In practice, multiple conflicting objectives and costly evaluations (e.g., wet-lab experiments) make the diversity of candidates

Each sublayer adds a skip-connection (ADD) and batch normalization (BN). The decoder sequentially chooses a node according to a probability distribution produced by the node embeddings to construct a solution. The scaled symmetric sampling method is shown in Algorithm 2. The scaled factor The uniform division of the weight space is illustrated as follows. Thus, its approximate Pareto optimal solutions are commonly pursued. V ehicles must serve all the customers and finally return to the depot.

In the inference process, the submodel is used to solve the corresponding subproblem. The input dimensions of the node features vary with different problems. A masking mechanism is adopted in each decoding step to ensure the solution feasibility. For MOTSP, the visited nodes are masked. NHDE-M usually spends relatively more inference time than MDRL with the same number of weights.

This paper presents a novel approach to multiobjective algorithms aimed at modeling the Pareto set using neural networks. Whereas previous methods mainly focused on identifying a finite number of solutions, our approach allows for the direct modeling of the entire Pareto set. Furthermore, we establish an equivalence between learning the complete Pareto set and maximizing the associated hypervolume, which enables the convergence analysis of hypervolume (as a new metric) for Pareto set learning. Specifically, our new analysis framework reveals the connection between the learned Pareto solution and its representation in a polar coordinate system. We evaluate our proposed approach on various benchmark problems and real-world problems, and the encouraging results make it a potentially viable alternative to existing multiobjective algorithms.

In this work, we study how the performance of a given direction changes with its sampling ratio in Multilingual Neural Machine Translation (MNMT). By training over 200 multilingual models with various model sizes, data sizes, and language directions, we find it interesting that the performance of certain translation direction does not always improve with the increase of its weight in the multi-task optimization objective. Accordingly, scalarization method leads to a multitask trade-off front that deviates from the traditional Pareto front when there exists data imbalance in the training corpus, which poses a great challenge to improve the overall performance of all directions. Based on our observations, we propose the Double Power Law to predict the unique performance trade-off front in MNMT, which is robust across various languages, data adequacy, and the number of tasks. Finally, we formulate the sample ratio selection problem in MNMT as an optimization problem based on the Double Power Law. In our experiments, it achieves better performance than temperature searching and gradient manipulation methods with only 1/5 to 1/2 of the total training budget.