Increasing ocean plastic pollution is irreversibly harming ecosystems and human economic activities. We partner with a non-profit organization and use optimization to help clean up oceans from plastic faster. Specifically, we optimize the route of their plastic collection system in the ocean to maximize the quantity of plastic collected over time. We formulate the problem … Read more
In this paper we introduce a new algorithm for the k-Shortest Simple Paths (k-SSP) problem with an asymptotic running time matching the state of the art from the literature. It is based on a black-box algorithm due to Roddity and Zwick that solves at most 2k instances of the Second Shortest Simple Path (2-SSP) problem … Read more
We study the problem of inferring sparse time-varying Markov random fields (MRFs) with different discrete and temporal regularizations on the parameters. Due to the intractability of discrete regularization, most approaches for solving this problem rely on the so-called maximum-likelihood estimation (MLE) with relaxed regularization, which neither results in ideal statistical properties nor scale to the … Read more
Stochastic Dual Dynamic Programming (SDDP) is a widely used and fundamental algorithm for solving multistage stochastic optimization problems. Although SDDP has been frequently applied to solve risk-averse models with the Conditional Value-at-Risk (CVaR), it is known that the estimation of upper bounds is a methodological challenge, and many methods are computationally intensive. In practice, this … Read more
For multistage stochastic programming problems with stagewise independent uncertainty, dynamic programming algorithms calculate polyhedral approximations for the value functions at each stage. The SDDP algorithm provides piecewise linear lower bounds, in the spirit of the L-shaped algorithm, and corresponding upper bounds took a longer time to appear. One strategy uses the primal dynamic programming recursion … Read more
Optimizing interpretable policies for Markov Decision Processes (MDPs) can be computationally intractable for large-scale MDPs, e.g., for monotone policies, the optimal interpretable policy depends on the initial state distribution, precluding standard dynamic programming techniques. Previous work has proposed Monotone Policy Iteration (MPI) to produce a feasible solution for warm starting a Mixed Integer Linear Program … Read more
Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations, subject to additive noise, with the goal of minimizing a quadratic cost function for the state and control variables. In this work, … Read more
Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). In this paper we mainly concentrate on SP and SOC modelling approaches. In these frameworks there are natural situations when the considered problems are convex. Classical approach to sequential optimization … Read more
Multi-stage robust optimization, in which decisions are taken sequentially as new information becomes available about the uncertain problem parameters, is a very versatile yet computationally challenging paradigm for decision-making under uncertainty. In this paper, we propose a new model and solution approach for multi-stage robust mixed-integer programs, which may contain both continuous and discrete decisions … Read more
We introduce a column elimination procedure for the capacitated vehicle routing problem. Our procedure maintains a decision diagram to represent a relaxation of the set of feasible routes, over which we define a constrained network flow. The optimal solution corresponds to a collection of paths in the decision diagram and yields a dual bound. The … Read more