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Register a new userA Method for Inferring Polymers Based on Linear Regression and Integer Programming
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Added by
Naveed Ahmed Azam
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property using both artificial neural networks and mixed integer linear programming. In this paper, we design a new method for inferring a polymer based on the framework. For this, we introduce a new way of representing a polymer as a form of monomer and define new descriptors that feature the structure of polymers. We also use linear regression as a building block of constructing a prediction function in the framework. The results of our computational experiments reveal a set of chemical properties on polymers to which a prediction function constructed with linear regression performs well. We also observe that the proposed method can infer polymers with up to 50 non-hydrogen atoms in a monomer form.
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Recently a novel framework has been proposed for designing the molecular structure of chemical compounds using both artificial neural networks (ANNs) and mixed integer linear programming (MILP). In the framework, we first define a feature vector $f(C)$ of a chemical graph $C$ and construct an ANN that maps $x=f(C)$ to a predicted value $eta(x)$ of a chemical property $pi$ to $C$. After this, we formulate an MILP that simulates the computation process of $f(C)$ from $C$ and that of $eta(x)$ from $x$. Given a target value $y^*$ of the chemical property $pi$, we infer a chemical graph $C^dagger$ such that $eta(f(C^dagger))=y^*$ by solving the MILP. In this paper, we use linear regression to construct a prediction function $eta$ instead of ANNs. For this, we derive an MILP formulation that simulates the computation process of a prediction function by linear regression. The results of computational experiments suggest our method can infer chemical graphs with around up to 50 non-hydrogen atoms.
Coarse-grained reconfigurable architectures (CGRAs) are programmable logic devices with large coarse-grained ALU-like logic blocks, and multi-bit datapath-style routing. CGRAs often have relatively restricted data routing networks, so they attract CAD mapping tools that use exact methods, such as Integer Linear Programming (ILP). However, tools that target general architectures must use large constraint systems to fully describe an architectures flexibility, resulting in lengthy run-times. In this paper, we propose to derive connectivity information from an otherwise generic device model, and use this to create simpler ILPs, which we combine in an iterative schedule and retain most of the exactness of a fully-generic ILP approach. This new approach has a speed-up geometric mean of 5.88x when considering benchmarks that do not hit a time-limit of 7.5 hours on the fully-generic ILP, and 37.6x otherwise. This was measured using the set of benchmarks used to originally evaluate the fully-generic approach and several more benchmarks representing computation tasks, over three different CGRA architectures. All run-times of the new approach are less than 20 minutes, with 90th percentile time of 410 seconds. The proposed mapping techniques are integrated into, and evaluated using the open-source CGRA-ME architecture modelling and exploration framework.
A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property using both artificial neural networks and mixed integer linear programming. In the framework, a chemical graph with a target chemical value is inferred as a feasible solution of a mixed integer linear program that represents a prediction function and other requirements on the structure of graphs. In this paper, we propose a procedure for generating other feasible solutions of the mixed integer linear program by searching the neighbor of output chemical graph in a search space. The procedure is combined in the framework as a new building block. The results of our computational experiments suggest that the proposed method can generate an additional number of new chemical graphs with up to 50 non-hydrogen atoms.
For a graph $G,$ the set $D subseteq V(G)$ is a porous exponential dominating set if $1 le sum_{d in D} left( 2 right)^{1-dist(d,v)}$ for every $v in V(G),$ where $dist(d,v)$ denotes the length of the shortest $dv$ path. The porous exponential dominating number of $G,$ denoted $gamma_e^*(G),$ is the minimum cardinality of a porous exponential dominating set. For any graph $G,$ a technique is derived to determine a lower bound for $gamma_e^*(G).$ Specifically for a grid graph $H,$ linear programing is used to sharpen bound found through the lower bound technique. Lower and upper bounds are determined for the porous exponential domination number of the King Grid $mathcal{K_n},$ the Slant Grid $mathcal{S_n},$ and the $n$-dimensional hypercube $Q_n.$
We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty allows us to prove the existence of minimizers of the integer optimal control problem. We introduce a local optimality concept for the problem, which arises from the infinite-dimensional perspective. In the case of a one-dimensional domain of the control function, we prove convergence of the iterates produced by our algorithm to points that satisfy first-order stationarity conditions for local optimality. We demonstrate the theoretical findings on a computational example.
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