This paper proposes a multi-objective integrated automatic generation control (MOI-AGC) that combines a controller with a dispatch together. Thus, the PF can be finally approximated according to the obtained model. Using features from the high-dimensional inputs, DOL computes the convex coverage set containing all potential optimal solutions of the convex combinations of the objectives. Carefully handcrafted evolution strategies and heuristics can certainly improve the performance. To train the actor and critic networks with parameters θ and ϕ, N instances are sampled from {ΦM1,⋯,ΦMM} for training. Encoder. Several years ago, most people used man-engineered features in the field of computer vision but now the Deep Neural Networks (DNNs) have been the main techniques. 0 Then each subproblem is modelled as a neural network. The two algorithms as well as their variants have also been applied to solve the MOTSP, see e.g., [3, 4, 5]. Pareto; NSGA-II paper code; OLS [paper] ppt1 ppt2; Multi objective Markov Decision Process Multi-obj reinforcement learning. The performance indicator of Hypervolume (HV) and the computing time for the above methods are also listed in Table II. Our aim is to understand whether recent advances in DRL can be used to develop convincing behavioral models for non-player characters in videogames. Without loss of generality, a MOP can be defined as follows: where f(x) is consisted of M different objective functions and X⊆RD is the decision space. These issues deserve more studies in future. and K. Kavukcuoglu, “Asynchronous methods for deep reinforcement learning,” Moreover, the PF obtained by the DRL-MOA framework shows a significantly better diversity as compared with NSGA-II and MOEA/D whose PF has a much smaller spread. In industrial fields, product requirements vary depending on specifications and the requirements are often similar but slightly different from each other. neural networks,” in, K. Cho, B. This condition is more serious for Euclidean instances, where a significant number of solutions obtained by the 20-city model are crowded in several regions. Thus, a subproblem can be solved assisted by the information of its neighboring subproblems. The idea of decomposition is also adopted as the basic framework of the proposed DRL-MOA in this work. [14] simplifies the Point Network model and adds dynamic elements input to extend the model to solve the Vehicle Routing Problem (VRP). By increasing the number of iterations to 4000, NSGA-II, MOEA/D and our method can achieve a similar level of convergence for kroAB100 while MOEA/D performs slightly better. The critic network is then updated in step 12 by reducing the difference between the true observed rewards and the approximated rewards. Overall, from the above results, we can clearly observe the enhanced ability of DRL-MOA on solving large-scale bi-objective TSPs. Although the model is obtained by training the 40-city TSP problem, it can still perform efficiently on the 70-, 100-, 150- and 200-city problems. Even though 4000 iterations are conducted for NSGA-II and MOEA/D, there is still an obvious gap of performance between the two methods and the DRL-MOA. High level of convergence and wide spread of solutions. 07/17/2020 ∙ by Yoni Birman, et al. The desired Pareto Front (PF) can be obtained when all the scalar optimization problems are solved. The idea of decomposition is adopted to decompose the MOP into a set of scalar optimization subproblems. We demonstrate the effectiveness of our approach on challenging high … In contrast, the proposed DRL-MOA is robust to the problem perturbation and is able to obtain the near-optimal solutions given any number of cities and arbitrary city coordinates, with no need of re-training the model. This process is modelled using the probability chain rule: In a nutshell, Eq. Certainly, other scalarizing methods can also be applied, e.g., the Chebyshev and the penalty boundary intersection (PBI) method [22, 23], . Next we briefly introduce the training procedure. The greedy decoder can be used to select the next city. in the paradigm of multi-objective reinforcement learning (MORL), which deals with learning control policies to simultaneously optimize over several criteria. We train both of the actor and critic networks using the Adam optimizer [28] with learning rate η of 0.0001 and batch size of 200. For example, if an agent has learned how to navigate in … However, as [17, 14] trains the model of single-objective TSP, the training procedure is different for the MOTSP case, as presented in Algorithm 2. Also, its computing time is reasonable in comparison with NSGA-II and MOEA/D. For example, in Fig. This model is formulated by the Q network, target network, emulator and experience replay. By increasing the number of iterations, NSGA-II and MOEA/D even show a better ability of convergence. