Alexander Schiendorfer

Cooperative Resource Allocation in Open Systems of Systems

Resource allocation is a common problem in many technical systems. In multi-agent systems, the decentralized or regionalized solution of this problem usually requires the agents to cooperate due to their limited resources and knowledge. At the same time, if these systems are of large scale, scalability issues can be addressed by a self-organizing hierarchical system structure that enables problem decomposition and compartmentalization. In open systems, various uncertainties—introduced by the environment as well as the agents’ possibly self-interested or even malicious behavior—have to be taken into account to be able to allocate the resources according to the actual demand. In this article, we present a trust- and cooperation-based algorithm that solves a dynamic resource allocation problem in open systems of systems. To measure and deal with uncertainties imposed by the environment and the agents at runtime, the algorithm uses the social concept of trust. In a hierarchical setting, we additionally show how agents create constraint models by learning the capabilities of subordinate agents if these are not able or willing to disclose this information. Throughout the article, the creation of power plant schedules in decentralized autonomous power management systems serves as a running example.

Synthesised constraint models for distributed energy management

Resource allocation is a task frequently encountered in energy management systems such as the coordination of power generators in a virtual power plant (unit commitment). Standard solutions require fixed parametrised optimisation models that the participants have to stick to without leaving room for tailored behaviour or individual preferences. We present a modelling methodology that allows organisations to specify optimisation goals independently of concrete participants and participants to craft more detailed models and state individual preferences. While considerable efforts have been spent on devising efficient control algorithms and detailed physical models in power management systems, practical aspects of unifying several heterogeneous models for optimisation have been widely ignored - a gap we aim to close. As a by-product, we give a formulation of warm and cold start-up times for power plants that improves existing power plant models. The concepts are detailed with the load-distribution problem faced in virtual power plants and evaluated on several random instances where we observe that a significant number of soft constraints of individual actors can be satisfied if considered.

Constraint Relationships for Soft Constraints

We introduce constraint relationships as a means to define qualitative preferences on the constraints of soft constraint problems. The approach is aimed at constraint satisfaction problems (CSPs) with a high number of constraints that make exact preference quantizations hard to maintain manually or hard to anticipate—especially if constraints or preferences change at runtime or are extracted from natural language text. Modelers express preferences over the satisfaction of constraints with a clear semantics regarding preferred tuples without assigning priorities to concrete domain values. We show how a CSP including a set of constraint relationships can linearly be transformed into a k-weighted CSP as a representative of c-semirings that is solved by widely available constraint solvers and compare it with existing techniques. We demonstrate the approach by using a typical example of a dynamic and interactive scheduling problem in AI.

Partial Valuation Structures for Qualitative Soft Constraints

Soft constraints have proved to be a versatile tool for the specification and implementation of decision making in adaptive systems. A plethora of formalisms have been devised to capture different notions of preference. Wirsing et al. have proposed partial valuation structures as a unifying algebraic structure for several soft constraint formalisms, including quantitative and qualitative ones, which, in particular, supports lexicographic products in a broad range of cases. We demonstrate the versatility of partial valuation structures by integrating the qualitative formalism of constraint relationships as well as the hybrid concept of constraint hierarchies. The latter inherently relies on lexicographic combinations, but it turns out that not all can be covered directly by partial valuation structures. We therefore investigate a notion for simulating partial valuation structures not amenable to lexicographic combinations by better suited ones. The concepts are illustrated by a case study in decentralized energy management.

Quality over Quantity in Soft Constraints

Partial constraint satisfaction and soft constraints enable to deal with over-constrained problems in practice. Constraint relationships have been introduced to provide a qualitative approach to specifying preferences over the constraints that should be satisfied. In contrast to quantitative approaches like weighted or fuzzy CSPs, the preferences just rely on a directed acyclic graph. The approach is particularly aimed at scenarios where soft-constraint problems stemming from several independently modeled agents have to be aggregated into one problem in a multi-agent system. Existing transformations into weighted CSP introduce unintended, additional preference decisions. We first illustrate the application of constraint relationships in a case study from energy management along with deficiencies of existing work. We then show how to embed constraint relationships into the soft constraint frameworks of partial valuation structures and further c-semi rings by means of free constructions. We finally provide a prototypical implementation of heuristics for the well-known branch-and-bound algorithm along with an empirical evaluation.

Towards Self-Organizing Swarms of Reconfigurable Self-Aware Robots

Designing complex adaptive systems for real world applications is a delicate challenge, especially when support for humans in crucial situations should be achieved. In this position paper, we propose a multi-agent based approach for physically reconfigurable, heterogeneous robot swarms. These can be deployed when there is a need to search, continuously observe and react, e.g. in disaster scenarios. We show first results that validate the feasibility of our approach.

