Preference-Based Improvements on Solutions of Multi-Agent Temporal Problems by Automated Negotiation

Scheduling problems arise in numerous real-world situations. In many of them, different agents are each responsible for their own part of a scheduling problem, although they are dependent on the schedules of other agents. Hence, the agents have to adjust their schedules to certain external constraints. General approaches for solving multi-agent scheduling problems return an arbitrary solution that satisfies all constraints, regardless of the quality of the schedule. However, in many cases, agents have certain preferences with respect to the schedule, for example, they want to do tasks in a certain order, to complete all tasks as early as possible, or to have a break between two tasks. In the current literature, scheduling frameworks with preferences are only defined for singleagent problems. We therefore extend the work on Simple Temporal Problems and Disjunctive Temporal Problems, and develop the frameworks of Multi-agent Simple Temporal Problems with Preferences and Multi-agent Disjunctive Temporal Problems with Preferences. Having defined frameworks for these problems, we develop methods for solving them. Existing approaches for Multi-agent Temporal Problems search for a decoupling, i.e. a collection of local subproblems, one for each agent, such that any combination of solutions to the local subproblems is a solution to the original shared problem. By this, the agents can solve the subproblems in parallel, and their privacy is respected. We propose to improve existing decoupling solutions, with the preferences of the different agents as performance criterion, by applying automated negotiation. Automated negotiation is in general a computationally efficient distributed process in which the agents do not have to reveal all their preference information, that deals with both cooperation and competition, and hence fits well into the multi-agent scheduling context. Two types of negotiation protocols are developed: First, we propose post-decoupling protocols for finding Pareto-improvements on a given decoupling. Next, we develop pre-decoupling negotiation protocols that can be applied in existing decoupling algorithms to improve the decoupling. Our results show that both the post-decoupling and the pre-decoupling negotiation methods improve existing decoupling algorithms with respect to the preferences of the agents. For a larger number of agents, the pre-decoupling negotiation algorithms turn out to be better. Furthermore, we compare our solutions with methods that have the flexibility of a solution as performance metric and show that our solutions are more flexible. Finally, the possibilities for further increasing social welfare by letting the agents also make non-Pareto improvements are discussed. List of Abbreviations 4DPC Triangulating Directional Path Consistency CSP Constraint Satisfaction Problem D4DPC Distributed Triangulating Directional Path Consistency D4PPC Distributed Triangulating Partial Path Consistency DPC Directional Path Consistency DTP Disjunctive Temporal Problem DTPP Disjunctive Temporal Problem with Preferences FPC Full Path Consistency MaDTP Multi-agent Disjunctive Temporal Problem MaDTPP Multi-agent Disjunctive Temporal Problem with Preferences MaDTP-TD MaDTP Temporal Decoupling MaSTP Multi-agent Simple Temporal Problem MaSTPP Multi-agent Simple Temporal Problem with Preferences MaTD Multi-agent Temporal Decoupling MaTDR Multi-agent Temporal Decoupling with Relaxation OMT Optimization Modulo Theories PPC Partial Path Consistency SMT Satisfiability Modulo Theories STN Simple Temporal Network STP Simple Temporal Problem STPP Simple Temporal Problem with Preferences VDTP Valued Disjunctive Temporal Problem