What does it mean to give the "appearance of design"?
Bear in mind that some religions consider everything - clouds, earth, water, stars, etc. - to have been directly designed by some god or gods. This would indicate that any physical process can give the "appearance of design," depending on the mindset of the person looking.
So let's change the question a little. The relevance of evolution to design is that evolution is an optimization process. Evolution optimizes the reproductive fitness of individuals (or of genes). An intelligent designer is also executing some mental optimization process: he has some idea of what would be fit for his purpose, and tries to optimize what he's making so that it is more fit for his purpose.
So let's change the question to, "What are some optimization processes that can be used to create complex structures?"
A list of optimization algorithms can be found here. Many variations of evolutionary algorithms are in that list. It does no good to just repeat all these algorithms here, but I would like to call out stochastic gradient descent in particular, due to its importance.
Stochastic gradient descent is the main method used to train large artificial neural networks, which are behind most of the recent advances in machine learning. The behavior of these networks is not specifically designed by humans, and in fact is not very well understood by humans, but they solve tasks as if they had some skill.
Note that evolutionary algorithms can also be used to train large artificial neural networks; stochastic gradient descent and evolutionary algorithms are similar in this way.
See also the principle of least action and the free energy principle for examples of how minimization and maximization are inherent in physics. Soap bubbles are minimal surfaces. Pendulums come to rest in a minimum-energy state. Maximization and minimization principles are everywhere in nature.