Towards optimal neuronal wiring through estimation of distribution algorithms

One of the greatest challenges of our time is to understand brain functions. Our goal is to study the existence of an optimal neuronal design, defined as the one that has a minimum total wiring. Many researchers have studied the problem of optimal wiring in neuronal trees. Here we propose a new approach. We start from point clouds formed by the branching points of real neuronal trees and we search for the optimal forest from these point clouds. To do this, we formalize the problem as a forest of degree constrained minimum spanning trees (DCMST). Since the DCMST problem is NP-hard, we will try to solve it using estimation of distribution algorithms, particularly in permutation domains.

[1]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[2]  Alexander Mendiburu,et al.  A review on estimation of distribution algorithms in permutation-based combinatorial optimization problems , 2012, Progress in Artificial Intelligence.

[3]  Pedro Larrañaga,et al.  Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators , 1999, Artificial Intelligence Review.

[4]  Thang Nguyen Bui,et al.  An ant-based algorithm for finding degree-constrained minimum spanning tree , 2006, GECCO.

[5]  Gary D. Knott,et al.  A numbering system for binary trees , 1977, CACM.

[6]  Alexander Borst,et al.  One Rule to Grow Them All: A General Theory of Neuronal Branching and Its Practical Application , 2010, PLoS Comput. Biol..

[7]  Ichiro Semba Generation of Binary Trees from Stack Permutations , 1982 .

[8]  Andreas T. Ernst,et al.  Comparison of Algorithms for the Degree Constrained Minimum Spanning Tree , 2001, J. Heuristics.

[9]  Hermann Cuntz,et al.  A scaling law derived from optimal dendritic wiring , 2012, Proceedings of the National Academy of Sciences.

[10]  J. Kruskal On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[11]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .

[12]  Wamiliana Wamiliana SOLVING THE DEGREE CONSTRAINED MINIMUM SPANNING TREE PROBLEM USING TABU AND MODIFIED PENALTY SEARCH METHODS , 2005 .

[13]  R. Prim Shortest connection networks and some generalizations , 1957 .

[14]  J. A. Lozano,et al.  Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms (Studies in Fuzziness and Soft Computing) , 2006 .