Dynamic Dual Bin Packing Using Fuzzy Objectives
نویسندگان
چکیده
This paper presents the use of genetic algorithms (GA) for solving the dual bin packing problem using fuzzy objectives. In bin packing problems, a list, L of items is to be packed into a minimum number of bins. In dual bin packing the items are packed into a maximum number of bins, assuring a minimum weight for each bin. We consider a class which we call dynamic dual bin packingg. Similar to the on-line algorithms, the items must be packed sequentially , however seeing more than one item at a time. The number of bins being packed at any time is xed. A bin is replaced by an empty one, as soon as it is lled. A GA is presented to solve this problem. The results show that the fuzzy packing scheme is essential to solving the problem , and due to the nature of the problem the GA behaves closely to that of a micro-GA.
منابع مشابه
Dual Inequalities for Stabilized Column Generation Revisited
Column generation (CG) models have several advantages over compact formulations, namely, they provide better LP bounds, may eliminate symmetry, and can hide non-linearities in their subproblems. However, users also encounter drawbacks in the form of slow convergency a.k.a. the tailing-off effect and the oscillation of the dual variables. Among different alternatives for stabilizing the CG proce...
متن کاملExtending Two-Dimensional Bin Packing Problem: Consideration of Priority for Items
In this paper a two-dimensional non-oriented guillotine bin packing problem is studied when items have different priorities. Our objective is to maximize the total profit which is total revenues minus costs of used bins and wasted area. A genetic algorithm is developed to solve this problem where a new coding scheme is introduced. To evaluate the performance of the proposed GA, first an upper b...
متن کاملA note on dual approximation algorithms for class constrained bin packing problems
In this paper we present a dual approximation scheme for the class constrained shelf bin packing problem. In this problem, we are given bins of capacity 1, and n items of Q different classes, each item e with class ce and size se. The problem is to pack the items into bins, such that two items of different classes packed in a same bin must be in different shelves. Items in a same shelf are pack...
متن کاملA survey of dual-feasible and superadditive functions
Dual-feasible functions are valuable tools that can be used to compute both lower bounds for different combinatorial problems and valid inequalities for integer programs. Several families of functions have been used in the literature. Some of them were defined explicitly, and others not. One of the main objectives of this paper is to survey these functions, and to state results concerning their...
متن کاملA Simple PTAS for the Dual Bin Packing Problem and Advice Complexity of Its Online Version
Recently, Renault (2016) studied the dual bin packing problem in the per-request advice model of online algorithms. He showed that given O(1/ǫ) advice bits for each input item allows approximating the dual bin packing problem online to within a factor of 1 + ǫ. Renault asked about the advice complexity of dual bin packing in the tape-advice model of online algorithms. We make progress on this q...
متن کامل