TY - JOUR
T1 - Maximum Satisfiability: Anatomy of the Fitness Landscape for a Hard Combinatorial Optimization Problem
AU - Tayaraninajaran, Mohammadhassan
AU - Prugel-Bennett, Adam
N1 - © 2011 IEEE - All rights reserved
PY - 2011/10/17
Y1 - 2011/10/17
N2 - The fitness landscape of MAX-3-SAT is investigated for random instances above the satisfiability phase transition. This paper includes a scaling analysis of the time to reach a local optimum, the number of local optima, the expected probability of reaching a local optimum as a function of its fitness, the expected fitness found by local search and the best fitness, the probability of reaching a global optimum, the size and relative positions of the global optima, the mean distance between the local and global optima, the expected fitness as a function of the Hamming distance from an optimum and their basins of attraction. These analyses show why the problem becomes hard for local search algorithms as the system size increases. The paper also shows how a recently proposed algorithm can exploit long-range correlations in the fitness landscape to improve on the state-of-the-art heuristic algorithms.
AB - The fitness landscape of MAX-3-SAT is investigated for random instances above the satisfiability phase transition. This paper includes a scaling analysis of the time to reach a local optimum, the number of local optima, the expected probability of reaching a local optimum as a function of its fitness, the expected fitness found by local search and the best fitness, the probability of reaching a global optimum, the size and relative positions of the global optima, the mean distance between the local and global optima, the expected fitness as a function of the Hamming distance from an optimum and their basins of attraction. These analyses show why the problem becomes hard for local search algorithms as the system size increases. The paper also shows how a recently proposed algorithm can exploit long-range correlations in the fitness landscape to improve on the state-of-the-art heuristic algorithms.
U2 - 10.1109/TEVC.2011.2163638
DO - 10.1109/TEVC.2011.2163638
M3 - Article
SN - 1089-778X
VL - 16
SP - 319
EP - 338
JO - IEEE Transactions on Evolutionary Computation
JF - IEEE Transactions on Evolutionary Computation
IS - 3
ER -