Local search for intractable problems (PS98, chapt. 19). Idea: for a feasible solution, define a neighborhood of feasible solutions Search neighborhood for a solution of lower cost; move to a better one (best or first-found)
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Link emphasizing proven optimality: GA Tech page
important contributions of Shen Lin (1965):
example, 48 cities: prob. 5%; with 100 runs,
prob. opt = 1 - .95^100 = 99.4%
weak neighborhoods are helped by good starts
led others to apply local search to other problems
Min-cost survivable networks (SWK 1969): find graph with given vertex-connectivity and min weight. X-change. Features: Starts and keeping feasible are key problems.
Offshore natural-gas pipelines (RFSSK70): find min cost delivery system for offshore natural gas.
Features: Costing is complicated and therefore expensive; Delta-change is a very small neighborhood.
Uniform graph partitioning (KL70): Split 2n nodes into two circuit boards so cost of inter-board edges is min. Stab for favorable sequence, accepting some down-turns (“variable-depth search”) until net is negative. (Applied to TSP in LK73.)