Selecting an optimum combination of items from a set of items, known as Knapsack Problems, is an important issue in the decision making domain. In this paper, a new approach is developed to solve a Multiple Attribute Knapsack Problem (MAKP) in which each combination of items is evaluated using some quantitative and qualitative attributes. The assumed qualitative attributes cannot be measured by a mathematical formulation but by a DM/expert. In this paper, a Genetic Algorithm (GA) model has been developed to generate different combinations as the sequential population of the GA model. To rate the qualitative attributes for each chromosome (or combination) in the population, a Neural Network (NN) model has been developed. The ratings (or scores) resulted from quantitative attributes (by NN) and qualitative attributes (by mathematical formulation) for each chromosome form a row of a decision matrix. Having the decision matrix and known weights of attributes, the combinations in each population are ranked by applying a MADM model. The ranks obtained for each chromosome shows the fitness of that chromosome. Using the GA model, the best combination is achieved. The results of conducted experiments show the capability of the proposed approach to deal with MAKP Problems.

In this paper, a new approximate method is presented to solve multi-dimensional Knapsack Problem by using multiple criteria decision making (MCDM). In order to, initially efficiency values for every item is calculated then items are ranked by using MCDM. Finally, items are selected in according to their rank.

In this paper, the researchers have proposed a multi-dimensional Knapsack model for project capital budgeting Problem in uncertain situation which has been modeled through fuzzy sets. The optimistic and pessimistic situations were considered and associated deterministic models were yielded. Numerical example has been supplied toillustrate the performance of proposed model. The results were promising in the sense of helping the decision makers.

This paper develops an approach to solve 0-1 multiple attribute Knapsack Problem (MAKP) in which some objectives are qualitative. The approach consists of two modules. The first module is a fuzzy expert system that evaluates the qualitative objectives. Acting as a framework, the second module generates the different combinations and finds the (near) optimal solution using a genetic algorithm model. The results of conducted experiments show the capability of proposed approach to deal with MAKP Problems.

Many portfolio optimization Problems deal with allocation of assets which carry a relatively high market price. Therefore, it is necessary to determine the integer value of assets when we deal with portfolio optimization. In addition, one of the main concerns with most portfolio optimization is associated with the type of constraints considered in different models. In many cases, the resulted Problem formulations do not yield in practical solutions. Therefore, it is necessary to apply some managerial decisions in order to make the results more practical. This paper presents a portfolio optimization based on an improved Knapsack Problem with the cardinality, floor and ceiling, budget, class, class limit and pre-assignment constraints for asset allocation. To handle the uncertainty associated with different parameters of the proposed model, we use robust optimization techniques. The model is also applied using some realistic data from US stock market. Genetic algorithm is also provided to solve the Problem for some instances.