  The Constrained Minimal Supersymmetric Standard Model (CMSSM) is one of the
simplest and most widely-studied supersymmetric extensions to the standard
model of particle physics. Nevertheless, current data do not sufficiently
constrain the model parameters in a way completely independent of priors,
statistical measures and scanning techniques. We present a new technique for
scanning supersymmetric parameter spaces, optimised for frequentist profile
likelihood analyses and based on Genetic Algorithms. We apply this technique to
the CMSSM, taking into account existing collider and cosmological data in our
global fit. We compare our method to the MultiNest algorithm, an efficient
Bayesian technique, paying particular attention to the best-fit points and
implications for particle masses at the LHC and dark matter searches. Our
global best-fit point lies in the focus point region. We find many
high-likelihood points in both the stau co-annihilation and focus point
regions, including a previously neglected section of the co-annihilation region
at large m_0. We show that there are many high-likelihood points in the CMSSM
parameter space commonly missed by existing scanning techniques, especially at
high masses. This has a significant influence on the derived confidence regions
for parameters and observables, and can dramatically change the entire
statistical inference of such scans.
