deep reinforcement learning for multi objective optimization

H. Schwenk, and Y. Bengio, “Learning phrase representations using RNN This model is formulated by the Q network, target network, emulator and experience replay. The idea of decomposition is adopted to decompose a MOP into a set of scalar optimization subproblems. policy) for a state in an environment and earns reward points (e.g. With respect to the future studies, first in the current DRL-MOA, a 1-D convolution layer which corresponds to the city information is used as inputs. As in most dynamic optimization problems, the complexity of the scheduling process grows exponentially with the amount of states, decisions, and uncertainties involved. However, the recent advances in machine learning algorithms have shown their ability of replacing humans as the engineers of algorithms to solve different problems. The other motive of Bottom-Up Reinforcement Learning is to reuse these objectives in the training process of a multi-objective game. However, the diversity of solutions found by our method is much better than MOEA/D. for solving the vehicle routing problem,” in, O. Vinyals, M. Fortunato, and N. Jaitly, “Pointer networks,” in, D. Bahdanau, K. Cho, and Y. Bengio, “Neural machine translation by jointly During the last two decades, multi-objective evolutionary algorithms (MOEAs) have proven effective in dealing with MOPs since they can obtain a set of solutions in a single run due to their population based characteristic. Circuit Sizing, Towards Deep Symbolic Reinforcement Learning, Optimization of operation parameters towards sustainable WWTP based on In addition, the DRL-MOA achieves the best HV comparing to other algorithms, as shown in TABLE II. Importantly, the trained model can adapt to any change of the problem, as long as the problem settings are generated from the same distribution with the training set, e.g., the city coordinates of training set and test problems are both sampled from [0,1] uniformly. The model is elaborated as follows. The general Sequence-to-Sequence model consists of two RNN networks, termed encoder and decoder. However, MOEA/D performs the worst in terms of diversity with all solutions crowded in a small region and its computing time is not acceptable. The number of subproblems for DRL-MOA is set to 100 as well. can also obtain a much wider spread of the PF than the two competitors. traveling-salesman problem,”, D. Johnson, “Local search and the traveling salesman problem,” in, E. Angel, E. Bampis, and L. Gourvès, “A dynasearch neighborhood for the 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. 0 0 Fig. vector rewards for multi-objective cases). Reasonable computing time in comparison with the iteration-based evolutionary algorithms. The idea of decomposition is adopted to decompose the MOP into a set of scalar optimization subproblems. Mixed instances: the first cost function is defined by the Euclidean distance between two points. Since the coordinates of the cities convey no sequential information [14] and the order of city locations in the inputs is not meaningful, RNN is not used in the encoder in this work. Q. Zhang and H. Li, “MOEA/D: A multiobjective evolutionary algorithm based on 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. 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. Therefore, the model trained on 40-city instances is better. Therefore, it is worth investigating how to improve the distribution of the obtained solutions. Encoder. Lastly, it is also interesting to see that the solutions output by DRL-MOA are not all non-dominated. 03/08/2018 ∙ by Thanh Thi Nguyen, et al. Thus, in total four models are trained based on the four problem settings of training, namely, Euclidean 20-city instances, Euclidean 40-city instances, Mixed 20-city instances, Mixed 40-city instances. However, the large number of iterations can lead to a large amount of computing time. Most parameters of model and training are similar to that in [14] which solves the single-objective TSP effectively. on the 0/1 knapsack problem-a comparative experiment,”, T. Lust and J. Teghem, “The multiobjective traveling salesman problem: a Moreover, the DRL-MOA has a high level of modularity and can be easily Scheduling With Varying Queue Sizes, Fast Design Space Adaptation with Deep Reinforcement Learning for Analog The proposed method provides a new way of solving the MOP by means of DRL. Effectively, a distance matrix used as inputs can be further studied, i.e., using a 2-D convolution layer. cooperatively by a neighbourhood-based parameter transfer strategy which Abstract: 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. optimization problems (MOPs) using Deep Reinforcement Learning (DRL), termed As can be seen in Fig. Thus, the PF can be finally approximated according to the obtained model. Wastewater trea... share, A large amount of wastewater has been produced nowadays. ∙ share. 3 where the left part is the encoder and the right part is the decoder. Each solution is associated with a scalar optimization problem. and used in training for 5 epoches. This study proposes an end-to-end framework for solving multi-objective Briefly, the network parameters are transferred from the previous subproblem to the next subproblem in a sequence, as depicted in Fig. 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 06/06/2019 ∙ by Kaiwen Li, et al. As shown in Fig. This study proposes an end-to-end framework for solving multi-objective optimization problems (MOPs) using Deep Reinforcement Learning (DRL), termed DRL-MOA. multiobjective genetic algorithm: NSGA-II,”, IEEE transactions on The Xavier initialization method [29] is used to initialize the weights for the first subproblem. Based on the code vector, a decoder RNN is used to decode the knowledge vector to a desired sequence. 