-------------------------------- Constraint Optimization Problems -------------------------------- This document defines COPs (Constraint Optimization Problems) and introduces the G-problem benchmark. COPs ----------------- A constrained optimization problem (COP) for numerical and continuous quantities in :math:`\mathbb{R}^d` is defined as: .. raw:: latex html \[ Min \quad f(\vec{x}), \quad \vec{x} \in [\vec{a},\vec{b}] \subset \mathbb{R}^d \] .. raw:: latex html \[ \text{subject to} \quad g_{i}(\vec{x}) \leq 0, \quad i=1,2,\ldots,m \] .. raw:: latex html $$ \quad\qquad\qquad h_{j}(\vec{x}) = 0, \quad j=1,2,\ldots,r $$ G-problem benchmark -------------------------------- The G-problem benchmark suite originates from a CEC 2006 competition [LiangRunar]_. It is a set of 24 constrained optimization problems (COPs, G-problems) G01, ..., G24 with various properties like dimension, number of equality / inequality constraints, feasibility ratio, etc. Eight of the 24 COPs have equality constraints. Although these problems were introduced as a suite in the technical report [LiangRunar]_ at CEC 2006, many of them have been used by different authors earlier. The G-problems are available in **SACOBRA_Py** as objects of class ``GCOP``: .. autoclass:: gCOP.GCOP .. [LiangRunar] J. Liang, T. P. Runarsson, E. Mezura-Montes, M. Clerc, P. Suganthan, C. C. Coello, and K. Deb, “Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization,” Journal of Applied Mechanics, vol. 41, p. 8, 2006. `http://www.lania.mx/~emezura/util/files/tr_cec06.pdf `_