Gv. Loganathan et al., DESIGN HEURISTIC FOR GLOBALLY MINIMUM-COST WATER-DISTRIBUTION SYSTEMS, Journal of water resources planning and management, 121(2), 1995, pp. 182-192
Two standard test problems that are nonconvex with multiple local mini
ma are considered. An outer flow search-inner optimization procedure i
s proposed for choosing better local minima. Each pipe network is judi
ciously subjected to the outer-search scheme that chooses alternative
flow configurations to find an optimal flow division among pipes. An i
nner linear program is used for the design of least-cost diameters. Th
e algorithm can also be used for the optimal design of parallel expans
ion of existing networks. Because the problem is nonconvex, two global
-search schemes, MULTISTART and ANNEALING, are used to permit a local-
optimum-seeking method to migrate among various local minima. MULTISTA
RT selectively saturates portions of the feasible region to identify t
he local minima. ANNEALING iteratively improves the objective function
by finding successive better points, and, to escape out of a local mi
nimum, it exercises the metropolis step, which requires an occasional
acceptance of a worse point. The optimal solutions thus found have sig
nificantly smaller costs than the ones reported previously by other re
searchers.