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Learning automata-based partitioning algorithms for stochastic grouping problems with non-equal partition sizes

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Abstract

It is very fascinating that the principles of Artificial Intelligence, that were proposed many decades ago, have remained to be the foundations of many of the modern-day techniques, and a brief summary of these principles is given in the paper itself. While this truism is valid for problem solving and game playing, in the context of this paper, we emphasize that it is also pertinent for the so-called partitioning problems. In this paper, we consider the general partitioning problem that has been studied for decades. Unlike the heuristic and search strategies, our attention focuses on learning automata (LA) and reinforcement learning methods, and their powerful ability to solve problems in stochastic environments. These render the latter tools to be applicable to various complex tasks. As we shall explain, LA have been employed for partitioning, and in particular, the paradigm of Object Migration Automata (OMA) has offered state-of-the-art adaptive methods for solving grouping and partitioning problems. However, because the number of possible partitions is combinatorially exponential, and of the NP-hardness of the underlying tasks, the existing state-of-the-art OMA algorithms can only solve problems of equal-sized groups. To resolve this, in this paper, we propose two new OMA variants that can solve both equally and unequally sized partitioning problems. The key here is to provide additional information to the algorithms, and in doing so, to expand the solution space. The first variant, the Greatest Common Divisor OMA (GCD-OMA), relaxes the constraint of having equally sized groups by mapping the actions onto a larger state space, and thus permitting it to solve problems where the group sizes have a GCD that is greater than unity. Subsequently, we propose a second variant named the Partition Size Required OMA (PSR-OMA) to make the algorithm more versatile. The PSR-OMA can handle groups of arbitrary sizes when the group sizes are known a priori. We demonstrate the proposed algorithms’ strength in solving stochastic grouping problems through extensive simulations, even with high noise levels. The GCD-OMA and the PSR-OMA represent the current state-of-the-art when it concerns resolving the extremely complex problem of partitioning and can be used in any of the numerous applications in which the OMA itself has been utilized .

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Notes

  1. The Pursuit OMA (POMA) is another version of the OMA. However, similar to the OMA variant, it suffers from a Deadlock situation. Therefore, the PEOMA is preferred over the POMA [20].

  2. Preliminary abridged versions of some of the results in this paper were first reported by Omslandseter et al. [13, 14] These papers contained significantly reduced versions of the algorithmic concepts and experimental results presented here.

  3. We emphasize that the results presented here are merely representative of all the experiments done in the course of this research. More detailed results are included in the thesis of the Second Author xx (Anonymized) and are abridged here in the interest of space and brevity.

  4. “Noise” is the proportion of queries presented to the automaton that do not belong together in \(\varDelta ^*\).

  5. The experimental results concerning the TPEOMA are currently being compiled for a separate publication, because it details a scheme in which one can create the partitioning with both real and “artificial” data, which is a fascinating concept.

  6. We emphasize that hyper-tuning of the \(\kappa\) and \(\tau\) parameter could have yielded even better results than those presented in this paper.

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Authors and Affiliations

  1. School of Computer Science, Carleton University, Ottawa, K1S 5B6, Canada

    B. John Oommen

  2. Department of Information and Communication Technology, University of Agder, Jon Lilletuns vei, 4879, Grimstad, Norway

    B. John Oommen, Rebekka Olsson Omslandseter & Lei Jiao

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  1. B. John Oommen
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  2. Rebekka Olsson Omslandseter
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  3. Lei Jiao
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Correspondence to B. John Oommen.

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Oommen, B.J., Omslandseter, R.O. & Jiao, L. Learning automata-based partitioning algorithms for stochastic grouping problems with non-equal partition sizes. Pattern Anal Applic 26, 751–772 (2023). https://doi.org/10.1007/s10044-023-01131-5

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