Open Science Research Excellence

Open Science Index

Commenced in January 2007 Frequency: Monthly Edition: International Paper Count: 3

3
794
A New Heuristic Approach for Large Size Zero-One Multi Knapsack Problem Using Intercept Matrix
Abstract:

This paper presents a heuristic to solve large size 0-1 Multi constrained Knapsack problem (01MKP) which is NP-hard. Many researchers are used heuristic operator to identify the redundant constraints of Linear Programming Problem before applying the regular procedure to solve it. We use the intercept matrix to identify the zero valued variables of 01MKP which is known as redundant variables. In this heuristic, first the dominance property of the intercept matrix of constraints is exploited to reduce the search space to find the optimal or near optimal solutions of 01MKP, second, we improve the solution by using the pseudo-utility ratio based on surrogate constraint of 01MKP. This heuristic is tested for benchmark problems of sizes upto 2500, taken from literature and the results are compared with optimum solutions. Space and computational complexity of solving 01MKP using this approach are also presented. The encouraging results especially for relatively large size test problems indicate that this heuristic can successfully be used for finding good solutions for highly constrained NP-hard problems.

2
8097
A New Heuristic Approach for the Large-Scale Generalized Assignment Problem
Abstract:

This paper presents a heuristic approach to solve the Generalized Assignment Problem (GAP) which is NP-hard. It is worth mentioning that many researches used to develop algorithms for identifying the redundant constraints and variables in linear programming model. Some of the algorithms are presented using intercept matrix of the constraints to identify redundant constraints and variables prior to the start of the solution process. Here a new heuristic approach based on the dominance property of the intercept matrix to find optimal or near optimal solution of the GAP is proposed. In this heuristic, redundant variables of the GAP are identified by applying the dominance property of the intercept matrix repeatedly. This heuristic approach is tested for 90 benchmark problems of sizes upto 4000, taken from OR-library and the results are compared with optimum solutions. Computational complexity is proved to be O(mn2) of solving GAP using this approach. The performance of our heuristic is compared with the best state-ofthe- art heuristic algorithms with respect to both the quality of the solutions. The encouraging results especially for relatively large size test problems indicate that this heuristic approach can successfully be used for finding good solutions for highly constrained NP-hard problems.

1
7847
Flexible Heuristics for Project Scheduling with Limited Resources
Authors:
Abstract:
Resource-constrained project scheduling is an NPhard optimisation problem. There are many different heuristic strategies how to shift activities in time when resource requirements exceed their available amounts. These strategies are frequently based on priorities of activities. In this paper, we assume that a suitable heuristic has been chosen to decide which activities should be performed immediately and which should be postponed and investigate the resource-constrained project scheduling problem (RCPSP) from the implementation point of view. We propose an efficient routine that, instead of shifting the activities, extends their duration. It makes it possible to break down their duration into active and sleeping subintervals. Then we can apply the classical Critical Path Method that needs only polynomial running time. This algorithm can simply be adapted for multiproject scheduling with limited resources.
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