Journal ArticleDOI
Two-phases Method and Branch and Bound Procedures to Solve the Bi–objective Knapsack Problem
TLDR
The classical 0–1 knapsack problem is considered with two objectives, and two methods of the “two–phases” type are developed to generate the set of efficient solutions.Abstract:
The classical 0–1 knapsack problem is considered with two objectives. Two methods of the “two–phases” type are developed to generate the set of efficient solutions. In the first phase, the set of supported efficient solutions is determined by optimizing a parameterized single-objective knapsack problem. Two versions are proposed for a second phase, determining the non-supported efficient solutions: both versions are Branch and Bound approaches, but one is “breadth first”, while the other is “depth first”. Extensive numerical experiments have been realized to compare the results of both methods.read more
Citations
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Journal ArticleDOI
A survey and annotated bibliography of multiobjective combinatorial optimization
TL;DR: The main parts of the paper are a section on the review of the available solution methodology, both exact and heuristic, and a sections on the annotation of the existing literature in the field organized problem by problem.
Journal ArticleDOI
MOSA method: a tool for solving multiobjective combinatorial optimization problems
TL;DR: In this paper, the authors developed the so-called MOSA (Multiobjective Simulated Annealing) method to approximate the set of efficient solutions of a MOCO problem.
Journal ArticleDOI
A survey of recent developments in multiobjective optimization
TL;DR: Recent developments in Multiobjective Optimization are discussed, including optimality conditions, applications, global optimization techniques, the new concept of epsilon Pareto optimal solution, and heuristics.
Journal ArticleDOI
A bi-objective model for robust resource-constrained project scheduling
M.A. Al-Fawzan,Mohamed Haouari +1 more
TL;DR: The concept of schedule robustness is introduced and a bi-objective resource-constrained project scheduling model is developed and a tabu search algorithm is developed in order to generate an approximate set of efficient solutions.
Journal ArticleDOI
A discussion of scalarization techniques for multiple objective integer programming
TL;DR: A new scalarization technique, the method of elastic constraints, is introduced, which is shown to be able to find all efficient solutions and overcome the computational burden of the scalarizations that use constraints on objective values.
References
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Book
Knapsack Problems: Algorithms and Computer Implementations
Silvano Martello,Paolo Toth +1 more
TL;DR: This paper focuses on the part of the knapsack problem where the problem of bin packing is concerned and investigates the role of computer codes in the solution of this problem.
Journal ArticleDOI
Pareto simulated annealing—a metaheuristic technique for multiple‐objective combinatorial optimization
TL;DR: Pareto simulated annealing as discussed by the authors uses a sample of so-called generating solutions to explore its neighborhood in a way similar to that of classical simulated anealing. But it does not consider the problem of finding a good approximation of the set of efficient solutions of a combinatorial optimization problem.
Journal ArticleDOI
Multi‐objective combinatorial optimization problems: A survey
E. L. Ulungu,Jacques Teghem +1 more
TL;DR: The present paper is intended to review the existing literature on multi-objective combinatorial optimization (MOCO) problems and examines various classical combinatorials problems in a multi-criteria framework.
Journal ArticleDOI
Generating the Discrete Efficient Frontier to the Capital Budgeting Problem
TL;DR: The heuristic algorithm, which is the first phase of the branch-and-bound algorithm, has an average error of about 2%.
Book ChapterDOI
Solving Multi-Objective Knapsack Problem by a Branch-and-Bound Procedure
TL;DR: In this paper, a classical knapsack problem with two objectives is considered in which concepts of supported and non supported efficient solutions are pointed out, and concepts of support and non-supportive solutions are discussed.