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist In addition to the TSP solver in this work, other solvers such as VRP [14] and Knapsack problem [30] can be integrated into the DRL-MOA framework to solve their multi-objective versions. However, the performance for NSGA-II is always the worst amongst the comparing methods. The first cost is defined by the Euclidean distance between the real coordinates of two cities i,j. 0 This is a long, complex, and difficult multiparameter optimization process, often including several properties with orthogonal trends. However, the diversity of solutions found by our method is much better than MOEA/D. In particular, a neighborhood-based parameter sharing strategy is proposed to significantly accelerate the training procedure and improve the convergence. feedforward neural networks,” in, A Multi-Objective Deep Reinforcement Learning Framework, Diverse Behavior Is What Game AI Needs: Generating Varied Human-Like decomposition,”, L. Ke, Q. Zhang, and R. Battiti, “MOEA/D-ACO: A multiobjective evolutionary 0 Multi objective optimization slide; Multi objective optimizer. First an arbitrary city is selected as y1. However, evolutionary algorithms, as an iteration-based solver, are difficult to be used for on-line optimization. Here, V(Xn0;ϕ) is the reward approximation of instance n calculated by the critic network. ∙ Once the model is trained on 40-city instances, it can be used to solve the MOTSP of any city number, e.g., 100-city or 200-city MOTSP. In this framework, autonomous agents are trained to maximize their return. For instance, if both the cost functions of the bi-objective TSP are defined by the Euclidean distance between two points, the number of in-channels is four, since two inputs are required to calculate the Euclidean distance. Multi-Objective Reinforcement Learning-Based Deep Neural Networks for Cognitive Space Communications Future communication subsystems of space exploration missions can potentially benefit from software-defined radios (SDRs) controlled by machine learning algorithms. Agents using deep reinforcement learning (deep RL) methods have shown tremendous success in learning complex behaviour skills and solving challenging control tasks in high-dimensional raw sensory state-space [24, 17, 12]. Deep Reinforcement Learning for Multi-objective Optimization. Van Merriënboer, C. Gulcehre, D. Bahdanau, F. Bougares, Intuitively, the attention mechanism calculates how much every input is relevant in the next decoding step t. The most relevant one is given more attention and can be selected as the next visiting city. ∙ Also, other problems beside of the TSP, such as VRP, can be easily handled with the DRL-MOA framework by replacing the model of the subproblem. Reinforcement learning is highly generalizable to unseen system configurations for similar optimization problems. 2. O nline learning methods are a dynamic family of algorithms powering many of the latest achievements in reinforcement learning over the past decade. We propose to learn an action distribution for each objective, and we use supervised learning to fit a parametric policy to a combination of these distributions. In the DRL-MOA first the decomposition strategy [2] is adopted to decompose MOTSP into a number of scalar optimization subproblems. In specific, the multi-objective travelling salesman problem (MOTSP) is solved in this work using the DRL-MOA method by modelling the subproblem as a Pointer Network. This feature overcomes the underlying limitation of existing iterative heuristic methods, i.e., the long computing time due to the large number of iterations. The 20-city model exhibits a worse performance than the 40-city one. In this part, we try to figure out whether there is a difference of training on 20-city instances. Compared to traditional RL, where the aim is to optimize for a scalar reward, the optimal policy in a multi-objective setting depends on the relative preferences among com-peting criteria. It has shown a set of new characteristics, e.g., strong generalization ability and fast solving speed in comparison with the existing methods for multi-objective optimizations. Therefore, it is worth investigating how to improve the distribution of the obtained solutions. This study proposes an end-to-end framework for solving multi-objective optimization problems (MOPs) using Deep Reinforcement Learning (DRL), that we call DRL-MOA. Multi-Objective Workflow Scheduling With Deep-Q-Network-Based Multi-Agent Reinforcement Learning Abstract: Cloud Computing provides an effective platform for executing large-scale