Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Randomized algorithms
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Theoretical Computer Science
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
Evolutionary Algorithms for Solving Multi-Objective Problems
Evolutionary Algorithms for Solving Multi-Objective Problems
How to analyse evolutionary algorithms
Theoretical Computer Science - Natural computing
Combining convergence and diversity in evolutionary multiobjective optimization
Evolutionary Computation
On the Optimization of Unimodal Functions with the (1 + 1) Evolutionary Algorithm
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
Fitness Landscapes Based on Sorting and Shortest Paths Problems
PPSN VII Proceedings of the 7th International Conference on Parallel Problem Solving from Nature
PPSN VII Proceedings of the 7th International Conference on Parallel Problem Solving from Nature
Evolutionary Search for Minimal Elements in Partially Ordered Finite Sets
EP '98 Proceedings of the 7th International Conference on Evolutionary Programming VII
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Approximating Multiobjective Knapsack Problems
Management Science
Running time analysis of evolutionary algorithmson a simplified multiobjective knapsack problem
Natural Computing: an international journal
Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy
Evolutionary Computation
How mutation and selection solve long-path problems in polynomial expected time
Evolutionary Computation
Rigorous hitting times for binary mutations
Evolutionary Computation
Multicriteria network design using evolutionary algorithm
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
Analysis of a simple evolutionary algorithm for minimization in euclidean spaces
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Convergence time analysis for the multi-objective counting ones problem
EMO'03 Proceedings of the 2nd international conference on Evolutionary multi-criterion optimization
Multiobjective EA approach for improved quality of solutions for spanning tree problem
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
The balance between proximity and diversity in multiobjective evolutionary algorithms
IEEE Transactions on Evolutionary Computation
Running time analysis of multiobjective evolutionary algorithms on pseudo-Boolean functions
IEEE Transactions on Evolutionary Computation
Proceedings of the 10th annual conference on Genetic and evolutionary computation
The impact of parametrization in memetic evolutionary algorithms
Theoretical Computer Science
Labeling algorithms for multiple objective integer knapsack problems
Computers and Operations Research
ISICA'07 Proceedings of the 2nd international conference on Advances in computation and intelligence
On the effect of populations in evolutionary multi-objective optimisation**
Evolutionary Computation
Advances in evolutionary multi-objective optimization
SSBSE'12 Proceedings of the 4th international conference on Search Based Software Engineering
Multiple objective scheduling of HPC workloads through dynamic prioritization
Proceedings of the High Performance Computing Symposium
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Multiobjective Evolutionary Algorithms (MOEAs) are increasingly being used for effectively solving many real-world problems, and many empirical results are available. However, theoretical analysis is limited to a few simple toy functions. In this work, we select the well-known knapsack problem for the analysis. The multiobjective knapsack problem in its general form is NP-complete. Moreover, the size of the set of Pareto-optimal solutions can grow exponentially with the number of items in the knapsack. Thus, we formalize a (1 + ε)-approximate set of the knapsack problem and attempt to present a rigorous running time analysis of a MOEA to obtain the formalized set. The algorithm used in the paper is based on a restricted mating pool with a separate archive to store the remaining population; we call the algorithm a Restricted Evolutionary Multiobjective Optimizer (REMO). We also analyze the running time of REMO on a special bi-objective linear function, known as LOTZ (Leading Ones : Trailing Zeros), whose Pareto set is shown to be a subset of the knapsack. An extension of the analysis to the Simple Evolutionary Multiobjective Optimizer (SEMO) is also presented. A strategy based on partitioning of the decision space into fitness layers is used for the analysis.