LAB.MCO Multi-objective Constrained Optimization

MANATEE software e-NVH Laboratory
Sub-module LAB.MCO
Function Multi-objective Constrained Optimization
Validation OP_001, OP_002, OP_003, OP_005
See also LAB.SA Sensitivity analysis and parameter sweep
LAB.MDE Multidimensional Design Explorer


Design optimization of electrical machines requires to reach several contradictory objectives at the same time (e.g. maximize torque output while minimizing acoustic noise level and cost). As an example, torque ripple is not correlated to low acoustic noise and vibration levels, and lower cost can lead to thinner yoke and higher sound levels.

This module of MANATEE software specialized in e-motor multiphysic simulation therefore solves global constrained multi-objective optimization problems, as well as local single objective optimization problem.


LAB.CMO module automatically couples MANATEE simulation models with two optimization algorithms (no Matlab toolbox needed):

  • NSGA-II [1]: a global optimization tool for constrained multiobjective mixed variable optimization
  • SQP [2]: a local optimizer for local single objective optimization

The module first enables to define in a user-friendly way objective and constraint function(s), as well as MANATEE input design variables to be varied during optimization. User-defined constraints and response variables can be easily scripted. A preliminary sensitivity analysis is advised to determine the most relevant variables to be included in the optimization process and reduce computation time. At the end of the optimization, several high-end graphical post processing of the Pareto fronts are available. Multidimensional optimal solutions can also be visualized conveniently with the multidimentional design explorer.

3D Pareto Front
3D Pareto Front

Graphical post-processing

The complete list of plot commands is available on MANATEE plot commands webpage. The following visualizations are more particularly related to this module:

How to’s



The following articles illustrates the importance of vibroacoustic and electromagnetic design optimization in electrical machines:


[1Non-dominated Sorting Genetic Algorithm

[2Sequential Quadratic Programming

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