Multi-task optimization is typically characterized by a fixed and finite set of optimization tasks. The present paper relaxes this condition by considering a non-fixed and potentially infinite set of optimization tasks defined in a parameterized, continuous and bounded task space. We refer to this unique problem setting as parametric multi-task optimization (PMTO). Assuming the bounds of the task parameters to be ($\boldsymbol{\theta}_l$, $\boldsymbol{\theta}_u$), a novel ($\boldsymbol{\theta}_l$, $\boldsymbol{\theta}_u$)-PMTO algorithm is crafted to enable joint search over tasks and their solutions. This joint search is supported by two approximation models: (1) for mapping solutions to the objective spaces of all tasks, which provably accelerates convergence by acting as a conduit for inter-task knowledge transfers, and (2) for probabilistically mapping tasks to the solution space, which facilitates evolutionary exploration of under-explored regions of the task space. At the end of a full ($\boldsymbol{\theta}_l$, $\boldsymbol{\theta}_u$)-PMTO run, the acquired models enable rapid identification of optimized solutions for any task lying within the specified bounds. This outcome is validated on both synthetic test problems and practical case studies, with the significant real-world applicability of PMTO shown towards fast reconfiguration of robot controllers under changing task conditions. The potential of PMTO to vastly speedup the search for solutions to minimax optimization problems is also demonstrated through an example in robust engineering design.

Recent studies in using deep reinforcement learning (DRL) to solve Job-shop scheduling problems (JSSP) focus on construction heuristics. However, their performance is still far from optimality, mainly because the underlying graph representation scheme is unsuitable for modeling partial solutions at each construction step. This paper proposes a novel DRL-based method to learn improvement heuristics for JSSP, where graph representation is employed to encode complete solutions. We design a Graph Neural Network based representation scheme, consisting of two modules to effectively capture the information of dynamic topology and different types of nodes in graphs encountered during the improvement process. To speed up solution evaluation during improvement, we design a novel message-passing mechanism that can evaluate multiple solutions simultaneously. Extensive experiments on classic benchmarks show that the improvement policy learned by our method outperforms state-of-the-art DRL-based methods by a large margin.

Priority dispatching rule (PDR) is widely used for solving real-world Job-shop scheduling problem (JSSP). However, the design of effective PDRs is a tedious task, requiring a myriad of specialized knowledge and often delivering limited performance. In this paper, we propose to automatically learn PDRs via an end-to-end deep reinforcement learning agent. We exploit the disjunctive graph representation of JSSP, and propose a Graph Neural Network based scheme to embed the states encountered during solving. The resulting policy network is size-agnostic, effectively enabling generalization on large-scale instances. Experiments show that the agent can learn high-quality PDRs from scratch with elementary raw features, and demonstrates strong performance against the best existing PDRs. The learned policies also perform well on much larger instances that are unseen in training.

Recently, a higher competition in logistics business introduces new challenges to the vehicle routing problem (VRP). Re-route planning, also known as dynamic VRP, is one of the important challenges. The re-route planning has to be performed when new customers request for deliveries while the delivery vehicles, i.e., trucks, are serving other customers. While the re-route planning has been studied in the literature, most of the existing works do not consider different uncertainties. Therefore, in this paper, we propose two systems, i.e., (i) an offline package pickup and delivery planning with stochastic demands (PDPSD) and (ii) a re-route package pickup and delivery planning with stochastic demands (Re-route PDPSD). Accordingly, we formulate the PDPSD system as a two-stage stochastic optimization. We then extend the PDPSD system to the Re-route PDPSD system with a re-route algorithm. Furthermore, we evaluate performance of the proposed systems by using the dataset from Solomon Benchmark suite and a real data from a Singapore logistics 1company. The results show that the PDPSD system can achieve the lower cost than that of the baseline model. In addition, the Re-route PDPSD system can help the supplier efficiently and successfully to serve more customers while the trucks are already on the road.