Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Topology Optimization and Canonical Duality Method   Topology optimization for general materials is correctly formulated as a
bi-level knapsack problem, which is considered to be NP-hard in global
optimization and computer science. By using canonical duality theory (CDT)
developed by the author, the linear knapsack problem can be solved analytically
to obtain global optimal solution at each design iteration. Both uniqueness,
existence, and NP-hardness are discussed. The novel CDT method for general
topology optimization is refined and tested by both 2-D and 3-D benchmark
problems. Numerical results show that without using filter and any other
artificial technique, the CDT method can produce exactly 0-1 optimal density
distribution with almost no checkerboard pattern. Its performance and novelty
are compared with the popular SIMP and BESO approaches. Additionally, some
mathematical and conceptual mistakes in literature are explicitly pointed out.
A brief review on the canonical duality theory for solving a unified problem in
multi-scale nonconvex/discrete systems is given in Appendix.

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The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
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The categories of this paper are: supr-con