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Anh Viet Do

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4 papers

2 author rows

IJCAI Conference 2023 Conference Paper

Diverse Approximations for Monotone Submodular Maximization Problems with a Matroid Constraint

Anh Viet Do
Mingyu Guo
Aneta Neumann
Frank Neumann

Finding diverse solutions to optimization problems has been of practical interest for several decades, and recently enjoyed increasing attention in research. While submodular optimization has been rigorously studied in many fields, its diverse solutions extension has not. In this study, we consider the most basic variants of submodular optimization, and propose two simple greedy algorithms, which are known to be effective at maximizing monotone submodular functions. These are equipped with parameters that control the trade-off between objective and diversity. Our theoretical contribution shows their approximation guarantees in both objective value and diversity, as functions of their respective parameters. Our experimental investigation with maximum vertex coverage instances demonstrates their empirical differences in terms of objective-diversity trade-offs.

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ECAI Conference 2023 Conference Paper

Optimizing Chance-Constrained Submodular Problems with Variable Uncertainties

Xiankun Yan
Anh Viet Do
Feng Shi 0003
Xiaoyu Qin 0001
Frank Neumann 0001

Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems, which capture a wide range of optimization problems with stochastic constraints. Previous studies considered submodular problems with stochastic knapsack constraints in the case where uncertainties are the same for each item that can be selected. However, uncertainty levels are usually variable with respect to the different stochastic components in real-world scenarios, and rigorous analysis for this setting is missing in the context of submodular optimization. This paper provides the first such analysis for this case, where the weights of items have the same expectation but different dispersion. We present greedy algorithms that can obtain a high-quality solution, i. e. , a constant approximation ratio to the given optimal solution from the deterministic setting. In the experiments, we demonstrate that the algorithms perform effectively on several chance-constrained instances of the maximum coverage problem and the influence maximization problem.

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NeurIPS Conference 2023 Conference Paper

Rigorous Runtime Analysis of MOEA/D for Solving Multi-Objective Minimum Weight Base Problems

Anh Viet Do
Aneta Neumann
Frank Neumann
Andrew Sutton

We study the multi-objective minimum weight base problem, an abstraction of classical NP-hard combinatorial problems such as the multi-objective minimum spanning tree problem. We prove some important properties of the convex hull of the non-dominated front, such as its approximation quality and an upper bound on the number of extreme points. Using these properties, we give the first run-time analysis of the MOEA/D algorithm for this problem, an evolutionary algorithm that effectively optimizes by decomposing the objectives into single-objective components. We show that the MOEA/D, given an appropriate decomposition setting, finds all extreme points within expected fixed-parameter polynomial time, in the oracle model. Experiments are conducted on random bi-objective minimum spanning tree instances, and the results agree with our theoretical findings. Furthermore, compared with a previously studied evolutionary algorithm for the problem GSEMO, MOEA/D finds all extreme points much faster across all instances.

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AAAI Conference 2021 Conference Paper

Pareto Optimization for Subset Selection with Dynamic Partition Matroid Constraints

Anh Viet Do
Frank Neumann

In this study, we consider the subset selection problems with submodular or monotone discrete objective functions under partition matroid constraints where the thresholds are dynamic. We focus on POMC, a simple Pareto optimization approach that has been shown to be effective on such problems. Our analysis departs from singular constraint problems and extends to problems of multiple constraints. We show that previous results of POMC’s performance also hold for multiple constraints. Our experimental investigations on random undirected maxcut problems demonstrate POMC’s competitiveness against the classical GREEDY algorithm with restart strategy.

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