Knapsack problems — An overview of recent advances. Part II: Multiple, multidimensional, and quadratic knapsack problems
نویسندگان
چکیده
After the seminal books by Martello and Toth (1990) Kellerer, Pferschy, Pisinger (2004), knapsack problems became a classical rich research area in combinatorial optimization. The purpose of this survey, structured two parts, is to cover developments appeared field after publication latter volume. Part I treats single their variants. present II covers multiple, multidimensional, quadratic problems, as well other relevant variants, such as, e.g., multiobjective online versions.
منابع مشابه
Upper Bounds for Large Scale Integer Quadratic Multidimensional Knapsack Problems
We consider the separable quadratic multi-knapsack problem (QMKP) which consists in maximizing a concave separable quadratic integer function subject to m linear capacity constraints. The aim of this paper is to develop an effective method to compute an upper bound for (QMKP) from a surrogate relaxation originally proposed in Djerdjour et al. (1988). The quality of three other upper bounds for...
متن کاملHard multidimensional multiple choice knapsack problems, an empirical study
Recent advances in algorithms for the multidimensional multiple choice knapsack problems have enabled us to solve rather large problem instances. However, these algorithms are evaluated with very limited benchmark instances. In this study, we propose new methods to systematically generate comprehensive benchmark instances. Some instances with special correlation properties between parameters ar...
متن کاملFinancial Planning with 0-1 Knapsack Problems, Part Ii: Using Domination Results to Solve Knapsack Problems
Part II uses domination results in knapsack problems to assist in generating solutions more rapidly and with less work. In particular, domination results are used to: (1) generate smaller problems so that less work is needed to solve the problems, and (2) speed up solution by pruning the variable sets that must be examined. Three solution processes are examined in Part II. Domination resultS ar...
متن کاملOverview of the Algorithms for Solving the Multidimensional Knapsack Problems
The multidimensional knapsack problem is defined as an optimization problem that is NP-hard combinatorial. The multidimensional knapsack problems have large applications, which include many applicable problems from different area, like cargo loading, cutting stock, bin-packing, financial and other management, etc. This paper reviews some researches published in the literature. The concentrate i...
متن کاملAn approximate dynamic programming approach to convex quadratic knapsack problems
Quadratic knapsack problem (QKP) has a central role in integer and combinatorial optimization, while efficient algorithms to general QKPs are currently very limited. We present an approximate dynamic programming (ADP) approach for solving convex QKPs where variables may take any integer value and all coefficients are real numbers. We approximate the function value using (a) continuous quadratic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Operations Research
سال: 2022
ISSN: ['0305-0548', '1873-765X']
DOI: https://doi.org/10.1016/j.cor.2021.105693