Short Term Unit Commitment as a Planning Problem

‘Unit Commitment’, setting online schedules for generating units in a power system to ensure supply meets demand, is integral to the secure, efficient, and economic daily operation of a power system. Conflicting desires for security of supply at minimum cost complicate this. Sustained research has produced methodologies within a guaranteed bound of optimality, given sufficient computing time. Regulatory requirements to reduce emissions in modern power systems have necessitated increased renewable generation, whose output cannot be directly controlled, increasing complex uncertainties. Traditional methods are thus less efficient, generating more costly schedules or requiring impractical increases in solution time. Meta-Heuristic approaches are studied to identify why this large body of work has had little industrial impact despite continued academic interest over many years. A discussion of lessons learned is given, and should be of interest to researchers presenting new Unit Commitment approaches, such as a Planning implementation. Automated Planning is a sub-field of Artificial Intelligence, where a timestamped sequence of predefined actions manipulating a system towards a goal configuration is sought. This differs from previous Unit Commitment formulations found in the literature. There are fewer times when a unit’s online status switches, representing a Planning action, than free variables in a traditional formulation. Efficient reasoning about these actions could reduce solution time, enabling Planning to tackle Unit Commitment problems with high levels of renewable generation. Existing Planning formulations for Unit Commitment have not been found. A successful formulation enumerating open challenges would constitute a good benchmark problem for the field. Thus, two models are presented. The first demonstrates the approach’s strength in temporal reasoning over numeric optimisation. The second balances this but current algorithms cannot handle it. Extensions to an existing algorithm are proposed alongside a discussion of immediate challenges and possible solutions. This is intended to form a base from which a successful methodology can be developed

Optimal Planning with State Constraints

In the classical planning model, state variables are assigned values in the initial state and remain unchanged unless explicitly affected by action effects. However, some properties of states are more naturally modelled not as direct effects of actions but instead as derived, in each state, from the primary variables via a set of rules. We refer to those rules as state constraints. The two types of state constraints that will be discussed here are numeric state constraints and logical rules that we will refer to as axioms. When using state constraints we make a distinction between primary variables, whose values are directly affected by action effects, and secondary variables, whose values are determined by state constraints. While primary variables have finite and discrete domains, as in classical planning, there is no such requirement for secondary variables. For example, using numeric state constraints allows us to have secondary variables whose values are real numbers. We show that state constraints are a construct that lets us combine classical planning methods with specialised solvers developed for other types of problems. For example, introducing numeric state constraints enables us to apply planning techniques in domains involving interconnected physical systems, such as power networks. To solve these types of problems optimally, we adapt commonly used methods from optimal classical planning, namely state-space search guided by admissible heuristics. In heuristics based on monotonic relaxation, the idea is that in a relaxed state each variable assumes a set of values instead of just a single value. With state constraints, the challenge becomes to evaluate the conditions, such as goals and action preconditions, that involve secondary variables. We employ consistency checking tools to evaluate whether these conditions are satisfied in the relaxed state. In our work with numerical constraints we use linear programming, while with axioms we use answer set programming and three value semantics. This allows us to build a relaxed planning graph and compute constraint-aware version of heuristics based on monotonic relaxation. We also adapt pattern database heuristics. We notice that an abstract state can be thought of as a state in the monotonic relaxation in which the variables in the pattern hold only one value, while the variables not in the pattern simultaneously hold all the values in their domains. This means that we can apply the same technique for evaluating conditions on secondary variables as we did for the monotonic relaxation and build pattern databases similarly as it is done in classical planning. To make better use of our heuristics, we modify the A* algorithm by combining two techniques that were previously used independently – partial expansion and preferred operators. Our modified algorithm, which we call PrefPEA, is most beneficial in cases where heuristic is expensive to compute, but accurate, and states have many successors

Progress in AI Planning Research and Applications

Planning has made significant progress since its inception in the 1970s, in terms both of the efficiency and sophistication of its algorithms and representations and its potential for application to real problems. In this paper we sketch the foundations of planning as a sub-field of Artificial Intelligence and the history of its development over the past three decades. Then some of the recent achievements within the field are discussed and provided some experimental data demonstrating the progress that has been made in the application of general planners to realistic and complex problems. The paper concludes by identifying some of the open issues that remain as important challenges for future research in planning

