Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
How to analyse evolutionary algorithms
Theoretical Computer Science - Natural computing
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
A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II
PPSN VI Proceedings of the 6th 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
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
HiPC'04 Proceedings of the 11th international conference on High Performance Computing
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
Performance assessment of multiobjective optimizers: an analysis and review
IEEE Transactions on Evolutionary Computation
Running time analysis of multiobjective evolutionary algorithms on pseudo-Boolean functions
IEEE Transactions on Evolutionary Computation
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Proceedings of the 10th annual conference on Genetic and evolutionary computation
The maximum hypervolume set yields near-optimal approximation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Tight bounds for the approximation ratio of the hypervolume indicator
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
The logarithmic hypervolume indicator
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Approximation quality of the hypervolume indicator
Artificial Intelligence
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In this paper, we suggest a multiobjective evolutionary algorithm based on a restricted mating pool (REMO) with a separate archive for storing the remaining population. Such archive based algorithms have been used for solving real-world applications, however, no theoretical results are available. In this paper, we present a rigorous running time complexity analysis for the algorithm on two simple discrete pseudo boolean functions and on the multiobjective knapsack problem which is known to be NP-complete. We use two well known simple functions LOTZ (Leading Zeros: Trailing Ones) and a quadratic function. For the knapsack problem we formalize a ( 1+ ε)-approximation set under a constraint on the weights of the items. We then generalize the idea by eliminating the constraints based on a principle of partitioning the items into blocks and analyze REMO on it. We use a simple strategy based on partitioning of the decision space into fitness layers for the analysis.