A Lagrangian Approach for Multiple Personalized Campaigns

The multicampaign assignment problem is a campaign model to overcome the multiple-recommendation problem that occurs when conducting several personalized campaigns simultaneously. In this paper, we propose a Lagrangian method for the problem. The original problem space is transformed to another simpler one by introducing Lagrange multipliers, which relax the constraints of the multicampaign assignment problem. When the Lagrangian vector is supplied, we can compute the optimal solution under this new environment in O(NK2) time, where N and K are the numbers of customers and campaigns, respectively. This is a linear-time method when the number of campaigns is constant. However, it is not easy to find a Lagrangian vector in exact accord with the given problem constraints. We thus combine the Lagrangian method with a genetic algorithm to find good near-feasible solutions. We verify the effectiveness of our evolutionary Lagrangian approach in both theoretical and experimental viewpoints. The suggested Lagrangian approach is practically attractive for large-scale real-world problems.