18,446 research outputs found

    Lexicographic optimization for the multi-container loading problem with open dimensions for a shoe manufacturer

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    Motivated by a real-world application, we present a multi-container loading problem with 3-open dimensions. We formulate it as a biobjective mixed-integer nonlinear program with lexicographic objectives in order to reflect the decision maker’s optimization priorities. The first objective is to minimize the number of containers, while the second objective is to minimize the volume of those containers. Besides showing the NP-hardness of this sequential optimization problem, we provide bounds for it which are used in the three proposed algorithms, as well as, on their evaluation when a certificate of optimality is not available. The first is an exact parametric-based approach to tackle the lexicographic optimization through the second objective of the problem. Nevertheless, given that the parametric programs correspond to large nonlinear mixed-integer optimizations, we present a heuristic that is entirely mathematical-programming based. The third algorithm enhances the solution quality of the heuristic. These algorithms are specifically tailored for the real-world application. The effectiveness and efficiency of the devised heuristics is demonstrated with numerical experiments

    Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control

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    Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e.g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start techniques. Following a line of work in approximate explicit MPC, the proposed learning-control algorithm, LNMS, gains computational advantage over MIP at little cost and is straightforward for practitioners to implement

    A parametric integer programming algorithm for bilevel mixed integer programs

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    We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and mixed integer bilevel problems. For the mixed integer case where the leader's variables are continuous, our algorithm also detects whether the infimum cost fails to be attained, a difficulty that has been identified but not directly addressed in the literature. In this case it yields a ``better than fully polynomial time'' approximation scheme with running time polynomial in the logarithm of the relative precision. For the pure integer case where the leader's variables are integer, and hence optimal solutions are guaranteed to exist, we present two algorithms which run in polynomial time when the total number of variables is fixed.Comment: 11 page

    A Finite-Time Cutting Plane Algorithm for Distributed Mixed Integer Linear Programming

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    Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class of optimization problems in a peer-to-peer network with no coordinator and with limited computation and communication capabilities. In the proposed algorithm, at each communication round, agents solve locally a small LP, generate suitable cutting planes, namely intersection cuts and cost-based cuts, and communicate a fixed number of active constraints, i.e., a candidate optimal basis. We prove that, if the cost is integer, the algorithm converges to the lexicographically minimal optimal solution in a finite number of communication rounds. Finally, through numerical computations, we analyze the algorithm convergence as a function of the network size.Comment: 6 pages, 3 figure

    Optimal management of bio-based energy supply chains under parametric uncertainty through a data-driven decision-support framework

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    This paper addresses the optimal management of a multi-objective bio-based energy supply chain network subjected to multiple sources of uncertainty. The complexity to obtain an optimal solution using traditional uncertainty management methods dramatically increases with the number of uncertain factors considered. Such a complexity produces that, if tractable, the problem is solved after a large computational effort. Therefore, in this work a data-driven decision-making framework is proposed to address this issue. Such a framework exploits machine learning techniques to efficiently approximate the optimal management decisions considering a set of uncertain parameters that continuously influence the process behavior as an input. A design of computer experiments technique is used in order to combine these parameters and produce a matrix of representative information. These data are used to optimize the deterministic multi-objective bio-based energy network problem through conventional optimization methods, leading to a detailed (but elementary) map of the optimal management decisions based on the uncertain parameters. Afterwards, the detailed data-driven relations are described/identified using an Ordinary Kriging meta-model. The result exhibits a very high accuracy of the parametric meta-models for predicting the optimal decision variables in comparison with the traditional stochastic approach. Besides, and more importantly, a dramatic reduction of the computational effort required to obtain these optimal values in response to the change of the uncertain parameters is achieved. Thus the use of the proposed data-driven decision tool promotes a time-effective optimal decision making, which represents a step forward to use data-driven strategy in large-scale/complex industrial problems.Peer ReviewedPostprint (published version
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