Sensitivity analysis in isotonic regression

AbstractThe isotonic regression problem is a specially structured quadratic programming problem which arises in various fields, such as production planning, inventory control, psychometry and statistics. The underlying graphical structure of the problem permits the development of easy and fast combinatorial solution algorithms. In this paper, we exploit this underlying structure, to develop efficient combinatorial methods for performing sensitivity analysis on the isotonic regression problem

Hard Knapsack Problems That Are Easy for Local Search

Chv'atal (1980) describes a class of zero-one knapsack problems provably difficult for branch and bound and dynamic programming algorithms. Chung et al. (1988) identifies a class of integer knapsack problems hard for branch and bound algorithms. We show that for both classes of problems local search provides optimal solutions quickly. Keywords : knapsack problem * local search * computational complexity Correspondence should be directed to the second author 1 Introduction Chv'atal (1980) describes a class of instances of zero-one knapsack problems due to Todd. ( We shall henceforth refer to these problems as the TODD class of problems. ) He shows that a wide class of algorithms --- including all based on branch and bound or dynamic programming --- find it difficult to solve problems in the TODD class. More precisely, the time required by these algorithms to solve instances of problems belonging to the TODD class grows as an exponential function of the problem parameters. Chung et a..

Calculation of Stability . . .

We present algorithms to calculate the stability radius of optimal or approximate solutions of binary programming problems with a min-sum or min{max objective function. Our algorithms run in polynomial time if the optimization problem itself is polynomially solvable. We also extend our results to the tolerance approach to sensitivity analysis

Sensitivity analysis of the greedy heuristic for binary knapsack problems

Greedy heuristics are a popular choice of heuristics when we have to solve a large variety of NP -hard combinatorial problems. In particular for binary knapsack problems, these heuristics generate good results. If some uncertainty exists beforehand regarding the value of any one element in the problem data, sensitivity analysis procedures can be used to know the tolerance limits within which the value may vary will not cause changes in the output. In this paper we provide a polynomial time characterization of such limits for greedy heuristics on two classes of binary knapsack problems, namely the 0-1 knapsack problem and the subset sum problem. We also study the relation between algorithms to solve knapsack problems and algorithms to solve their sensitivity analysis problems, the conditions under which the sensitivity analysis of the heuristic generates bounds for the toler-ance limits for the optimal solutions, and the empirical behavior of the greedy output when there is a change in the problem data.