An integer programming approach to optimal control problems in context-sensitive probabilistic Boolean networks

Kobayashi, Koichi; Hiraishi, Kunihiko

doi:10.1016/j.automatica.2011.01.035

Cited by 63 publications

(38 citation statements)

References 12 publications

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“…In the last decade, many results on control of BNs and PBNs have been obtained so far (see, e.g., [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]). Especially, analysis and control methods using the semi-tensor product (STP) method have been widely studied (see, e.g., [33][34][35][36][37][38][39][40][41][42][43]).…”

Section: Introductionmentioning

confidence: 99%

“…It is also significant to restrict topics and explain details. In this review paper, our previously proposed methods [23,24] in optimal external control of PBNs, i.e., a polynomial optimization approach and an integer programming approach are explained. Comparing our methods with other existing methods, the main advantage of our methods is that a relatively large-scale PBN can be handled.…”

Section: Introductionmentioning

confidence: 99%

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Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Kobayashi

Hiraishi

2017

Algorithms

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Abstract:Control of gene regulatory networks is one of the fundamental topics in systems biology. In the last decade, control theory of Boolean networks (BNs), which is well known as a model of gene regulatory networks, has been widely studied. In this review paper, our previously proposed methods on optimal control of probabilistic Boolean networks (PBNs) are introduced. First, the outline of PBNs is explained. Next, an optimal control method using polynomial optimization is explained. The finite-time optimal control problem is reduced to a polynomial optimization problem. Furthermore, another finite-time optimal control problem, which can be reduced to an integer programming problem, is also explained.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Kobayashi

Hiraishi

2017

Algorithms

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“…Therefore, it might be possible to extend BNs so that certain kinds of real values and/or non 0-1 integer values can be handled. In particular, by introducing real valued variables, it might be possible to cope with some uncertainty as suggested in [6], [22], [23], where uncertainty or stochasticity plays an important role in some biological systems. Such extensions of BNs along with efficient ILP formalizations might be useful and should be studied further.…”

Section: Discussionmentioning

confidence: 99%

“…It is to be noted that Chen et al, and Kobayashi and Hiraishi recently proposed ILP-based methods for control of probabilistic Boolean networks (PBNs) [6], [22], [23], where PBN is a probabilistic extension of BN. There are some similarities between our proposed method and their methods.…”

Section: Introductionmentioning

confidence: 99%

“…There are some similarities between our proposed method and their methods. However, a preliminary conference version of this paper [3] appeared earlier than their papers [6], [22], [23], and they did not treat attractor detection or control of attractors. It should also be noted that this version was considerably enhanced from [3]: additional heuristic is introduced to improve the efficiency for the case of K = 3, more detailed computational experiments are performed, and a proof of Theorem 1 is given.…”

Section: Introductionmentioning

confidence: 99%

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Integer Programming-Based Approach to Attractor Detection and Control of Boolean Networks

Akutsu

Zhao

Hayashida

et al. 2012

IEICE Trans. Inf. & Syst.

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SUMMARYThe Boolean network (BN) can be used to create discrete mathematical models of gene regulatory networks. In this paper, we consider three problems on BNs that are known to be NP-hard: detection of a singleton attractor, finding a control strategy that shifts a BN from a given initial state to the desired state, and control of attractors. We propose integer programming-based methods which solve these problems in a unified manner. Then, we present results of computational experiments which suggest that the proposed methods are useful for solving moderate size instances of these problems. We also show that control of attractors is Σ p 2 -hard, which suggests that control of attractors is harder than the other two problems.

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Bayesian selection probability estimation for probabilistic Boolean networks

Toyoda

2019

Asian Journal of Control

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A Bayesian approach to estimate selection probabilities of probabilistic Boolean networks is developed in this study. The concepts of inverse Boolean function and updatable set are introduced to specify states which can be used to update a Bayesian posterior distribution. The analysis on convergence of the posteriors is carried out by exploiting the combination of semi‐tensor product technique and state decomposition algorithm for Markov chain. Finally, some numerical examples demonstrate the proposed estimation algorithm.

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An integer programming approach to optimal control problems in context-sensitive probabilistic Boolean networks

Cited by 63 publications

References 12 publications

Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Integer Programming-Based Approach to Attractor Detection and Control of Boolean Networks

Bayesian selection probability estimation for probabilistic Boolean networks

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