Optimisation Algorithms for Engineering Design Problems

Optimisation algorithms form the backbone of modern engineering design, enabling automated search for optimal configurations under complex physical, structural and performance constraints. Broadly speaking, these methods span deterministic techniques—such as gradient-based and convex programming—and stochastic metaheuristics, which draw inspiration from nature, mathematics or physics. Metaheuristic approaches are particularly valuable when design spaces are non-convex, multi-modal or characterised by competing objectives such as minimising weight while maximising strength or reducing cost while improving reliability. Key challenges in engineering design include balancing exploration (global search) and exploitation (local refinement), handling discrete and continuous variables, and addressing single- versus multi-objective criteria. Recent advances focus on hybridisation of algorithms to leverage complementary search behaviours, adaptive control of algorithm parameters, and parallel implementations for high-dimensional problems. Applications range from structural topology optimisation and aerodynamic shape design to thermal management and mechatronic system synthesis. By combining rigorous mathematical models with flexible search heuristics, contemporary optimisation algorithms accelerate development cycles, reduce material usage and improve overall system performance on a global scale.

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A newly proposed arithmetic-inspired metaheuristic models the behaviour of addition, subtraction, multiplication and division operators to guide candidate solutions through exploration and exploitation phases. Benchmarked on classical test suites and applied to real-world engineering design problems, it demonstrates competitive performance against established algorithms, highlighting its potential as a general-purpose optimiser for tasks such as spring, beam and pressure vessel design.

Hybridisation strategies have emerged to overcome individual algorithmic shortcomings. One approach combines an arithmetic-based optimiser with a nature-inspired bird of prey algorithm, introducing an adaptive energy parameter and a piecewise linear control map. This hybrid exhibits accelerated convergence and higher precision on benchmark functions and three classical engineering design scenarios, illustrating how cross-fertilisation of search strategies can enhance global and local search balance.

Another hybrid framework integrates an arithmetic optimisation core with a golden sine search operator, dividing the population into subgroups that exchange information during iterations. Supplemented by Levy flight perturbations and a novel mutation mechanism, this method shows marked improvements in convergence speed and solution quality when tested on a standard competition suite and multiple industrial engineering design cases, including heat exchanger and structural layout problems.

Optimisation Algorithms for Engineering Design Problems publication trend

The graph below shows the total number of articles in optimisation algorithms for engineering design problems across all publications each year (not limited to Nature Index journals).

Technical terms

Metaheuristic algorithm: A high-level, problem-independent search framework that uses stochastic processes to explore large or complex design spaces without requiring gradient information.

Exploration vs Exploitation: Dual modes of search where exploration seeks diverse regions of the design space, and exploitation refines existing solutions for local improvement.

Hybrid algorithm: An optimisation method that combines elements from two or more algorithms to leverage their respective strengths and mitigate weaknesses.

Multi-objective optimisation: The process of simultaneously optimising two or more conflicting objectives, often yielding a set of trade-off solutions known as the Pareto front.

Convergence behaviour: The pattern and rate at which an optimisation algorithm approaches its final solution, indicating efficiency and reliability in finding optima.

References

1. The Arithmetic Optimization Algorithm. Computer Methods in Applied Mechanics and Engineering (2021).
2. Advanced arithmetic optimization algorithm for solving mechanical engineering design problems. PLOS ONE (2021).
3. AOAAO: The Hybrid Algorithm of Arithmetic Optimization Algorithm With Aquila Optimizer. IEEE Access (2022).
4. A Hybrid Arithmetic Optimization and Golden Sine Algorithm for Solving Industrial Engineering Design Problems. Mathematics (2022).