Search

Algorithms that involve both forecasting and optimization are at the core of solutions to many difficult real-world problems, such as in supply chains (inventory optimization), traffic, and in the transition towards carbon-free energy generation in battery/load/production scheduling in sustainable energy systems. Typically, in these scenarios we want to solve an optimization problem that depends on unknown future values, which therefore need to be forecast. As both forecasting and optimization are difficult problems in their own right, relatively few research has been done in this area. This paper presents the findings of the ``IEEE-CIS Technical Challenge on Predict+Optimize for Renewable Energy Scheduling," held in 2021. We present a comparison and evaluation of the seven highest-ranked solutions in the competition, to provide researchers with a benchmark problem and to establish the state of the art for this benchmark, with the aim to foster and facilitate research in this area. The competition used data from the Monash Microgrid, as well as weather data and energy market data. It then focused on two main challenges: forecasting renewable energy production and demand, and obtaining an optimal schedule for the activities (lectures) and on-site batteries that lead to the lowest cost of energy. The most accurate forecasts were obtained by gradient-boosted tree and random forest models, and optimization was mostly performed using mixed integer linear and quadratic programming. The winning method predicted different scenarios and optimized over all scenarios jointly using a sample average approximation method.

The classic problem of constrained pathfinding is a well-studied, yet challenging, topic in AI with a broad range of applications in various areas such as communication and transportation. The Weight Constrained Shortest Path Problem (WCSPP), the base form of constrained pathfinding with only one side constraint, aims to plan a cost-optimum path with limited weight/resource usage. Given the bi-criteria nature of the problem (i.e., dealing with the cost and weight of paths), methods addressing the WCSPP have some common properties with bi-objective search. This paper leverages the recent state-of-the-art techniques in both constrained pathfinding and bi-objective search and presents two new solution approaches to the WCSPP on the basis of A* search, both capable of solving hard WCSPP instances on very large graphs. We empirically evaluate the performance of our algorithms on a set of large and realistic problem instances and show their advantages over the state-of-the-art algorithms in both time and space metrics. This paper also investigates the importance of priority queues in constrained search with A*. We show with extensive experiments on both realistic and randomised graphs how bucket-based queues without tie-breaking can effectively improve the algorithmic performance of exhaustive A*-based bi-criteria searches., Comment: 62 pages, 16 figures, 7 tables

Bi-objective search is a well-known algorithmic problem, concerned with finding a set of optimal solutions in a two-dimensional domain. This problem has a wide variety of applications such as planning in transport systems or optimal control in energy systems. Recently, bi-objective A*-based search (BOA*) has shown state-of-the-art performance in large networks. This paper develops a bi-directional and parallel variant of BOA*, enriched with several speed-up heuristics. Our experimental results on 1,000 benchmark cases show that our bi-directional A* algorithm for bi-objective search (BOBA*) can optimally solve all of the benchmark cases within the time limit, outperforming the state of the art BOA*, bi-objective Dijkstra and bi-directional bi-objective Dijkstra by an average runtime improvement of a factor of five over all of the benchmark instances., Comment: 16 pages, 4 figures, in Proceedings of The European Symposium on Algorithms 2021 (ESA21), Changes: including the backward search of BOBA*

To support N-1 pre-fault transient stability assessment, this paper introduces a new data collection method in a data-driven algorithm incorporating the knowledge of power system dynamics. The domain knowledge on how the disturbance effect will propagate from the fault location to the rest of the network is leveraged to recognise the dominant conditions that determine the stability of a system. Accordingly, we introduce a new concept called Fault-Affected Area, which provides crucial information regarding the unstable region of operation. This information is embedded in an augmented dataset to train an ensemble model using an instance transfer learning framework. The test results on the IEEE 39-bus system verify that this model can accurately predict the stability of previously unseen operational scenarios while reducing the risk of false prediction of unstable instances compared to standard approaches., Comment: Accepted at the 2021 IEEE PES General Meeting, July 25-29 2020, Washington, DC, USA

Efficient optimisation algorithms have become important tools for finding high-quality solutions to hard, real-world problems such as production scheduling, timetabling, or vehicle routing. These algorithms are typically "black boxes" that work on mathematical models of the problem to solve. However, many problems are difficult to fully specify, and require a "human in the loop" who collaborates with the algorithm by refining the model and guiding the search to produce acceptable solutions. Recently, the Problem-Solving Loop was introduced as a high-level model of such interactive optimisation. Here, we present and evaluate nine recommendations for the design of interactive visualisation tools supporting the Problem-Solving Loop. They range from the choice of visual representation for solutions and constraints to the use of a solution gallery to support exploration of alternate solutions. We first examined the applicability of the recommendations by investigating how well they had been supported in previous interactive optimisation tools. We then evaluated the recommendations in the context of the vehicle routing problem with time windows (VRPTW). To do so we built a sophisticated interactive visual system for solving VRPTW that was informed by the recommendations. Ten participants then used this system to solve a variety of routing problems. We report on participant comments and interaction patterns with the tool. These showed the tool was regarded as highly usable and the results generally supported the usefulness of the underlying recommendations., Comment: 9+2 pages, 6 figures, VAST 2020

