100 research outputs found
Genetic Transfer or Population Diversification? Deciphering the Secret Ingredients of Evolutionary Multitask Optimization
Evolutionary multitasking has recently emerged as a novel paradigm that
enables the similarities and/or latent complementarities (if present) between
distinct optimization tasks to be exploited in an autonomous manner simply by
solving them together with a unified solution representation scheme. An
important matter underpinning future algorithmic advancements is to develop a
better understanding of the driving force behind successful multitask
problem-solving. In this regard, two (seemingly disparate) ideas have been put
forward, namely, (a) implicit genetic transfer as the key ingredient
facilitating the exchange of high-quality genetic material across tasks, and
(b) population diversification resulting in effective global search of the
unified search space encompassing all tasks. In this paper, we present some
empirical results that provide a clearer picture of the relationship between
the two aforementioned propositions. For the numerical experiments we make use
of Sudoku puzzles as case studies, mainly because of their feature that
outwardly unlike puzzle statements can often have nearly identical final
solutions. The experiments reveal that while on many occasions genetic transfer
and population diversity may be viewed as two sides of the same coin, the wider
implication of genetic transfer, as shall be shown herein, captures the true
essence of evolutionary multitasking to the fullest.Comment: 7 pages, 6 figure
Softened Symbol Grounding for Neuro-symbolic Systems
Neuro-symbolic learning generally consists of two separated worlds, i.e.,
neural network training and symbolic constraint solving, whose success hinges
on symbol grounding, a fundamental problem in AI. This paper presents a novel,
softened symbol grounding process, bridging the gap between the two worlds, and
resulting in an effective and efficient neuro-symbolic learning framework.
Technically, the framework features (1) modeling of symbol solution states as a
Boltzmann distribution, which avoids expensive state searching and facilitates
mutually beneficial interactions between network training and symbolic
reasoning;(2) a new MCMC technique leveraging projection and SMT solvers, which
efficiently samples from disconnected symbol solution spaces; (3) an annealing
mechanism that can escape from %being trapped into sub-optimal symbol
groundings. Experiments with three representative neuro symbolic learning tasks
demonstrate that, owining to its superior symbol grounding capability, our
framework successfully solves problems well beyond the frontier of the existing
proposals.Comment: Published as a conference paper at ICLR 2023. Code is available at
https://github.com/SoftWiser-group/Soften-NeSy-learnin
Solving Sudoku with Ant Colony Optimization
In this paper we present a new algorithm for the well-known and computationally-challenging Sudoku puzzle game. Our Ant Colony Optimization-based method significantly out-performs the state-of-the-art algorithm on the hardest, large instances of Sudoku. We provide evidence that – compared to traditional backtracking methods – our algorithm offers a much more efficient search of the solution space, and demonstrate the utility of a novel anti-stagnation operator. This work lays the foundation for future work on a general-purpose puzzle solver, and establishes Japanese pencil puzzles as a suitable platform for benchmarking a wide range of algorithms
Analyzing the effectiveness of quantum annealing with meta-learning
The field of Quantum Computing has gathered significant popularity in recent years and a large number of papers have studied its effectiveness in tackling many tasks. We focus in particular on Quantum Annealing (QA), a meta-heuristic solver for Quadratic Unconstrained Binary Optimization (QUBO) problems. It is known that the effectiveness of QA is dependent on the task itself, as is the case for classical solvers, but there is not yet a clear understanding of which are the characteristics of a problem that make it difficult to solve with QA. In this work, we propose a new methodology to study the effectiveness of QA based on meta-learning models. To do so, we first build a dataset composed of more than five thousand instances of ten different optimization problems. We define a set of more than a hundred features to describe their characteristics and solve them with both QA and three classical solvers. We publish this dataset online for future research. Then, we train multiple meta-models to predict whether QA would solve that instance effectively and use them to probe which features with the strongest impact on the effectiveness of QA. Our results indicate that it is possible to accurately predict the effectiveness of QA, validating our methodology. Furthermore, we observe that the distribution of the problem coefficients representing the bias and coupling terms is very informative in identifying the probability of finding good solutions, while the density of these coefficients alone is not enough. The methodology we propose allows to open new research directions to further our understanding of the effectiveness of QA, by probing specific dimensions or by developing new QUBO formulations that are better suited for the particular nature of QA. Furthermore, the proposed methodology is flexible and can be extended or used to study other quantum or classical solvers
SudoQ -- a quantum variant of the popular game
We introduce SudoQ, a quantum version of the classical game Sudoku. Allowing
the entries of the grid to be (non-commutative) projections instead of
integers, the solution set of SudoQ puzzles can be much larger than in the
classical (commutative) setting. We introduce and analyze a randomized
algorithm for computing solutions of SudoQ puzzles. Finally, we state two
important conjectures relating the quantum and the classical solutions of SudoQ
puzzles, corroborated by analytical and numerical evidence.Comment: Python code and examples available at
https://github.com/inechita/Sudo
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