Multiple optima in local search
Journal of Algorithms
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A survey of very large-scale neighborhood search techniques
Discrete Applied Mathematics
Polynomial transformations and data-independent neighborhood functions
Discrete Applied Mathematics
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The paper proves that data-independent neighborhood functions with the smooth property (all strict local optima are global optima) for maximum 3-satisfiability (MAX 3-SAT) must contain all possible solutions for large instances. Data-independent neighborhood functions with the smooth property for 0-1 knapsack are shown to have size with the same order of magnitude as the cardinality of the solution space. Data-independent neighborhood functions with the smooth property for traveling salesman problem (TSP) are shown to have exponential size. These results also hold for certain polynomially solvable sub-problems of MAX 3-SAT, 0-1 knapsack and TSP.