Variable neighborhood programming for symbolic regression
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Variable neighborhood programming for symbolic regression Souhir Elleuch1 · Bassem Jarboui2 · Nenad Mladenovic3 · Jun Pei4 Received: 31 March 2020 / Accepted: 28 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In the field of automatic programming (AP), the solution of a problem is a program, which is usually represented by an AP-tree. A tree is built using functional and terminal nodes. For solving AP problems, we propose a new neighborhood structure that adapts the classical “elementary tree transformation” (ETT) into this specific AP-tree. The ETT is the process of removing an edge and adding another one to obtain a new feasible tree. Experimental comparison with reduced VNP, i.e., with VNP without local search, genetic programming, and artificial bee colony programming shows clearly advantages of the new proposed BVNP method, in terms of speed of convergence and computational stability. Keywords Artificial intelligence · Automatic programming · Variable neighborhood programming · Elementary tree transformation · Symbolic regression
1 Introduction 1.1 Problem In the fields of Artificial Intelligence (AI) and Machine learning, there is a fast-growing interest in developing techniques to solve problems automatically. The term Automatic Programming (AP) indicates that programs are automatically generated without human intervention. The solution to an AP problem is a program that is usually rep-
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Souhir Elleuch [email protected]
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Department of Management Information Systems and Production Management, College of Business and Economics, Qassim University, Buraydah, Saudi Arabia
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Higher Colleges of Technology, Abu Dhabi, UAE
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Research Center on Digital Supply Chain and Operations Management, Department of Industrial and Systems Engineering, Khalifa University, Abu Dhabi, UAE
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School of Management, Hefei University of Technology, Hefei, China
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resented by the tree, that we will call an AP-tree. Such a tree has different types of nodes, i.e., some nodes present operations and some other variables and constants. An illustrative example will be given in Sect. 2.1. 1.2 Literature Genetic programming (GP) is the well-known technique in AP. It is based on Genetic Algorithm (GA) operators (Koza [1]), performed at AP-tree. GP is used in many AI fields, such as Symbolic regression [2–4], Forecasting [5,6], Data-mining [7], and Classification [8]. There are many GP based methods that include local searches [6,9]. Good results are obtained by using such methods for solving the Symbolic regression problem [9] and Energy consumption forecasting problem [6]. In [10], Automatic Programming via Iterated Local Search (APRILS) is proposed, where the local search is presented by a selection of random solutions obtained by mutation. Recently, a new AP method, called Reduced Variable Neighborhood Programming (RVNP), based on the Variable Neighborhood Search (VNS) meta-heuristic [11] was introduced by Elleuch et al. [12]. In fact, the neighborhood of a program i
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