The transition to a new low emission energy future results in a changing mix of generation and load types due to significant growth in renewable energy penetration and reduction in system inertia due to the exit of ageing fossil fuel power plants. This increases technical challenges for electrical grid planning and operation. This study introduces a new decomposition approach to account for the system security for short term planning using conventional machine learning tools. The immediate value of this work is that it provides extendable and computationally efficient guidelines for using supervised learning tools to assess first swing transient stability status. To provide an unbiased evaluation of the final model fit on the training dataset, the proposed approach was examined on a previously unseen test set. It distinguished stable and unstable cases in the test set accurately, with only 0.57% error, and showed a high precision in predicting the time of instability, with 6.8% error and mean absolute error as small as 0.0145.

Autonomous droop control PV inverters have improved voltage regulation compared to the inverters without grid support functions, but more flexible control techniques will be required as the number of solar photovoltaic (PV) installations increases. This paper studies three inverter future deployment scenarios with droop control inverters, non-exporting inverters, and coordinated inverter control (CIC). The network operation and the interaction between various inverter control methods are studied by simulating inverter operation on two low-voltage networks. Considering 30% PV penetration as the base case, we demonstrate that coordinated inverters can mitigate overvoltages and voltage fluctuations caused by the tripping of passive inverters in 85% of PV location cases when at least as many coordinated as passive inverters are deployed on the 114-node test feeder. However, this rate reduced to 37% with the IEEE 906-node network demonstrating that the deployment of coordinated inverter control may not be able to reverse passive inverter-related voltage disturbances when the build-up of passive inverters has reached a certain threshold. The aggregated PV output from coordinated inverters can be also used to provide grid support services. When the low-voltage networks operate close to the upper voltage limits, the change in the power output from coordinated inverters following a regulation request may be partially offset by passive inverters. Considering an equal number of passive and coordinated inverters, this paper shows that for each unit of the down-regulation request delivered by coordinated inverters, passive inverter output may increase by up to 0.2 units and decrease by up to 0.45 units during coordinated inverter up-regulation., Comment: 11 pages, 10 figures

Coordinated photovoltaic inverter control with centralized coordination of curtailment can increase the amount of energy sent from low-voltage (LV) distribution networks to the grid while respecting voltage constraints. First, this paper quantifies the improvement of such an approach relative to autonomous droop control, in terms of PV curtailment and line losses in balanced networks. It then extends the coordinated inverter control to unbalanced distribution networks. Finally, it formulates a control algorithm for different objectives such as the fairer distribution of PV curtailment and rewarding PV customers for utilizing the excess power locally. The coordinated inverter control algorithm is tested on the 114-node and 906-bus LV European test feeders with cable sizes between 50mm^2 and 240mm^2 and validated with reference to OpenDSS. The results demonstrate that coordinated inverter control is superior when applied to high impedance LV networks and LV networks constrained by the distribution transformer capacity limits compared to autonomous inverters. On the 95mm^2 overhead line, it yields a 2% increase on average in the utilized PV output with up to 5% increase for some PV locations at higher penetration levels. Up to a 20% increase in PV hosting capacity was observed for location scenarios with PV system clustering., Comment: 11 pages, 14 figures

The integration of a high share of solar photovoltaics (PV) in distribution networks requires advanced voltage control technologies or network augmentation, both associated with significant investment costs. An alternative is to prevent new customers from installing solar PV systems, but this is against the common goal of increasing renewable energy generation. This paper demonstrates that solar PV curtailment in low voltage areas can be reduced and fairly distributed among PV owners by centrally coordinating the operation of PV inverters. The optimal inverter active and reactive power operation points are computed by solving a multi-objective optimization problem with a fairness objective. The main results show that fair optimal inverter dispatch (FOID) results in less power curtailment than passive voltage regulation based on Volt/VAr droop control, especially at high solar PV to load ratios. The effectiveness of the model is demonstrated on a residential low voltage network., Comment: 6 pages, 5 figures, 2019 IEEE Milan PowerTech

