# 3An Introduction to Metaheuristics

As we saw throughout the last two chapters, by attempting to optimize the workings of a supply chain, we will have the opportunity to deal with quite a few problems that crop up at different stages in the chain or at different points in the time horizon (short-term, medium-term, or long-term). The term “*optimize*”, behind which lie numerous logistic issues, is here meant in its mathematical sense. Each solution is assessed quantitatively by means of a function called objective, so that any two solutions can be compared. Optimizing the supply chain consists then in finding the best solution in relation to the objective we have thus defined. Metaheuristics are optimization techniques that are quite suitable as solving aids for logistic problems. First we will endeavor to give a definition of metaheuristics and to define the scope of their applications. Then we will deal with local search before introducing some metaheuristic procedures by separating individualbased methods from population-based ones.

## 3.1. Optimization problems

Generally an optimization problem can be defined as the problem of finding a solution *X** in a domain *S* that optimizes a function *H* often called cost function or objective function. More formally, let *X* = (*x*_{1},*x*_{2},…, *x*_{n}) be a vector made up of *n* real or integer variables, *S* the set of feasible solutions – i.e. verifying the set of constraints of the problem – and *H*: *S →* the objective function. An optimization problem consists ...