## Framework

LEAQ comes with a flexible and modular framework. Thus, each model or module can be called independently, allowing, for instance, simultaneous calls on a multiprocessor machine.

The integrated assessment model can be used in two modes:

**Simulation**: each module is called subsequently: first the energy model, then the emissions allocation, and finally the air quality model. This mode is used to assess various energy scenarios and their impacts in terms of air quality.**Optimization**: each module is called to provide information to the optimization engine, which can solve a meta-model written under the form of an optimization problem. Two classes of optimization problem are generally used:

- the
*cost-efficient approach*, where the energy model is constrained by a maximum level of air pollution. - the
*cost-benefit approach*, where the cost objective function includes both the economic cost related to the energy sector and the impact cost induced by the air quality, to determine the "optimal compromise" between economy and air quality.

- the

## Oracle-based optimization engine

**LEAQ** is built upon the Oracle-based optimization engine (Babonneau, 2004). It is an approach to solve convex optimization problems where the information pertaining to the function to be minimized and/or the feasible set takes the form of a linear outer approximation revealed by an oracle. A compatible **oracle** has been developed and integrated in the **LEAQ** model to deliver this information to the **OBOE** **engine**.

To solve a given optimization meta-model, the algorithm is the following:

- Ask for a
*"emission trajectory"*to the**OBOE engine** - Send this
*"emission trajectory"*to the**oracle**- If the "emission trajectory" are satisfaying the air quality constraint, run
**ETEM Luxembourg** - Otherwise, run
**AUSTAL2000-AYLTP**and some auxiliary runs to get the model sensitivity

- If the "emission trajectory" are satisfaying the air quality constraint, run
- The
**oracle**gives back the information useful for the**OBOE engine** - Ask again the
**OBOE engine**with the information- If the Test termination pass, the optimal
*"emission trajectory"*has been found - Otherwise, it returns a new
*"emission trajectory"*and, go to 2.

- If the Test termination pass, the optimal

The **OBOE engine** works only with a convex information, which is generally not the case with AUSTAL2000-AYLTP. The optimization engine integrates some routines which filter the information, in order than **OBOE** can find the solution in a space close to the convexity.