Local v Global optimisation

*How do we know we have found the ‘optimal’ solution and not just a good one? *

An important difference between the PrimeSolve model and other providers that do offer a limited form of optimisation, is the use of global versus local optimisation. Optimization is the process of finding the point that minimises a function. More specifically:

A local minimum of a function is a point where the function value is smaller than or equal to the value at nearby points, but possibly greater than at a distant point. A global minimum is a point where the function value is smaller than or equal to the value at all other feasible points.

Generally, optimisation solvers find a local optimum. They find the optimum in the basin of attraction of the starting point. In contrast, the solver used by PrimeSolve is designed to search through more than one basin of attraction. In practice, what this means is that PrimeSolve has been built to scan for all optimal possibilities, whereas competitor optimisation calculators to date only scan for local optimal possibilities – meaning they can miss out on recommending the most optimal solution overall.

To ensure the global optimal solution is found, PrimeSolve has built customised calculation routines that enable us to define the problem type is defined as mixed integer (see appendix 2 for more detail), which ensure linearity is maintained.