Constraint Satisfaction Problems (CSPs) typically have many solutions that satisfy all constraints. Often though, some solutions are preferred over others, that is, some solutions dominate other solutions. We present solution dominance as a formal framework to reason about such settings. We define Constraint Dominance Problems (CDPs) as CSPs with a dominance relation, that is, a preorder over the solutions of the CSP. This framework captures many well-known variants of constraint satisfaction, including optimization, multi-objective optimization, Max-CSP, minimal models, minimum correction subsets as well as optimization over CP-nets and arbitrary dominance relations. We extend MiniZinc, a declarative language for modeling CSPs, to CDPs by introducing dominance nogoods; these can be derived from dominance relations in a principled way. A generic method for solving arbitrary CDPs incrementally calls a CSP solver and is compatible with any existing solver that supports MiniZinc. This encourages experimenting with different solution dominance relations for a problem, as well as comparing different solvers without having to modify their implementations., Comment: Presented at the ModRef18 workshop at CP18

Strings are extensively used in modern programming languages and constraints over strings of unknown length occur in a wide range of real-world applications such as software analysis and verification, testing, model checking, and web security. Nevertheless, practically no CP solver natively supports string constraints. We introduce string variables and a suitable set of string constraints as builtin features of the MiniZinc modelling language. Furthermore, we define an interpreter for converting a MiniZinc model with strings into a FlatZinc instance relying on only integer variables. This provides a user-friendly interface for modelling combinatorial problems with strings, and enables both string and non-string solvers to actually solve such problems., Comment: Pre-proceedings paper presented at the 26th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2016), Edinburgh, Scotland UK, 6-8 September 2016 (arXiv:1608.02534)

The ability to model search in a constraint solver can be an essential asset for solving combinatorial problems. However, existing infrastructure for defining search heuristics is often inadequate. Either modeling capabilities are extremely limited or users are faced with a general-purpose programming language whose features are not tailored towards writing search heuristics. As a result, major improvements in performance may remain unexplored. This article introduces search combinators, a lightweight and solver-independent method that bridges the gap between a conceptually simple modeling language for search (high-level, functional and naturally compositional) and an efficient implementation (low-level, imperative and highly non-modular). By allowing the user to define application-tailored search strategies from a small set of primitives, search combinators effectively provide a rich domain-specific language (DSL) for modeling search to the user. Remarkably, this DSL comes at a low implementation cost to the developer of a constraint solver. The article discusses two modular implementation approaches and shows, by empirical evaluation, that search combinators can be implemented without overhead compared to a native, direct implementation in a constraint solver.

When implementing a propagator for a constraint, one must decide about variants: When implementing min, should one also implement max? Should one implement linear constraints both with unit and non-unit coefficients? Constraint variants are ubiquitous: implementing them requires considerable (if not prohibitive) effort and decreases maintainability, but will deliver better performance than resorting to constraint decomposition. This paper shows how to use views to derive perfect propagator variants. A model for views and derived propagators is introduced. Derived propagators are proved to be indeed perfect in that they inherit essential properties such as correctness and domain and bounds consistency. Techniques for systematically deriving propagators such as transformation, generalization, specialization, and type conversion are developed. The paper introduces an implementation architecture for views that is independent of the underlying constraint programming system. A detailed evaluation of views implemented in Gecode shows that derived propagators are efficient and that views often incur no overhead. Without views, Gecode would either require 180 000 rather than 40 000 lines of propagator code, or would lack many efficient propagator variants. Compared to 8 000 lines of code for views, the reduction in code for propagators yields a 1750% return on investment., Comment: 28 pages, 7 tables, 3 figures

When implementing a propagator for a constraint, one must decide about variants: When implementing min, should one also implement max? Should one implement linear equations both with and without coefficients? Constraint variants are ubiquitous: implementing them requires considerable (if not prohibitive) effort and decreases maintainability, but will deliver better performance. This paper shows how to use variable views, previously introduced for an implementation architecture, to derive perfect propagator variants. A model for views and derived propagators is introduced. Derived propagators are proved to be indeed perfect in that they inherit essential properties such as correctness and domain and bounds consistency. Techniques for systematically deriving propagators such as transformation, generalization, specialization, and channeling are developed for several variable domains. We evaluate the massive impact of derived propagators. Without derived propagators, Gecode would require 140000 rather than 40000 lines of code for propagators., Comment: 17 pages, 2 tables

We describe decomposition during search (DDS), an integration of And/Or tree search into propagation-based constraint solvers. The presented search algorithm dynamically decomposes sub-problems of a constraint satisfaction problem into independent partial problems, avoiding redundant work. The paper discusses how DDS interacts with key features that make propagation-based solvers successful: constraint propagation, especially for global constraints, and dynamic search heuristics. We have implemented DDS for the Gecode constraint programming library. Two applications, solution counting in graph coloring and protein structure prediction, exemplify the benefits of DDS in practice., Comment: 20 pages, 9 figures, 2 tables; longer, more detailed version