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...

Very large-scale neighborhood search (VLSNS) is a technique intensively used in single-objective optimization. However, there is almost no study of VLSNS for multiobjective optimization. We show in this paper that this technique is very efficient for the resolution of multiobjective combinatorial optimization problems. Two problems are considered: the multiobjective multidimensional knapsack pr...

Connectedness of efficient solutions is a powerful property in multiple objective combinatorial optimization since it allows the construction of the complete efficient set using neighborhood search techniques. In this paper we show that, however, most of the classical multiple objective combinatorial optimization problems do not possess the connectedness property in general, including, among ot...

We consider the following zero-sum game related to the knapsack problem. Given an instance of the knapsack problem, Alice chooses a knapsack solution and Bob chooses a cardinality k with knowing Alice’s solution. Then, Alice obtains a payoff equal to the ratio of the profit of the best k items in her solution to that of the best solution of size at most k. For α > 0, a knapsack solution is call...

Abstract We consider the product knapsack problem, which is variant of classical 0-1 problem where objective consists maximizing profits selected items. These are allowed to be positive or negative. present first fully polynomial-time approximation scheme for known weakly -hard. Moreover, we analyze quality achieved by a natural extension greedy procedure problem.

The Combinatorial problems are real world decision making problem with discrete and disjunctive choices. When these decision making problems involve more than one conflicting objective and constraint, it turns the polynomial time problem into NP-hard. Thus, the straight forward approaches to solve multi-objective problems would not give an optimal solution. In such case evolutionary based meta-...

Software maintenance is an important step in the software lifecycle. module clustering a HHMO_CF_GDA optimization problem involving several targets that require minimization of coupling and maximization cohesion. Moreover, multi-objective involves assembling specific group modules according to cluster criteria. classifies into different clusters enhance process. A structure with low high cohesi...

Rollout algorithms have enjoyed success across a variety of domains as heuristic solution procedures for stochastic dynamic programs (SDPs). However, because most rollout implementations are closely tied to specific problems, the visibility of advances in rollout methods is limited, thereby making it difficult for researchers in other fields to extract general procedures and apply them to diffe...

A common approach in multiobjective optimization is to perform the decision making process after the search process: first, a search heuristic approximates the set of Pareto-optimal solutions, and then the decision maker chooses an appropriate trade-off solution from the resulting approximation set. Both processes are strongly affected by the number of optimization criteria. The more objectives...