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# MOP

Multi-Objective Problems (MOP)

\begin{align} \vec f(\vec x) \to \vec F \\ \text{subjected to} \\ \vec g(\vec x) & \le \vec 0 \\ \vec h(\vec x) & = \vec 0 \\ \vec x_l \le & \vec x \le \vec x_u \\ \vec x \in & R^n \\ \vec f: R^n \to R^m\\ \vec F \in (R \cup \{-\infty,\infty\})^m\\ \end{align}

(since v 0.38)
interalg
BSD Dmitrey Can handle global constrained MOPs with specifiable accuracies and both discrete and continuous variables. You can be 100% sure your result covers whole Pareto front according to the required tolerances on objective functions. If you want to speedup interalg on a MOP, first of all pay attention to its parameter maxActiveNodes and interalg MOP parameter sigma, and nProc (default: 1) for multi-CPU systems. Trajectories for different nProc should be same, but sometimes differ due to roundoff errors.

future plans for interalg include some speedup and better multiprocessing, possibility to start from a Pareto front obtained by another (inexact) MOP solver

• wikipedia webpage for multi-objective optimization
• NLP (nonlinear problems)
• MINLP (mixed-integer nonlinear problems)
• GLP (global nonlinear problems)