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Register a new userA Covariance Matrix Self-Adaptation Evolution Strategy for Optimization under Linear Constraints
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Michael Hellwig
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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This paper addresses the development of a covariance matrix self-adaptation evolution strategy (CMSA-ES) for solving optimization problems with linear constraints. The proposed algorithm is referred to as Linear Constraint CMSA-ES (lcCMSA-ES). It uses a specially built mutation operator together with repair by projection to satisfy the constraints. The lcCMSA-ES evolves itself on a linear manifold defined by the constraints. The objective function is only evaluated at feasible search points (interior point method). This is a property often required in application domains such as simulation optimization and finite element methods. The algorithm is tested on a variety of different test problems revealing considerable results.
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This paper presents a novel mechanism to adapt surrogate-assisted population-based algorithms. This mechanism is applied to ACM-ES, a recently proposed surrogate-assisted variant of CMA-ES. The resulting algorithm, saACM-ES, adjusts online the lifelength of the current surrogate model (the number of CMA-ES generations before learning a new surrogate) and the surrogate hyper-parameters. Both heuristics significantly improve the quality of the surrogate model, yielding a significant speed-up of saACM-ES compared to the ACM-ES and CMA-ES baselines. The empirical validation of saACM-ES on the BBOB-2012 noiseless testbed demonstrates the efficiency and the scalability w.r.t the problem dimension and the population size of the proposed approach, that reaches new best results on some of the benchmark problems.
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Over the past decades, more and more methods gain a giant development due to the development of technology. Evolutionary Algorithms are widely used as a heuristic method. However, the budget of computation increases exponentially when the dimensions increase. In this paper, we will use the dimensionality reduction method Principal component analysis (PCA) to reduce the dimension during the iteration of Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which is a good Evolutionary Algorithm that is presented as the numeric type and useful for different kinds of problems. We assess the performance of our new methods in terms of convergence rate on multi-modal problems from the Black-Box Optimization Benchmarking (BBOB) problem set and we also use the framework COmparing Continuous Optimizers (COCO) to see how the new method going and compare it to the other algorithms.
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In this paper, we study reinforcement learning (RL) algorithms to solve real-world decision problems with the objective of maximizing the long-term reward as well as satisfying cumulative constraints. We propose a novel first-order policy optimization method, Interior-point Policy Optimization (IPO), which augments the objective with logarithmic barrier functions, inspired by the interior-point method. Our proposed method is easy to implement with performance guarantees and can handle general types of cumulative multiconstraint settings. We conduct extensive evaluations to compare our approach with state-of-the-art baselines. Our algorithm outperforms the baseline algorithms, in terms of reward maximization and constraint satisfaction.
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