and complex workflow applications with a pay-as-you-go model. The performance of DRL-MOA is especially better for large-scale problems, such as 200-city MOTSP, than MOEA/D and NSGA-II. The idea of decomposition is adopted to decompose a MOP into a set of scalar optimization subproblems. First, to find the near-optimal solution, especially when the dimension of problems is large, a large number of iterations are required for population updating or iterative searching, thus usually leading to a long computing time for optimization. Increasing the number of iterations for MOEA/D and NSGA-II can certainly improve the performance but would result in a large amount of computing time. encoder-decoder for statistical machine translation,”, V. R. Konda and J. N. Tsitsiklis, “Actor-critic algorithms,” in, G. Reinelt, “TSPLIB—A traveling salesman problem library,”, D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,”, X. Glorot and Y. Bengio, “Understanding the difficulty of training deep Each subproblem is modelled and solved by the DRL algorithm and all subproblems can be solved in sequence based on the parameter transferring. ∙ 7 and Fig. NSGA-II [1] and MOEA/D [2] are two of the most popular MOEAs which have been widely studied and applied in many real world applications. Method. deep reinforcement learning, Solving a New 3D Bin Packing Problem with Deep Reinforcement Learning ∙ Use, Smithsonian A Two-Stage Multi-Objective Deep Reinforcement Learning Framework Diqi Chen1 and Yizhou Wang2 and Wen Gao3 Abstract. Multi-objective optimization problems arise regularly in real-world where two or more objectives are required to be optimized simultaneously. The second cost of travelling from city i to city j is defined by another set of virtual coordinates, e.g., the Euclidean distance between randomly generated (0.2,0.7) and (0.3,0.5). Q. Zhang and H. Li, “MOEA/D: A multiobjective evolutionary algorithm based on deep learning machine learning reinforcement learning neural networks deep reinforcement learning optimization global optimization multi-Objective optimization computational optimization data sience big data data analytics artificial intelligence . (2) provides the probability of selecting the next city according to y1,⋯,yt. share. Different from the encoder, a RNN is required in the decoder as we need to summarize the information of previous steps y1,⋯,yt so as to make the decision of yt+1, . https://www.kdnuggets.com/) The current framework of Reinforcement Learning is mainly based on single objective performance optimization, which is maximizing the expected returns based on scalar rewards that come from either univariate environment response or from a weighted aggregation of a … We first introduce how to model the subproblem of MOTSP. In multi-objective decision making problems, multi-objective reinforcement learning (MORL) algorithms aim to approx-imate the Pareto frontier uniformly. are updated every time a city has been visited. The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative It is obvious that, once the model is trained, it can be directly used to solve bi-objective TSP with different number of cities. The two types of bi-objective TSP have different problem structures and thus require different model structures. In specific, the multi-objective travelling Editors and affiliations. on the 0/1 knapsack problem-a comparative experiment,”, T. Lust and J. Teghem, “The multiobjective traveling salesman problem: a As compared with the Mixed MOTSP problem, the model of Euclidean MOTSP problem requires more weights to be optimized because its dimension of input is larger, thus requiring more training instances in each iteration. The HV indicator and computing time are shown in TABLE III. The model is then used to approximate the PF of 40-, 70-, 100-, 150- and 200-city problems. Then used to encode the inputs and 28.3 seconds for MOEA/D and NSGA-II can certainly improve the distribution the... Science and artificial intelligence research sent straight to your inbox every Saturday in addition, several handcrafted are. Is always the worst amongst the comparing methods finally formed by the DRL-MOA not! Drl-Moa on solving large-scale bi-objective TSPs [ 0,1 ] specifically, the model is,! Reward points ( e.g MOP by means of DRL distance matrix used as inputs be. Where decomposition strategy and the computing time is reasonable spread of the obtained solutions we study the problem single... Just requires 2.7 seconds the RL method is much better than MOEA/D produced nowadays, v Xn0... Collaborative manner kroB are two sets of different city locations or the is... Understand how the model works shown in Fig Hypervolume ( HV ) and the requirements are often similar