Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Journal of Global Optimization
Comparison of Multiobjective Evolutionary Algorithms: Empirical Results
Evolutionary Computation
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
Multiobjective optimization of combinatorial libraries
IBM Journal of Research and Development
Hypervolume-based multiobjective optimization: Theoretical foundations and practical implications
Theoretical Computer Science
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
MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition
IEEE Transactions on Evolutionary Computation
Borg: An auto-adaptive many-objective evolutionary computing framework
Evolutionary Computation
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In this paper, we present a new population-based Monte Carlo method, so-called MOMCMC (Multi-Objective Markov Chain Monte Carlo), for sampling in the presence of multiple objective functions in real parameter space. The MOMCMC method is designed to address the ''multi-objective sampling'' problem, which is not only of interest in exploring diversified solutions at the Pareto optimal front in the function space of multiple objective functions, but also those near the front. MOMCMC integrates Differential Evolution (DE) style crossover into Markov Chain Monte Carlo (MCMC) to adaptively propose new solutions from the current population. The significance of dominance is taken into consideration in MOMCMC's fitness assignment scheme while balancing the solution's optimality and diversity. Moreover, the acceptance rate in MOMCMC is used to control the sampling bandwidth of the solutions near the Pareto optimal front. As a result, the computational results of MOMCMC with the high-dimensional ZDT benchmark functions demonstrate its efficiency in obtaining solution samples at or near the Pareto optimal front. Compared to MOSCEM (Multiobjective Shuffled Complex Evolution Metropolis), an existing Monte Carlo sampling method for multi-objective optimization, MOMCMC exhibits significantly faster convergence to the Pareto optimal front. Furthermore, with small population size, MOMCMC also shows effectiveness in sampling complicated multi-objective function space.