A multivariate optimization problem searches for the best values of several decision variables at once. Vehicle fuel economy illustrates the progression: optimize speed alone for a univariate problem, speed and acceleration for a bivariate problem, or speed, acceleration, and tire pressure for a multivariate problem. section 2.1.1
Classify a multivariate problem by the variables it contains and by the broader structure of its search:
- Use continuous optimization when variables take real values, integer or discrete optimization when they take whole-number values, and mixed-integer optimization when both types occur. section 2.1.1
- Treat ordered selections as permutations and unordered selections as combinations; repetition may be allowed or disallowed. section 2.1.1
- Further distinguish problems by objectives, constraints, objective-function landscape, linearity, operational role, search scope, speed, and determinism. section 2.5
Routing several cities
The traveling salesman problem chooses an ordered route through all 13 cities in the Greater Toronto Area, optimizing a criterion such as distance or travel time. The route is multivariate because many linked choices determine the candidate solution, and its ordered structure makes it a permutation-style problem. section 2.1.1
