53 research outputs found
New Characterizations and Efficient Local Search for General Integer Linear Programming
Integer linear programming (ILP) models a wide range of practical
combinatorial optimization problems and has significant impacts in industry and
management sectors. This work proposes new characterizations of ILP with the
concept of boundary solutions. Motivated by the new characterizations, we
develop an efficient local search solver, which is the first local search
solver for general ILP validated on a large heterogeneous problem dataset. We
propose a new local search framework that switches between three modes, namely
Search, Improve, and Restore modes. We design tailored operators adapted to
different modes, thus improving the quality of the current solution according
to different situations. For the Search and Restore modes, we propose an
operator named tight move, which adaptively modifies variables' values, trying
to make some constraint tight. For the Improve mode, an efficient operator lift
move is proposed to improve the quality of the objective function while
maintaining feasibility. Putting these together, we develop a local search
solver for integer linear programming called Local-ILP. Experiments conducted
on the MIPLIB dataset show the effectiveness of our solver in solving
large-scale hard integer linear programming problems within a reasonably short
time. Local-ILP is competitive and complementary to the state-of-the-art
commercial solver Gurobi and significantly outperforms the state-of-the-art
non-commercial solver SCIP. Moreover, our solver establishes new records for 6
MIPLIB open instances. The theoretical analysis of our algorithm is also
presented, which shows our algorithm could avoid visiting unnecessary regions
and also maintain good connectivity of targeted solutions.Comment: 36 pages, 2 figures, 7 table
Unified Human-Scene Interaction via Prompted Chain-of-Contacts
Human-Scene Interaction (HSI) is a vital component of fields like embodied AI
and virtual reality. Despite advancements in motion quality and physical
plausibility, two pivotal factors, versatile interaction control and the
development of a user-friendly interface, require further exploration before
the practical application of HSI. This paper presents a unified HSI framework,
UniHSI, which supports unified control of diverse interactions through language
commands. This framework is built upon the definition of interaction as Chain
of Contacts (CoC): steps of human joint-object part pairs, which is inspired by
the strong correlation between interaction types and human-object contact
regions. Based on the definition, UniHSI constitutes a Large Language Model
(LLM) Planner to translate language prompts into task plans in the form of CoC,
and a Unified Controller that turns CoC into uniform task execution. To
facilitate training and evaluation, we collect a new dataset named ScenePlan
that encompasses thousands of task plans generated by LLMs based on diverse
scenarios. Comprehensive experiments demonstrate the effectiveness of our
framework in versatile task execution and generalizability to real scanned
scenes. The project page is at https://github.com/OpenRobotLab/UniHSI .Comment: A unified Human-Scene Interaction framework that supports versatile
interactions through language commands.Project URL:
https://xizaoqu.github.io/unihsi/ . Code:
https://github.com/OpenRobotLab/UniHS
Two Weighting Local Search for Minimum Vertex Cover
Minimum Vertex Cover (MinVC) is a well known NP-hard combinatorial optimization problem, and local search has been shown to be one of the most effective approaches to this problem. State-of-the-art MinVC local search algorithms employ edge weighting techniques and prefer to select vertices with higher weighted score. These algorithms are not robust and especially have poor performance on instances with structures which defeat greedy heuristics. In this paper, we propose a vertex weighting scheme to address this shortcoming, and combine it within the current best MinVC local search algorithm NuMVC, leading to a new algorithm called TwMVC. Our experiments show that TwMVC outperforms NuMVC on the standard benchmarks namely DIMACS and BHOSLIB. To the best of our knowledge, TwMVC is the first MinVC algorithm that attains the best known solution for all instances in both benchmarks. Further, TwMVC shows superiority on a benchmark of real-world networks
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