# Understanding Phase Transitions with Local Optima Networks: Number Partitioning as a Case Study The dataset contains landscape data for "Understanding Phase Transitions with Local Optima Networks: Number Partitioning as a Case Study", G. Ochoa, N. Veerapen, F. Daolio, M. Tomassini. The 17th European Conference on Evolutionary Computation in Combinatorial Optimisation (EvoCOP 2017), 19-21 April 2017, Amsterdam, The Netherlands. The dataset describes the network structure of the local optima networks (LON) for Number Partitioning Problem (NPP) instances of size 10, 15 and 20, and with values of parameter k from 0.4 to 1.2 in steps of 0.1. The networks are built through full enumeration using code adapted from: - Local Optima Networks of the Quadratic Assignment Problem. F. Daolio, S. Verel, G. Ochoa, M. Tomassini. 2010 IEEE Congress on Evolutionary Computation (CEC 2010), pp. 1-8, 2010. - Communities of minima in local optima networks of combinatorial spaces. F. Daolio, M. Tomassini, S. Verel, G. Ochoa. Physica A: Statistical Mechanics and its Applications 390(9), pp. 1684-1694, 2011. The code may be downloaded from http://www-lisic.univ-littoral.fr/~verel/RESEARCH/codeLON-0.1.zip ## Naming convention Files are split into folders based on size (size10, size15, size20). Each file name within follows the npp----.zip pattern, where - is the size of the instance - is the value of the k parameter - is the seed used to generate the instance - is the number of bit-flips that define the neighbourhood structure - is 0 if distances less than are used and 1 if only is used. In this paper, only 0 is used. Each zip file contains four files: dat - contains the instance data edges - contains edge data nodes - contains nodes data fitness - contains fitness data for all solutions in the search space ## File structure ### dat file The first line contains a number indicating the size. The second line contains the numbers that need to be partitioned. ### edges file The file contains 3 columns representing the edges of the LON: 1 - node id of one end of the edge 2 - node id of the other end of the edge 3 - transition probability of the edge ### nodes file The file contains 3 columns representing the nodes of the LON: 1 - node id 2 - node fitness 3 - size of the attraction basin represented by the node, fractions are present when solutions in the basin also belong to another ### fitness file The file contains at least 8 columns representing the solutions: 1 - solution integer representation 2 - solution binary representation 3 - fitness 4 - neutral network id, corresponds to a node id if the neutral network consists of local optima 5 - size of the neutral network 6 - number of doors in the neutral network 7 - id of the node (basin) the solution belongs to 8 - probability of ending in the node (basin) of the previous column Any further column pairs repeat columns 7 and 8 when a solution is part of more than 1 basin.