nonlinear knapsack problems (nkp) are the alternative formulation for the multiple-choice knapsack problems. a powerful approach for solving nkp is dynamic programming which may obtain the global op-timal solution even in the case of discrete solution space for these problems. despite the power of this solu-tion approach, it computationally performs very slowly when the solution space of the pr...

A special class of the knapsack problem is called the separable nonlinear knapsack problem. This problem has received considerable attention recently because of its numerous applications. Dynamic programming is one of the basic approaches for solving this problem. Unfortunately, the size of state-pace will dramatically increase and cause the dimensionality problem. In this paper, an efficient a...

A special class of the knapsack problem is called the separable nonlinear knapsack problem. This problem has received considerable attention recently because of its numerous applications. Dynamic programming is one of the basic approaches for solving this problem. Unfortunately, the size of state-pace will dramatically increase and cause the dimensionality problem. In this paper, an efficient a...

In mathematical programming, constraint qualifications are essential elements for duality theory. Recently, necessary and sufficient constraint qualifications for Lagrange duality results have been investigated. Also, surrogate duality enables one to replace the problem by a simpler one in which the constraint function is a scalar one. However, as far as we know, a necessary and sufficient cons...

Surrogate constraint methods have been embedded in a variety of mathematical programming applications over the past thirty years, yet their potential uses and underlying principles remain incompletely understood by a large segment of the optimization community. In a number of significant domains of combinatorial optimization, researchers have produced solution strategies without recognizing tha...

The Osorio and Glover (2003) use of dual surrogate analysis is exploited to fix variables in capacitated facility location problems (CFLP). The surrogate constraint is obtained by weighting the original problem constraints by their associated dual values in the LP relaxation. A known solution is used to convert the objective function in a constraint that forces the solution to be less or equal ...

A surrogate constraint is an inequality implied by the constraints of an integ~r program, and designed to capture useful information that cannot be extra~ted from the parent constraints individually but is nevertheless a consequepce of their conjunction. The use of such constraints as originally propo~ed by the author has recently been extended in an important way by EGON! BALAS and ARTHUR GEOF...

Surrogate constraint analysis has been applied effectively to a variety of combinatorial optimization problems, as a foundation for both exact and heuristic methods. In the heuristic domain, surrogate constraint methods are particularly suited to the creation of associated learning procedures and to the application of probabilistic decisions. We show that these approaches are natural and effect...

A preprocessing procedure that uses a local guided search defined in terms of a neighborhood structure to get a feasible solution (UB) and the Osorio and Glover[18, 20] exploiting of surrogate constraints and constraint pairing is applied to the traveling salesman problem. The surrogate constraint is obtained by weighting the original problem constraints by their associated dual values in the l...