Novel 'cuckoo search algorithm' beats particle swarm optimization in engineering design

In 2009, engineer Xin-She Yang of the University of Cambridge (now a Senior Research Scientist at National Physical Lab), UK and Suash Deb of the C. V. Raman College of Engineering, in Bhubaneswar, India, conceived of a new way to design engineering structures. The approach could be used to improve everything from the ubiquitous spring to welded beams, that would make them safer, stronger, and last longer.

They now describe how they have improved significantly their approach in the International Journal of Mathematical Modelling and Numerical Optimisation. The new "cuckoo search" technique has been demonstrated successfully and is far better, they say, than other approaches including the advanced particle swarm optimisation approach.

Almost every design optimisation problem in engineering is a complex blend of many different design variables, each with its own set of complex constraints. Mapping out these constraints so that a design can be carried out more efficiently requires a breakdown of the various properties of all the materials involved, their behaviour under maximum stress, flexibility, load capacity, size, shape, density, overall mass. As such, any computer program written to help with the process of engineering design, whether that is a component of a suspension bridge or a spring in a child's toy has to be able to cope with all these paramaters, values, and constraints simultaneously.

Various researchers have developed so-called search algorithms that seek out the optimal design by looking at how a product might turn out if it were constructed with a wide range of constraints and parameters. Techniques such as the hill-climbing and Nelder-Mead downhill methods have been used widely, but are unsuitable for optimisation.

Instead, researchers have turned to nature for inspiration. The concept of genetic algorithms can be used to evolve an answer based on the principle of survival of the fittest in which designs that are below par are discarded in preference for better ones. Other approaches such as particle swarm optimisation, model themselves on the movements of flocks of birds, swarming bees, or schools of fish, and home in on an answer by swarming through the solution space until they hit the best design.

Yang and Deb saw limitations in all these methods and turned to the behaviour of the parasitic bird, the cuckoo, for an entirely different approach.

Cuckoos have an aggressive reproduction strategy that involves the female laying her fertilised eggs in the nest of another species so that the surrogate parents unwittingly raise her brood. Sometimes the cuckoo's egg in the nest is discovered and the surrogate parents throw it out or abandon the nest and start their own brood elsewhere.

The team base their design search on three simple principles that emerge from the cuckoo's strategy:

• First, each cuckoo lays one egg (a design solution) at a time, and dumps it in a randomly chosen nest.
• Second, the best nests with a high quality egg (better solution) carry over to the next generation.
• Third, the number of available host nests is fixed, and a host and there is a finite probability of the cuckoo in the nest being discovered.

The team have encapsulated these three principles in a mathematical formula that they then converted to computer software code. The various design parameters and constraints are fed to the software, which tests each "egg" discarding some based on lack of fitness and sending the successful solutions through a second round and so on until an optimal solution emerges.

The team has carried out standard mathematical design tests on their cuckoo search, which itself has now been optimised and also compared it with particle swarm optimisation and other techniques to show that it is more efficient than these other approaches to engineering design of a welded beam and a spring, two key engineering components of many structures.

The team adds that while their approach is effective a yet more powerful approach to engineering design might be to combine the strengths of cuckoo search and particle swarm.