To meet the ever-growing demand of quality and competitiveness, iterative physical prototyping is now often replaced by 'digital prototyping' of a 'good design', which aims to meet multiple objectives such as maximised output, energy efficiency, highest speed and cost-effectiveness. The design problem concerns both finding the best design within a known range (i.e., through 'learning' or 'optimisation') and finding a new and better design beyond the existing ones (i.e., through creation and invention). This is equivalent to a search problem in an almost certainly, multidimensional (multivariate), multi-modal space with a single (or weighted) objective or multiple objectives.

Normalized objective function: cost vs. fitness

Using single-objective CAutoD as an example, if the objective function, either as a cost function$J\in [0,\infty )$, or inversely, as a fitness function$f\in (0,1]$[1] where a computer program was written.

To meet the ever-growing demand of quality and competitiveness, iterative physical prototyping is now often replaced by 'digital prototyping' of a 'good design', which aims to meet multiple objectives such as maximised output, energy efficiency, highest speed and cost-effectiveness. The design problem concerns both finding the best design within a known range (i.e., through 'learning' or 'optimisation') and finding a new and better design beyond the existing ones (i.e., through creation and invention). This is equivalent to a search problem in an almost certainly, multidimensional (multivariate), multi-modal space with a single (or weighted) objective or multiple objectives.

Normalized objective function: cost vs. fitness

Using single-objective CAutoD as an example, if the objective function, either as a cost function$J\in [0,\infty )$, or inversely, as a fitness function$f\in (0,1]$, where

$f={\textstyle \frac{J}{1+J}}$

Using single-objective CAutoD as an example, if the objective function, either as a cost function$J\in [0,\infty )$, or inversely, as a fitness function$f\in (0,1]$, where

In practice, the objective value may be noisy or even non-numerical, and hence its gradient information may be unreliable or unavailable. This is particularly true when the problem is multi-objective. At present, many designs and refinements are mainly made through a manual trial-and-error process with the help of a CAD simulation package. Usually, such a posteriori learning or adjustments need to be repeated many times until a ‘satisfactory’ or ‘optimal’ design emerges.

Exhaustive search

In practice, the objective value may be noisy or even non-numerical, and hence its gradient information may be unreliable or unavailable. This is particularly true when the problem is multi-objective. At present, many designs and refinements are mainly made through a manual trial-and-error process with the help of a CAD simulation package. Usually, such a posteriori learning or adjustments need to be repeated many times until a ‘satisfactory’ or ‘optimal’ design emerges.

Exhaustive search

In theory, this adjustment process can be aut

In theory, this adjustment process can be automated by computerised search, such as exhaustive search. As this is an exponential algorithm, it may not deliver solutions in practice within a limited period of time.

Search in polynomial time

To

To reduce the search time, the biologically-inspired evolutionary algorithm (EA) can be used instead, which is a (non-deterministic) polynomial algorithm. The EA based multi-objective "search team" can be interfaced with an existing CAD simulation package in a batch mode. The EA encodes the design parameters (encoding being necessary if some parameters are non-numerical) to refine multiple candidates through parallel and interactive search. In the search process, 'selection' is performed using 'survival of the fittest' a posteriori learning. To obtain the next 'generation' of possible solutions, some parameter values are exchanged between two candidates (by an operation called 'crossover') and new values introduced (by an operation called 'mutation'). This way, the evolutionary technique makes use of past trial information in a similarly intelligent manner to the human designer.

The EA based optimal designs can start from the designer's existing design database, or from an initial generation of candidate designs obtained randomly. A number of finely evolved top-performing candidates will represent several automatically optimized digital prototypes.

There are websites that demonstrate interactive evolutionary algorithms for

The EA based optimal designs can start from the designer's existing design database, or from an initial generation of candidate designs obtained randomly. A number of finely evolved top-performing candidates will represent several automatically optimized digital prototypes.

There are websites that demonstrate interactive evolutionary algorithms for design. EndlessForms.com allows you to evolve 3D objects online and have them 3D printed. PicBreeder.org allows you to do the same for 2D images.