Correlation length, isotropy and meta-stable states
Proceedings of the 16th annual international conference of the Center for Nonlinear Studies on Landscape paradigms in physics and biology : concepts, structures and dynamics: concepts, structures and dynamics
A tractable Walsh analysis of SAT and its implications for genetic algorithms
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
On the classification of NP-complete problems in terms of their correlation coefficient
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
On the landscape ruggedness of the quadratic assignment problem
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
SIAM Review
QAPLIB – A Quadratic Assignment ProblemLibrary
Journal of Global Optimization
Understanding elementary landscapes
Proceedings of the 10th annual conference on Genetic and evolutionary computation
A polynomial time computation of the exact correlation structure of k-satisfiability landscapes
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Partial neighborhoods of elementary landscapes
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Elementary landscape decomposition of the quadratic assignment problem
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Applying Elementary Landscape Analysis to Search-Based Software Engineering
SSBSE '10 Proceedings of the 2nd International Symposium on Search Based Software Engineering
Exact computation of the expectation curves of the bit-flip mutation using landscapes theory
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Elementary landscape decomposition of the test suite minimization problem
SSBSE'11 Proceedings of the Third international conference on Search based software engineering
EvoCOP'12 Proceedings of the 12th European conference on Evolutionary Computation in Combinatorial Optimization
Quasi-elementary landscapes and superpositions of elementary landscapes
LION'12 Proceedings of the 6th international conference on Learning and Intelligent Optimization
Problem understanding through landscape theory
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
Recent advances in problem understanding: changes in the landscape a year on
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
Fitness function distributions over generalized search neighborhoods in the q-ary hypercube
Evolutionary Computation
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A small number of combinatorial optimization problems have search spaces that correspond to elementary landscapes, where the objective function f is an eigenfunction of the Laplacian that describes the neighborhood structure of the search space. Many problems are not elementary; however, the objective function of a combinatorial optimization problem can always be expressed as a superposition of multiple elementary landscapes if the underlying neighborhood used is symmetric. This paper presents theoretical results that provide the foundation for algebraic methods that can be used to decompose the objective function of an arbitrary combinatorial optimization problem into a sum of subfunctions, where each subfunction is an elementary landscape. Many steps of this process can be automated, and indeed a software tool could be developed that assists the researcher in finding a landscape decomposition. This methodology is then used to show that the subset sum problem is a superposition of two elementary landscapes, and to show that the quadratic assignment problem is a superposition of three elementary landscapes.