In this article, we propose a new algorithm for the resolution of mixed integer bi-level linear problem (MIBLP). The algorithm is based on the decomposition of the initial problem into the restricted master problem (RMP) and a series of problems named slave problems (SP). The proposed approach is based on Benders decomposition method where in each iteration a set of variables are fixed which ar...

Partially Observable Markov Decision Processes (POMDPs) are powerful models for planning under uncertainty in partially observable domains. However, computing optimal solutions for POMDPs is challenging because of the high computational requirements of POMDP solution algorithms. Several algorithms use a subroutine to prune dominated vectors in value functions, which requires a large number of l...

We consider stochastic influence maximization problems arising in social networks. In contrast to existing studies that involve greedy approximation algorithms with a 63% performance guarantee, our work focuses on solving the problem optimally. We propose a Benders decomposition algorithm to find the optimal solution to the problem with a finite number of samples. We show that the submodularity...

We consider convex optimization problems formulated using dynamic programming equations. Such problems can be solved using the Dual Dynamic Programming algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to select the most relevant Benders cuts. We propose a limited memory variant of Level 1 and show the convergence of DDP combined with the Territory algorithm,...

Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications, such as pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel problems which the upper level problem features some integer variables lower enjoys strong duality. We propose dedicated Benders decomposition method for solving prob...

This paper introduces a formulation and a solution methodology for the problem of optimizing the supply chain (or logistics network) of a manufacturing firm. The problem is modeled as a linear mixed-integer program with binary variables associated with design decisions such as location, product range assignment and transportation mode selection, and continuous variables representing the flows o...

With the introduction of alternative fuel vehicles into the transportation system, the refueling station location research has been touted in the literature. The flow refueling location problem (FRLP) locates p stations in order to maximize the flow volume that can be accommodated in a road network respecting the range limitations of the vehicles. This paper introduces the hybrid charging stati...