Knapsack problems with sigmoid utilities: Approximation algorithms via hybrid optimization - Srivastava, Vaibhav; Bullo, Francesco (European journal of operational research, 2014)
•Root cause analysis of hardness of problems with sigmoid utility.•Design of hybrid algorithms merging continuous and discrete optimization.•Constant factor algorithm for knapsack problem with sigmoid utility.•Constant factor algorithm for generalized assignment problem with sigmoid utility.•Approximation algorithm for bin-packing problem with sigmoid utility. We study a class of non-convex optimization problems involving sigmoid functions. We show that sigmoid functions impart a combinatorial element to the optimization variables and make the global optimization computationally hard. We formulate versions of the knapsack problem, the generalized assignment problem and the bin-packing problem with sigmoid utilities. We merge approximation algorithms from discrete optimization with algorithms from continuous optimization to develop approximation algorithms for these NP-hard problems with sigmoid utilities.