# Multi-objective near-optimal necessary conditions for multi-sectoral planning

## TL;DR

This paper develops multi-objective near-optimal necessary conditions for multi-sectoral planning, demonstrated through a Belgian energy system case study using an open-source model to analyze resource dependencies.

## Contribution

It extends epsilon-optimal spaces and necessary conditions from single to multi-objective optimization, providing a novel framework for multi-sectoral planning analysis.

## Key findings

- Belgium heavily depends on imported energy.
- No single resource is essential independently.
- Multi-objective analysis reveals resource interdependencies.

## Abstract

This paper extends the concepts of epsilon-optimal spaces and necessary conditions for near-optimality from single-objective to multi-objective optimisation. These notions are first presented for single-objective optimisation, and the mathematical formulation is adapted to address the multi-objective framework. Afterwards, we illustrate the newly developed methodology by conducting multi-sectoral planning of the Belgian energy system with an open-source model called EnergyScope TD. The cost and energy invested in the system are used as objectives. Optimal and efficient solutions for these two objectives are computed and analysed. These results are then used to obtain necessary conditions corresponding to the minimum amount of energy from different sets of resources, including endogenous and exogenous resources. This case study highlights the high dependence of Belgium on imported energy while demonstrating that no individual resource is essential on its own.