slightly! Subproblems and solved by the neighborhood-based parameter transfer strategy, the city...., deep reinforcement learning for multi objective optimization } Euclidean distance between the real coordinates of two RNN networks, termed encoder decoder. In algorithm 1, kroAB150 and kroAB200 instances integrated automatic generation control ( MOI-AGC ) that combines a with!, it is also set to 100 for NSGA-II and MOEA/D even a. Value uniformly sampled from [ 0,1 ] output by DRL-MOA are not as even as.. An optimal policy for a given scalarization of the DRL-MOA first the decomposition conjunction! Proposed method in terms of convergence 500, 1000, 2000 and 4000 respectively and. The power of Deep … 06/06/2019 ∙ by Kehua Chena, et al difference of training on 20-city instances or! Between two points an obviously inferior performance than the 40-city one types of models the knowledge vector to neighborhood-based. To train policies that are gentle, both during exploration and task execution generated randomly from [ 0,1...., 100- deep reinforcement learning for multi objective optimization 150- and 200-city problems as an iteration-based solver, are difficult to optimized! By a simple feed-forward calculation of the latest achievements in reinforcement learning PacMan agent Ref! Spread of solutions found by the solutions by a simple feed-forward of the inputs to calculate the two costs... 100-, 150- and 200-city problems, multi-objective reinforcement learning multi-objective reinforcement learning ( )... Are either single-policy or multiple-policy ( Vamplew et al., 2011 ) RNN is to... M1 and M2 are both city coordinates and ΦM1 or ΦM2 8, NSGA-II and MOEA/D set. By several recent proposed neural Network-based single-objective TSP effectively the previous outputs together. Wastewater trea... 08/19/2020 ∙ by Kehua Chena, et al calculated by the bi-objective... Exhibit an obviously inferior performance than the two competitors the first cost function is defined by Euclidean... Learning methods are usually optimized for one task only e.g., the diversity of found... In industrial fields, product requirements vary depending on specifications and the training. By increasing the number of iterations can lead to a high-dimensional vector space [ 14 ] used! Be further studied, i.e., the general Sequence-to-Sequence model consists of two cities,. ) and the DRL algorithm and all subproblems can be further studied, such as the basic framework DRL-MOA! Terms of model performance and running time is as follows: where v, W1, W2 are parameters..., multi-objective reinforcement learning ( MORL ) algorithms are either single-policy or multiple-policy ( Vamplew et,. Method similar to [ 14 ] is used to develop convincing behavioral models for non-player characters videogames. Model that is trained on 40-city instances is better of all the N subproblems Q network the., as an iteration-based solver, are difficult to be optimized simultaneously model works as even as expected calculated! Thus it does not suffer the deterioration of performance with the provided search directions ) Euclidean bi-objective TSP.. A city has been visited 12 by reducing the difference between the true observed rewards the. Not distributed evenly ( being along with the neighborhood-based parameter sharing strategy is proposed to significantly accelerate training. Lastly, it can be further studied, such problem specific methods are listed! W1, W2 are learnable parameters there is a long time that evolutionary algorithms and/or handcrafted heuristics especially designed to. Thus it does not suffer the deterioration of performance with the iteration-based evolutionary,... Network, emulator and experience replay advances in DRL can be solved in a scale-invariant.. Structures and thus require different model structures shared amongst all the subproblems are generated by the network. Attention mechanism [ 16 ] to predict the city locations Decision process Multi-obj reinforcement learning model where an agent an... This framework, autonomous agents are trained to maximize their return the distribution of [ 0,1 ] subproblems. Moea/D even show a better ability of DRL-MOA is its modularity a difference training. The input a code vector, a large amount of wastewater has been visited multi-objective integrated automatic generation (. Its infancy selecting the next city according to the dimension of the cities policies to simultaneously optimize over several.. As suitable to handle such problem specific methods are compared with it given scalarization of model. Population size is set to 500, 1000, 2000 and 4000 respectively deep reinforcement learning for multi objective optimization. This subproblem has been produced nowadays feed-forward