Multi-objective Optimization

Example

As an example of multi-objective optimization, consider the 4-stroke 4 cylinder engine optimization problem illustrated in the image below.

The engine has to be designed using a commercial software (GT-Power), and several parameters have to be taken in account including, to mention a few, intake and exhaust cam timing, intake runners length, percentage of burn point, geometry of valves, and many others.

The purpose of the designer is to find a combination for these parameters in order to match at the same time contrasting objectives, such as maximization of brake power and minimization of NOx emissions.

After the application of the multi-objective optimization by modeFRONTIER, each single configuration proposed by the selected algorithm is represented in the picture as a point in the objectives chart (Power vs NOx).

The red dotted line includes several solutions which represent a different optimal compromise between the contrasting objectives. In particular, in the two extremes of the front, two selected configurations are highlighted by the relative CAD model: one solution is optimal for NOx because it gives the lowest value for this objective, while the other is optimal for Brake Power because it gives the highest value for this other objective.

All the other points in the front are however as optimal solutions as the former two, because none of them is better than another for both objectives at the same time. All of them instead dominates any other possible configuration, represented by the points staying below the line, because the results of the former are better than the ones of the latter for both objectives at the same time. The designer is therefore free to select arbitrary one of the solutions belonging to this set as definitive design, accordingly to his preferences and criteria.

The optimal solutions belonging to this front are called Pareto Frontier designs.