Learning scalable and transferable multi-robot/machine sequential assignment planning via graph embedding

Can the success of reinforcement learning methods for simple combinatorial optimization problems be extended to multi-robot sequential assignment planning? In addition to the challenge of achieving near-optimal performance in large problems, transferability to an unseen number of robots and tasks is another key challenge for real-world applications. In this paper, we suggest a method that achieves the first success in both challenges for robot/machine scheduling problems. Our method comprises of three components. First, we show a robot scheduling problem can be expressed as a random probabilistic graphical model (PGM). We develop a mean-field inference method for random PGM and use it for Q-function inference. Second, we show that transferability can be achieved by carefully designing two-step sequential encoding of problem state. Third, we resolve the computational scalability issue of fitted Q-iteration by suggesting a heuristic auction-based Q-iteration fitting method enabled by transferability we achieved. We apply our method to discrete-time, discrete space problems (Multi-Robot Reward Collection (MRRC)) and scalably achieve 97% optimality with transferability. This optimality is maintained under stochastic contexts. By extending our method to continuous time, continuous space formulation, we claim to be the first learning-based method with scalable performance among multi-machine scheduling problems; our method scalability achieves comparable performance to popular metaheuristics in Identical parallel machine scheduling (IPMS) problems

Decentralized Resource Scheduling in Grid/Cloud Computing

In the Grid/Cloud environment, applications or services and resources belong to different organizations with different objectives. Entities in the Grid/Cloud are autonomous and self-interested; however, they are willing to share their resources and services to achieve their individual and collective goals. In such open environment, the scheduling decision is a challenge given the decentralized nature of the environment. Each entity has specific requirements and objectives that need to achieve. In this thesis, we review the Grid/Cloud computing technologies, environment characteristics and structure and indicate the challenges within the resource scheduling. We capture the Grid/Cloud scheduling model based on the complete requirement of the environment. We further create a mapping between the Grid/Cloud scheduling problem and the combinatorial allocation problem and propose an adequate economic-based optimization model based on the characteristic and the structure nature of the Grid/Cloud. By adequacy, we mean that a comprehensive view of required properties of the Grid/Cloud is captured. We utilize the captured properties and propose a bidding language that is expressive where entities have the ability to specify any set of preferences in the Grid/Cloud and simple as entities have the ability to express structured preferences directly. We propose a winner determination model and mechanism that utilizes the proposed bidding language and finds a scheduling solution. Our proposed approach integrates concepts and principles of mechanism design and classical scheduling theory. Furthermore, we argue that in such open environment privacy concerns by nature is part of the requirement in the Grid/Cloud. Hence, any scheduling decision within the Grid/Cloud computing environment is to incorporate the feasibility of privacy protection of an entity. Each entity has specific requirements in terms of scheduling and privacy preferences. We analyze the privacy problem in the Grid/Cloud computing environment and propose an economic based model and solution architecture that provides a scheduling solution given privacy concerns in the Grid/Cloud. Finally, as a demonstration of the applicability of the approach, we apply our solution by integrating with Globus toolkit (a well adopted tool to enable Grid/Cloud computing environment). We also, created simulation experimental results to capture the economic and time efficiency of the proposed solution

2 Combinatorial Models for Multi-agent Scheduling Problems

Abstract Scheduling models deal with the best way of carrying out a set of jobs on given processing resources. Typically, the jobs belong to a single decision maker, who wants to find the most profitable way of organizing and exploiting available resources, and a single objective function is specified. If different objectives are present, there can be multiple objective functions, but still the models refer to a centralized framework, in which a single decision maker, given data on the jobs and the system, computes the best schedule for the whole system. This approach does not apply to those situations in which the allocation process involves different subjects (agents), each having his/her own set of jobs, and there is no central authority who can solve possible conflicts in resource usage over time. In this case, the role of the model must be partially redefined, since rather than computing "optimal" solutions, the model is asked to provide useful elements for the negotiation process, which eventually leads to a stable and acceptable resource allocation. Multi-agent scheduling models are dealt with by several distinct disciplines (besides optimization, we mention game theory, artificial intelligence etc), possibly indicated by different terms. We are not going to review the whole scope in detail, but rather we will concentrate on combinatorial models, and how they can be employed for the purpose on hand. We will consider two major mechanisms for generating schedules, auctions and bargaining models, corresponding to different information exchange scenarios

Coordination mechanisms with mathematical programming models for decentralized decision-making, a literature review

[EN] The increase in the complexity of supply chains requires greater efforts to align the activities of all its members in order to improve the creation of value of their products or services offered to customers. In general, the information is asymmetric; each member has its own objective and limitations that may be in conflict with other members. Operations managements face the challenge of coordinating activities in such a way that the supply chain as a whole remains competitive, while each member improves by cooperating. This document aims to offer a systematic review of the collaborative planning in the last decade on the mechanisms of coordination in mathematical programming models that allow us to position existing concepts and identify areas where more research is needed.Rius-Sorolla, G.; Maheut, J.; Estelles Miguel, S.; García Sabater, JP. (2020). Coordination mechanisms with mathematical programming models for decentralized decision-making, a literature review. 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