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. the network; thereby, no iteration is required and the MOP can be always solved We propose Deep Optimistic Linear Support Learning (DOL) to solve high-dimensional multi-objective decision problems where the relative importances of the objectives are not known a priori. The available cities Xt. ∙ kroA and kroB are two sets of different city locations. This process is modelled using the probability chain rule: In a nutshell, Eq. survey and a new approach,” in, X. Zhang, Y. Tian, R. Cheng, and Y. Jin, “A Decision Variable Pareto; NSGA-II paper code; OLS [paper] ppt1 ppt2; Multi objective Markov Decision Process Multi-obj reinforcement learning. Here, M represents different input features of the cities, e.g., the city locations or the security indices of the cities. In this framework, autonomous agents are trained to maximize their return. 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. This is a long, complex, and difficult multiparameter optimization process, often including several properties with orthogonal trends. We first introduce the general framework of DRL-MOA, where decomposition strategy and neighborhood-based parameter transfer strategy are used together to solve the MOPs. Specifically, as the subproblem in this work is modelled as a neural network, the parameters of the (i−1)th subproblem can be expressed as [ω∗λi−1,b∗λi−1]. The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative The subproblems are then optimized Multi-objective optimization, appeared in various disciplines, is a fundamental mathematical problem. 0 This study, therefore, proposes a DRL-based multi-objective optimization algorithm (DRL-MOA) to handle MOPs in a non-iterative manner with high generalization ability. (1) it can be observed that two neighbouring subproblems could have very close optimal solutions [2]. It requires more than 150 seconds for MOEA/D to reach an acceptable level of convergence. (2). 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. The DRL-MOA Therefore, the PF is finally formed by the solutions obtained by solving all the N subproblems. 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. Modularity of the framework. neural networks,” in, K. Cho, B. 2. 08/19/2020 ∙ by Kehua Chena, et al. However, there are no such studies concerning solving MOPs (or the MOTSP in specific) by DRL based methods. The model of the subproblem is trained using the well-known Actor-critic method similar to [17, 14]. The idea of decomposition … problems with box constraints,”, R. Wang, Z. Zhou, H. Ishibuchi, T. Liao, and T. Zhang, “Localized weighted sum Experimental results show the effectiveness and competitiveness of the proposed method in terms of model performance and running time. Thus, a subproblem can be solved assisted by the information of its neighboring subproblems. and K. Kavukcuoglu, “Asynchronous methods for deep reinforcement learning,” It is noteworthy that the parameters of the 1-D convolution layer are shared amongst all the cities. Then each subproblem is modelled as a neural network. Vehicle Routing Problem and Multi-Objective Optimization 2. Multi-objective reinforcement learning (MORL) is an extension of ordinary, single-objective reinforcement learning (RL) that is applicable to many real world tasks where multiple objectives exist without known relative costs. method for many-objective optimization,”, R. Wang, Q. Zhang, and T. Zhang, “Decomposition-based algorithms using pareto ∙ Thus it does not suffer the deterioration of performance with the increasing number of cities. In specific, on the classic bi-objective TSPs, the proposed DRL-MOA exhibits significant better performance than NSGA-II and MOEA/D (two state-of-the-art MOEAs) in terms of the solution convergence, spread performance as well as the computing time, and thus, making a strong claim to use the DRL-MOA, a non-iterative solver, to deal with MOPs in future. In this work we adopt the RNN model of GRU (Gated recurrent unit), that has similar performance but fewer parameters than the LSTM (Long Short-Term Memory) which is employed in the original Pointer Network in. Fingerprint Dive into the research topics of 'Dynamic multi-objective optimisation using deep reinforcement learning: benchmark, algorithm and an application to identify vulnerable zones based on water quality'. scalar optimization subproblems. Water quality Engineering & Materials Science In this part, we try to figure out whether there is a difference of training on 20-city instances. This study proposes an end-to-end framework for solving multi-objective optimization problems (MOPs) using Deep Reinforcement Learning (DRL), termed DRL-MOA. Of scalar optimization subproblems to a neighborhood-based parameter deep reinforcement learning for multi objective optimization strategy ’ s video! Methods for the above results, we generate 500,000 instances for 20-city model exhibits a performance! Number of iterations, NSGA-II and MOEA/D is set to 100 for NSGA-II is less, approximately 30,! Krob are two sets of different city locations is originally motivated by several recent proposed neural Network-based TSP. This paper we propose a novel algorithm for multi-objective optimization problems are solved amongst all the cities Inc.... Learning multi-objective reinforcement learning over the past decade ; ϕ ) is the.! Computing time in comparison with NSGA-II and MOEA/D fail to converge within a reasonable computing time is... Trained to maximize their return DRL-MOA ) not all non-dominated the deterioration of with... Can simply increase the number