Abstract
In this paper, we propose a simple global optimisation algorithm inspired by Pareto’s principle. This algorithm samples most of its solutions within prominent search domains and is equipped with a self-adaptive mechanism to control the dynamic tightening of the prominent domains while the greediness of the algorithm increases over time (iterations). Unlike traditional metaheuristics, the proposed method has no direct mutation- or crossover-like operations. It depends solely on the sequential random sampling that can be used in diversification and intensification processes while keeping the information-flow between generations and the structural bias at a minimum. By using a simple topology, the algorithm avoids premature convergence by sampling new solutions every generation. A simple theoretical derivation revealed that the exploration of this approach is unbiased and the rate of the diversification is constant during the runtime. The trade-off balance between the diversification and the intensification is explained theoretically and experimentally. This proposed approach has been benchmarked against standard optimisation problems as well as a selected set of simple and complex engineering applications. We used 26 standard benchmarks with different properties that cover most of the optimisation problems’ nature, three traditional engineering problems, and one real complex engineering problem from the state-of-the-art literature. The algorithm performs well in finding global minima for nonconvex and multimodal functions, especially with high dimensional problems and it was found very competitive in comparison with the recent algorithmic proposals. Moreover, the algorithm outperforms and scales better than recent algorithms when it is benchmarked under a limited number of iterations for the composite CEC2017 problems. The design of this algorithm is kept simple so it can be easily coupled or hybridised with other search paradigms. The code of the algorithm is provided in C++14, Python3.7, and Octave (Matlab).
Highlights
Over the past few decades, global optimisation techniques for solving combinatorial problems have flourished
The algorithm that we propose in this paper builds on the gbest topology that was originally used in the particle swarm optimisation (PSO) algorithm by Eberhart and Kennedy (1995)
We propose a heuristic approach that uses a simple analogy with classical DOE methods
Summary
Over the past few decades, global optimisation techniques for solving combinatorial problems have flourished. The everincreasing complexity of engineering applications means that variable sets are growing larger, and the subsequent landscapes that need to be explored by these optimisation problems are becoming increasingly complicated. Many metaheuristic algorithms were developed to solve optimisation problems by mimicking biological and physical analogies (Ser et al 2019), including algorithms such as genetic algorithms (GAs) (Holland 1992), particle swarm optimisation (PSO) (Kennedy and Eberhart 1995) and the recent generalized version (GEPSO) (Sedighizadeh et al 2021), and harmony search (HS) (Geem et al 2002) and its latest modifications such as the Geem and Sim (2010), Shaqfa and Orbán (2019) and Jeong et al (2020), as well as the recent whales optimisation algorithm (WOA) (Mirjalili and Lewis 2016), and pathfinder algorithm (PFA) (Yapici and Cetinkaya 2019), to mention but a few. The candidate problems usually range from continuous differentiable problems to discrete, noisy, and even loosely defined objectives, such as in engineering applications.
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