Extending classical planning with state constraints: Heuristics and search for optimal planning

We present a principled way of extending a classical AI planning formalism with systems of state constraints, which relate - sometimes determine - the values of variables in each state traversed by the plan. This extension occupies an attractive middle ground between expressivity and complexity. It enables modelling a new range of problems, as well as formulating more efficient models of classical planning problems. An example of the former is planning-based control of networked physical systems - power networks, for example - in which a local, discrete control action can have global effects on continuous quantities, such as altering flows across the entire network. At the same time, our extension remains decidable as long as the satisfiability of sets of state constraints is decidable, including in the presence of numeric state variables, and we demonstrate that effective techniques for cost-optimal planning known in the classical setting - in particular, relaxation-based admissible heuristics - can be adapted to the extended formalism. In this paper, we apply our approach to constraints in the form of linear or non-linear equations over numeric state variables, but the approach is independent of the type of state constraints, as long as there exists a procedure that decides their consistency. The planner and the constraint solver interact through a well-defined, narrow interface, in which the solver requires no specialisation to the planning contextThis work was supported by ARC project DP140104219, “Robust AI Planning for Hybrid Systems”, and in part by ARO grant W911NF1210471 and ONR grant N000141210430

The matching relaxation for a class of generalized set partitioning problems

This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing maximum weighted matchings in suitable graphs. Besides providing dual bounds, the relaxations are also used on a variable reduction technique and a matheuristic. We show how that general method can be tailored to sample applications, and also perform a successful computational evaluation with benchmark instances of a problem in maritime logistics.Comment: 33 pages. A preliminary (4-page) version of this paper was presented at CTW 2016 (Cologne-Twente Workshop on Graphs and Combinatorial Optimization), with proceedings on Electronic Notes in Discrete Mathematic

Hybrid Offline/Online Methods for Optimization Under Uncertainty

This work considers multi-stage optimization problems under uncertainty. In this context, at each stage some uncertainty is revealed and some decision must be made: the need to account for multiple future developments makes stochastic optimization incredibly challenging. Due to such a complexity, the most popular approaches depend on the temporal granularity of the decisions to be made. These approaches are, in general, sampling-based methods and heuristics. Long-term strategic decisions (which are often very impactful) are typically solved via expensive, but more accurate, sampling-based approaches. Short-term operational decisions often need to be made over multiple steps, within a short time frame: they are commonly addressed via polynomial-time heuristics, while more advanced sampling-based methods are applicable only if their computational cost is carefully managed. We will refer to the first class of problems (and solution approaches) as offline and to the second as online. These phases are typically solved in isolation, despite being strongly interconnected. Starting from the idea of providing multiple options to balance the solution quality/time trade-off in optimization problem featuring offline and online phases, we propose different methods that have broad applicability. These methods have been firstly motivated by applications in real-word energy problems that involve distinct offline and online phases: for example, in Distributed Energy Management Systems we may need to define (offline) a daily production schedule for an industrial plant, and then manage (online) its power supply on a hour by hour basis. Then we show that our methods can be applied to a variety of practical application scenarios in very different domains with both discrete and numeric decision variables

Planning as Optimization: Dynamically Discovering Optimal Configurations for Runtime Situations

The large number of possible configurations of modern software-based systems, combined with the large number of possible environmental situations of such systems, prohibits enumerating all adaptation options at design time and necessitates planning at run time to dynamically identify an appropriate configuration for a situation. While numerous planning techniques exist, they typically assume a detailed state-based model of the system and that the situations that warrant adaptations are known. Both of these assumptions can be violated in complex, real-world systems. As a result, adaptation planning must rely on simple models that capture what can be changed (input parameters) and observed in the system and environment (output and context parameters). We therefore propose planning as optimization: the use of optimization strategies to discover optimal system configurations at runtime for each distinct situation that is also dynamically identified at runtime. We apply our approach to CrowdNav, an open-source traffic routing system with the characteristics of a real-world system. We identify situations via clustering and conduct an empirical study that compares Bayesian optimization and two types of evolutionary optimization (NSGA-II and novelty search) in CrowdNav