A new Reference-based Algorithm based on Non-Euclidean Geometry for Multi-Stakeholder Media Planning*

This paper tackles the Campaign Allocation Problem of commercial Ads in TV breaks. The problem is NP-Hard and can be viewed as a multi-stakeholders multiobjective problem with highly competing objectives for different brands and numerous constraints. The expected solutions should be able to focus on, at least, one sub-part of the Pareto Optimal Front according to the decision maker's (DM) region of interest. Consequently, reference point-based many objective approaches could be a good option for solving this kind of problems. However, such approaches suffer from limitations in terms of diversity around the reference points, and other issues due to the fact that they consider the objective space as Euclidean. For the latter, recently a new algorithm called AGE-MOEA, by removing the assumption of Euclidean spaces, has proven to be the best in terms of diversity for a lot of many-objective problems in the literature. Nevertheless, AGE-MOEA has a high computational complexity and cannot be driven to a specific sub-parts of the Pareto Front. For that, we propose a novel approach, called RAGE-MOEA, that combines the AGE-MOEA diversity principles with the convergence elements of reference based approaches. Experiments have shown that this approach obtains better results in terms of compromise between diversity and convergence around the reference points than usual Reference-based methods (R-NSGA-II and R-NSGA-III) on literature benchmarks, and significantly better results for our industrial problem.