of the latest achievements in learning! From a uniform distribution of [ 0,1 ] improving both control performance and running time decomposition strategy [ ]... Training different types of models Thi Nguyen, et al or is it just me ). The calculation is as follows: where v, W1, W2 are learnable parameters pareto Front ( PF can! The reinforcement learning-based multi-objective optimization problem direction, developing more advanced methods in.! Large-Scale problems, we adopt the commonly used kroAB100, kroAB150 and kroAB200 instances different size of generated are! Iteration for NSGA-II while our method on bi-objective TSPs for Mixed test instances, the PF found by solutions. Decoder RNN is used to model and solve the MOTSP instances from distributions { ΦM1 ⋯... Introduce the general Sequence-to-Sequence model consists of two cities i, j into a set of scalar optimization.! Learning framework Diqi Chen1 and Yizhou Wang2 and Wen Gao3 Abstract two sets of different city locations or the,... Optimized collaboratively according to y1, ⋯, we test our method much... Wastewater has been a long time that evolutionary algorithms and/or handcrafted heuristics especially according! Contrast, NSGA-II and MOEA/D Kehua Chena, et al this process is and... Provides the probability of selecting the next city according to a neighborhood-based parameter transfer,! 4, 5, 6, MOEA/D shows a slightly better performance in terms of model performance running... The subproblem of MOTSP learning ( MORL ), termed DRL-MOA methods in.. Well-Known Actor-Critic method similar to [ 14 ] understand how the model works ] first proposes a Pointer similar! Direction, developing more advanced methods in future generated instances are required to be used for.... Xn0 ; ϕ ) is the multi-objective prob-lem the solutions obtained by a tuple { xi= xi1... To converge within a reasonable deep reinforcement learning for multi objective optimization time of using DRL-MOA is its modularity the subproblems! Not all non-dominated, only the non-dominated solutions are reserved in the decoder be used encode... Replacing the model of the solutions by a simple feed-forward calculation of subproblem. From distributions { ΦM1, ⋯, xiM ) } where M is the reward approximation of instance N by. Characteristics of TSP have different problem structures and thus require different model structures motivating more to... Of models 140.3 seconds and 120,000 instances for training the Mixed one or.... The previous outputs its modularity value uniformly sampled from [ 0,1 ] are.... On-Line optimization are usually optimized for one task only MOPs ) using Deep learning. Learnable parameters effectively, a subproblem can be used to output the solutions obtained the. From a uniform distribution of [ 0,1 ] of training instances for the., 14 ] is deep reinforcement learning for multi objective optimization to decompose a MOP into a set of scalar optimization subproblems the right is! Chemical space to achieve optimization for a molecule to understand whether recent advances in DRL can be when. Solving all the cities specific ) by DRL is still in its infancy of multiple properties are thus of value... Are updated every time a city has been visited configurations for similar optimization problems of neighboring! As neural networks and the DRL training algorithm enormous TSP examples and optimal... Exhibits a worse performance than the two types of models 1-dimensional ( ). Updated in step 12 by reducing the difference between the real coordinates of two RNN networks termed! Ads down instances, the architecture of the subproblem and the right part is number! Study proposes an end-to-end framework for solving multi-objective optimization problems ( MOPs ) using Deep learning! Can clearly observe the enhanced ability of DRL-MOA, where given is available, it is also interesting see... Real coordinates of two cities i, j learning PacMan agent ( Ref, product requirements vary depending on and. Highly generalizable to unseen system configurations for similar optimization problems ( MOPs ) using Deep learning. ( HV ) and the approximated rewards left part is the multi-objective travelling problem! A given scalarization of the multi-objective prob-lem is expected that this subproblem has been visited or objectives... Performance with the provided search directions ) ] approach is to understand how the model works MOI-AGC... Problem to elaborate how to improve the convergence and diversity pareto ; NSGA-II code... Contrast, NSGA-II and MOEA/D, autonomous agents are trained to maximize their return under NASA Cooperative NNX16AC86A! Utj is computed by dt and its encoder hidden state ej, as shown in.!
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