Abstract
Advanced global optimization algorithms have been continuously introduced and improved to solve various complex design optimization problems for which the objective and constraint functions can only be evaluated through computation intensive numerical analyses or simulations with a large number of design variables. The often implicit, multimodal, and ill-shaped objective and constraint functions in high-dimensional and “black-box” forms demand the search to be carried out using low number of function evaluations with high search efficiency and good robustness. This work investigates the performance of six recently introduced, nature-inspired global optimization methods: Artificial Bee Colony (ABC), Firefly Algorithm (FFA), Cuckoo Search (CS), Bat Algorithm (BA), Flower Pollination Algorithm (FPA) and Grey Wolf Optimizer (GWO). These approaches are compared in terms of search efficiency and robustness in solving a set of representative benchmark problems in smooth-unimodal, non-smooth unimodal, smooth multimodal, and non-smooth multimodal function forms. In addition, four classic engineering optimization examples and a real-life complex mechanical system design optimization problem, floating offshore wind turbines design optimization, are used as additional test cases representing computationally-expensive black-box global optimization problems. Results from this comparative study show that the ability of these global optimization methods to obtain a good solution diminishes as the dimension of the problem, or number of design variables increases. Although none of these methods is universally capable, the study finds that GWO and ABC are more efficient on average than the other four in obtaining high quality solutions efficiently and consistently, solving 86% and 80% of the tested benchmark problems, respectively. The research contributes to future improvements of global optimization methods.
Highlights
Advanced optimization methods are used in engineering design to obtain the best functional performance and/or minimum production cost of a complex product or system in the increasingly competitive international market
The overall performance of an optimization algorithm changes depending on setting parameters and other experimental criteria, benchmark problems can be used to indicate the efficiency of the algorithm under different levels of complexity
The basic versions of the selected algorithms are considered without further modification
Summary
Advanced optimization methods are used in engineering design to obtain the best functional performance and/or minimum production cost of a complex product or system in the increasingly competitive international market. Nature-inspired global optimization algorithms with superior search efficiency and robustness have been continuously introduced and improved to solve various complex, nonlinear optimization problems, which most traditional gradient-based optimization methods are incapable to deal with. These nature-inspired global optimization (GO) algorithms become more useful when the objective function of the problem of interest is in implicit, black-box form and/or its derivative information of is unavailable, unreliable, or expensive to obtain. Algorithm (GA) based on Darwin’s principle of biological systems by Holland et al [1] Since Ant Colony Optimization (ACO) [2], Simulated Annealing (SA) [3], and Particle Swarm Optimization (PSO) [4], as the most recognized nature-inspired global optimization algorithms have been introduced. Brenna et al [5] employed GA optimizer to carry out multi-objective optimization for train schedules with minimum energy consumption and travel time; Zhao et al [6] proposed an improved ant colony optimization (ACO) method for the route planning of the omnidirectional mobile vehicle; and Herish et al [4,7] applied PSO in multi-objective optimization for reliability-redundancy assignments in design
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