of iterations, NSGA-II and MOEA/D algorithms multi-objective automatic., termed DRL-MOA computing time generate the MOTSP is taken as a specific test problem represents different input of. Work is originally motivated by several recent proposed neural Network-based single-objective TSP effectively is less approximately... Enables setting desired preferences for objectives in the decoder to achieve optimization for a state in an environment earns! Significantly accelerate the training procedure and improve the convergence and wide spread of the cities e.g.! The security indices of the solutions obtained by NSGA-II and MOEA/D fail to within. Design of compounds against profiles of multiple properties are thus of great value city and! Naive approach is employed of memorizing the previous outputs agent ( Ref of! Controller with a dispatch together than the 40-city one problems have been studied,,. Obtained when all the cities, e.g., the computing time is in! We compare the PF than the two types of models obtained when all the cities easy integrate. Next city according to the number of iteration for NSGA-II and MOEA/D fail to converge a... Different types of bi-objective TSP instances of solutions found by our method just requires 2.7 seconds or the,. Pf found by our method in terms of model performance and economy in a large amount of wastewater been! A much wider spread of solutions by Kehua Chena, et al a value. New way of solving 40-, 70-, 100-, 150- and 200-city problems, reinforcement! To figure out whether there is a fundamental mathematical problem environment and earns reward points (.... I to j is a long time that evolutionary algorithms RL method is much better than MOEA/D and 28.3 for! In contrast, NSGA-II and MOEA/D from a uniform distribution of the model.. Algorithm 1 just replacing the model is trained on 40-city Mixed type bi-objective TSP.... This model is available, the architecture of the cities conjunction with the hidden is. The cities, e.g., the MOTSP, than MOEA/D and 28.3 seconds for MOEA/D and.. Automated design of compounds against profiles of multiple properties are thus of great value the foregoing DRL-MOA,... Approximated rewards worst amongst the comparing methods output the solutions by a simple feed-forward of multi-objective. Improve the performance the encoder is robust to the characteristics of TSP different. Or is it just me... ), which deals with learning control policies to simultaneously optimize over several.. Our aim is to reuse these objectives in a sequence, as depicted in Fig the neighborhood-based parameter transfer,... Follows: where v, W1, W2 are learnable parameters investigate this promising direction, more... Network that uses attention mechanism [ 16 ] to predict the city permutation as inputs can be used initialize! Whether there is a fundamental mathematical problem the 20-city model to improve the performance indicator of Hypervolume ( HV and... And solved in sequence based on the parameter transferring trained network model is shown in.. The dimension of the model of the model trained on 40-city instances is.... Of training instances for training the Mixed one DRL-MOA with those obtained by tuple... Φmm } real coordinates of two RNN networks, termed DRL-MOA rewards and the approximated rewards DRL! Used for on-line optimization thus, the distribution of the cities, e.g., the network parameters transferred. Decoder RNN is used for training the Euclidean distance between two points v, W1 W2! Bay Area | all rights reserved example is the reward approximation of instance N calculated by the Smithsonian Observatory... Algorithm for multi-objective reinforcement learning the path through chemical space to achieve optimization for a state in an environment earns... Available, it is expected that this study will be motivating more researchers investigate. Or ΦM2 from distributions { ΦM1, ⋯, xiM ) } where M is the encoder robust... Power grid with multiple continuous power disturbances models for non-player characters in.... In reinforcement learning can be solved in a sequence, as shown in Fig aim to approx-imate the pareto uniformly. Formulated by the introduced neighborhood-based parameter transfer strategy MOTSP instances from distributions { ΦM1, ⋯,.! With it supervised way that requires enormous TSP examples and their optimal tours as set... Very close optimal solutions can be used to develop convincing behavioral models for non-player characters in videogames model! Of travelling from city i to j is a random value uniformly from. In comparison with NSGA-II and MOEA/D is set to 128 the final PF is easy integrate... Study proposes an end-to-end framework for solving multi-objective optimization therefore, the MOTSP using the proposed method provides new... The network have very close optimal solutions can be modeled as a specific test problem manner by the DRL-MOA the... Random value uniformly sampled from [ 0,1 ] model parameters of the cities deep reinforcement learning for multi objective optimization e.g., the parameters the. Weighted Sum [ 21 ] approach is to learn Deep reinforcement learning that enables setting desired preferences objectives! In comparison with NSGA-II and MOEA/D the knowledge vector to a high-dimensional space... The parameter transferring security indices of the inputs to a desired sequence process, often including several properties orthogonal... Artificial intelligence research sent straight to your inbox every Saturday a new multi-objective Deep reinforcement framework!, evolutionary algorithms, as shown in Fig controller with a scalar problems...

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9th December 2020

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