Showing papers by "Tamás Terlaky published in 2021"
TL;DR: The neighborhood search mixed-integer linear optimization (NS-MILO) method is extended, which provides an effective heuristic solution approach based on exact solution methods for MILO problems and provides high-quality solutions for large-scale discrete MTSO problems in a reasonable time.
Abstract: Discrete multi-load truss sizing optimization (MTSO) problems are challenging to solve due to their combinatorial, nonlinear, and non-convex nature. This study highlights two important characteristics of the feasible set of MTSO problems considered here, in which force balance equations, Hooke’s law, yield stress, bound constraints on displacements, and local bucking are taken into account. Namely, we use the linear or bilinear nature of the problem to take advantage of re-scaling properties of both the problem’s design and auxiliary variables, as well as to extend the superposition principle to the case in which nonlinear stress constraints are considered. Taking advantage of these characteristics, we extend the neighborhood search mixed-integer linear optimization (NS-MILO) method (Shahabsafa et al. in SMO 63: 21–38, 2018), which provides an effective heuristic solution approach based on exact solution methods for MILO problems. Through extensive computational experiments, we demonstrate that the extended NS-MILO method provides high-quality solutions for large-scale discrete MTSO problems in a reasonable time.
6 citations
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TL;DR: In this article, the authors consider the M$k-colorable subgraph (M$k$CS) problem, in which the aim is to find an induced $k$-colorably subgraph with maximum cardinality in a given graph.
Abstract: Quantum devices can be used to solve constrained combinatorial optimization (COPT) problems thanks to the use of penalization methods to embed the COPT problem's constraints in its objective to obtain a quadratic unconstrained binary optimization (QUBO) reformulation of the COPT. However, the particular way in which this penalization is carried out, affects the value of the penalty parameters, as well as the number of additional binary variables that are needed to obtain the desired QUBO reformulation. In turn, these factors substantially affect the ability of quantum computers to efficiently solve these constrained COPT problems. This efficiency is key towards the goal of using quantum computers to solve constrained COPT problems more efficiently than with classical computers. Along these lines, we consider an important constrained COPT problem; namely, the maximum $k$-colorable subgraph (M$k$CS) problem, in which the aim is to find an induced $k$-colorable subgraph with maximum cardinality in a given graph. This problem arises in channel assignment in spectrum sharing networks, VLSI design, human genetic research, and cybersecurity. We derive two QUBO reformulations for the M$k$CS problem, and fully characterize the range of the penalty parameters that can be used in the QUBO reformulations. Further, one of the QUBO reformulations of the M$k$CS problem is obtained without the need to introduce additional binary variables. To illustrate the benefits of obtaining and characterizing these QUBO reformulations, we benchmark different QUBO reformulations of the M$k$CS problem by performing numerical tests on D-Wave's quantum annealing devices. These tests also illustrate the numerical power gained by using the latest D-Wave's quantum annealing device.
5 citations
01 Dec 2021
TL;DR: In this article, the authors explore search strategies for the design of parameterized quantum circuits and propose several optimization approaches including random search plus survival of the fittest, reinforcement learning with classical and hybrid quantum classical controllers, and Bayesian optimization as decision makers to design a quantum circuit in an automated way for a specific task such as multi-labeled classification over a dataset.
Abstract: This article explores search strategies for the design of parameterized quantum circuits. We propose several optimization approaches including random search plus survival of the fittest, reinforcement learning both with classical and hybrid quantum classical controllers, and Bayesian optimization as decision makers to design a quantum circuit in an automated way for a specific task such as multi-labeled classification over a dataset. We introduce nontrivial circuit architectures that are arduous to be hand-designed and efficient in terms of trainability. In addition, we introduce reuploading of initial data into quantum circuits as an option to find more general designs. We numerically show that some of the suggested architectures for the Iris dataset accomplish better results compared to the established parameterized quantum circuit designs in the literature. In addition, we investigate the trainability of these structures on the unseen dataset Glass. We report meaningful advantages over the benchmarks for the classification of the Glass dataset which supports the fact that the suggested designs are inherently more trainable.
5 citations
TL;DR: In this article, the authors study the parametric analysis of a second-order conic optimization problem, where the objective function is perturbed along a fixed direction, and characterize the notions of so-called invariancy set and nonlinearity interval, which serve as stability regions of the optimal partition.
Abstract: In this paper, using an optimal partition approach, we study the parametric analysis of a second-order conic optimization problem, where the objective function is perturbed along a fixed direction. We characterize the notions of so-called invariancy set and nonlinearity interval, which serve as stability regions of the optimal partition. We then propose, under the strict complementarity condition, an iterative procedure to compute a nonlinearity interval of the optimal partition. Furthermore, under primal and dual nondegeneracy conditions, we show that a boundary point of a nonlinearity interval can be numerically identified from a nonlinear reformulation of the parametric second-order conic optimization problem. Our theoretical results are supported by numerical experiments.
4 citations
TL;DR: It is proved that necessary conditions for kinematic stability can be used to speed up the solution of discrete TTDSO problems, and the MILO solver provides optimal or near optimal solutions for trusses with up to 990 bars.
Abstract: Kinematic stability is an often overlooked, but crucial, aspect when mathematical optimization models are developed for truss topology design and sizing optimization (TTDSO) problems. In this paper, we propose a novel mixed integer linear optimization (MILO) model for the TTDSO problem with discrete cross-sectional areas and Euler buckling constraints. Random perturbations of external forces are used to obtain kinematically stable structures. We prove that, by considering appropriate perturbed external forces, the resulting structure is kinematically stable with probability one. Furthermore, we show that necessary conditions for kinematic stability can be used to speed up the solution of discrete TTDSO problems. Using the proposed TTDSO model, the MILO solver provides optimal or near optimal solutions for trusses with up to 990 bars.
4 citations
TL;DR: This paper proposes formulating discrete ply-angle and thickness topology optimization problems as a mixed-integer second-order cone optimization (MISOCO) problem, and develops valid inequality constraints to tighten the continuous relaxation of the MISOCO reformulation.
Abstract: Discrete variable topology optimization problems are usually solved by using solid isotropic material with penalization (SIMP), genetic algorithms (GA), or mixed-integer nonlinear optimization (MINLO). In this paper, we propose formulating discrete ply-angle and thickness topology optimization problems as a mixed-integer second-order cone optimization (MISOCO) problem. Unlike SIMP and GA methods, MISOCO efficiently finds the problem’s globally optimal solution. Furthermore, in contrast with existing MISOCO formulations of discrete ply-angle optimization problems, our reformulations allow the structure to change topology, consider the more realistic Tsai–Wu stress yield criteria constraint, and eliminate checkerboard patterns using simple linear constraints. We address two types of discrete ply-angle and thickness problems: a structural mass minimization problem and a compliance optimization problem where the objective is to maximize the structural stiffness. For each element, one first chooses if the element is present or not in the structure. One can then choose the element’s ply-angle and thickness from a finite set of possibilities for the former case. The discrete design space for ply-angle and thickness is a result of manufacturing limitations. To improve the problem’s MISOCO solution approach, we develop valid inequality constraints to tighten the continuous relaxation of the MISOCO reformulation. We compare the performance of various MISOCO solvers: Gurobi, CPLEX, and MOSEK to solve the MISOCO reformulation. We also use BARON to solve the original MINLO formulations of the problems. Our results show that solving the MISOCO problem’s formulation using MOSEK is the most efficient solution approach.
1 citations