that the FPA parameters that minimize mean prediction errors do not always offer the most robust predictions. At the end of this study, recommendations are made for setting the optimal FPA parameters as a function of problem dimensions and affordable computational cost. [Abstract copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021.

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