Abstraction of Heterogeneous Supplier Models in Hierarchical Resource Allocation

Resource allocation problems such as finding a production schedule given a set of suppliers’ capabilities are generally hard to solve due to their combinatorial nature, in particular beyond a certain problem size. Large-scale instances among them, however, are prominent in several applications relevant to smart grids including unit commitment and demand response. Decomposition constitutes a classical tool to deal with this increasing complexity. We present a hierarchical “regio-central” decomposition based on abstraction that is designed to change its structure at runtime. It requires two techniques: (1) synthesizing several models of suppliers into one optimization problem and (2) abstracting the direct composition of several suppliers to reduce the complexity of high-level optimization problems. The problems we consider involve limited maximal and, in particular, minimal capacities along with on/off constraints. We suggest a formalization termed supply automata to capture suppliers and present algorithms for synthesis and abstraction. Our evaluation reveals that the obtained solutions are comparable to central solutions in terms of cost efficiency (within 1 % of the optimum) but scale significantly better (between a third and a half of the runtime) in the case study of scheduling virtual power plants.

Active Learning for Efficient Sampling of Control Models of Collectives

Many large-scale systems benefit from an organizational structure to provide for problem decomposition. A pivotal problem solving setting is given by hierarchical control systems familiar from hierarchical task networks. If these structures can be modified autonomously by, e.g., Coalition formation and reconfiguration, adequate decisions on higher levels require a faithful abstracted model of a collective of agents. An illustrative example is found in calculating schedules for a set of power plants organized in a hierarchy of Autonomous Virtual Power Plants. Functional dependencies over the combinatorial domain, such as the joint costs or rates of change of power production, are approximated by repeatedly sampling input-output pairs and substituting the actual functions by piecewise linear functions. However, if the sampled data points are weakly informative, the resulting abstracted high-level optimization introduces severe errors. Furthermore, obtaining additional point labels amounts to solving computationally hard optimization problems. Building on prior work, we propose to apply techniques from active learning to maximize the information gained by each additional point. Our results show that significantly better allocations in terms of cost-efficiency (up to 33.7 % reduction in costs in our case study) can be found with fewer but carefully selected sampling points using Decision Forests.

MiniBrass: Soft constraints for MiniZinc

Over-constrained problems are ubiquitous in real-world decision and optimization problems. Plenty of modeling formalisms for various problem domains involving soft constraints have been proposed, such as weighted, fuzzy, or probabilistic constraints. All of them were shown to be instances of algebraic structures. In terms of modeling languages, however, the field of soft constraints lags behind the state of the art in classical constraint optimization. We introduce MiniBrass, a versatile soft constraint modeling language building on the unifying algebraic framework of partially ordered valuation structures (PVS) that is implemented as an extension of MiniZinc and MiniSearch. We first demonstrate the adequacy of PVS to naturally augment partial orders with a combination operation as used in soft constraints. Moreover, we provide the most general construction of a c-semiring from an arbitrary PVS. Both arguments draw upon elements from category theory. MiniBrass turns these theoretical considerations into practice: It offers a generic extensible PVS type system, reusable implementations of specific soft constraint formalisms as PVS types, operators for complex PVS products, and morphisms to transform PVS. MiniBrass models are compiled into MiniZinc to benefit from the wide range of solvers supporting FlatZinc. We evaluated MiniBrass on 28 “softened” MiniZinc benchmark problems with six different solvers. The results demonstrate the feasibility of our approach.

Specification and Design of Trust-Based Open Self-Organising Systems

In open multi-agent systems, we can make only little assumptions about the system’s scale, the behaviour of participating agents, and its environment. Especially with regard to mission-critical systems, the ability to deal with a large number of heterogeneous agents that are exposed to an uncertain environment becomes a major concern: Because failures can have massive consequences for people, industries, and public services, it is of utmost importance that such systems achieve their goals under all circumstances. A prominent example are power management systems whose paramount goal is to balance production and consumption. In this context, we tackle challenges comprising how to specify and design these systems to allow for their efficient and robust operation. Among other things, we introduce constraint-based specification techniques to address the system’s heterogeneity and show trust models that allow to measure, anticipate, and deal with uncertainties. On this basis, we present algorithms for self-organisation and self-optimisation that enable the formation of scalable system structures at runtime and allow for efficient and robust resource allocation under adverse conditions. Throughout the chapter, the problem of balancing production and consumption in decentralised autonomous power management systems serves as a case study.