Peter J. Stuckey

University of Melbourne | MSD · Department of Computing and Information Systems

Instant-runoff voting (IRV) is used in several countries around the world. It requires voters to rank candidates in order of preference, and uses a counting algorithm that is more complex than systems such as first-past-the-post or scoring rules. An even more complex system, the single transferable vote (STV), is used when multiple candidates need...

Instant-runoff voting (IRV) is used in several countries around the world. It requires voters to rank candidates in order of preference, and uses a counting algorithm that is more complex than systems such as first-past-the-post or scoring rules. An even more complex system, the single transferable vote (STV), is used when multiple candidates need...

Multi-Train Path Finding (MTPF) is a coordination problem that asks us to plan collision-free paths for a team of moving agents, where each agent occupies a sequence of locations at any given time. MTPF is useful for planning a range of real-world vehicles, including rail trains and road convoys. MTPF is closely related to another coordination prob...

The Euclidean Shortest Path Problem (ESPP) asks us to find a minimum length path between two points on a 2D plane while avoiding a set of polygonal obstacles. Existing approaches for ESPP, based on Dijkstra or A* search, are primal methods that gradually build up longer and longer valid paths until they reach the target. In this paper we define an...

The Euclidean shortest path problem (ESPP) is a well studied problem with many practical applications. Recently a new efficient online approach to this problem, RayScan, has been developed, based on ray shooting and polygon scanning. In this paper we show how we can improve RayScan by carefully reasoning about polygon scans. We also look into how R...

Ranked voting systems, such as instant-runoff voting (IRV) and single transferable vote (STV), are used in many places around the world. They are more complex than plurality and scoring rules, presenting a challenge for auditing their outcomes: there is no known risk-limiting audit (RLA) method for STV other than a full hand count. We present a new...

Multi-Agent Path Finding (MAPF) is the problem of planning collision-free paths for multiple agents in a shared environment. In this paper, we propose a novel algorithm MAPF-LNS2 based on large neighborhood search for solving MAPF efficiently. Starting from a set of paths that contain collisions, MAPF-LNS2 repeatedly selects a subset of colliding a...

Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths for multiple agents that minimize the sum of path costs. EECBS is a leading two-level algorithm that solves MAPF bounded-suboptimally, that is, within some factor w of the minimum sum of path costs C*. It uses focal search to find bounded-suboptimal paths on the low leve...

The predict+optimize problem combines machine learning and combinatorial optimization by predicting the problem coefficients first and then using these coefficients to solve the optimization problem. While this problem can be solved in two separate stages, recent research shows end to end models can achieve better results. This requires differentia...

Tree ensembles (TEs) denote a prevalent machine learning model that do not offer guarantees of interpretability, that represent a challenge from the perspective of explainable artificial intelligence. Besides model agnostic approaches, recent work proposed to explain TEs with formally-defined explanations, which are computed with oracles for propos...

Motivation: Alignments are correspondences between sequences. How reliable are alignments of amino acid sequences of proteins, and what inferences about protein relationships can be drawn? Using techniques not previously applied to these questions, by weighting every possible sequence alignment by its posterior probability we derive a formal mathe...

The rise of AI methods to make predictions and decisions has led to a pressing need for more explainable artificial intelligence (XAI) methods. One common approach for XAI is to produce a post-hoc explanation, explaining why a black box ML model made a certain prediction. Formal approaches to post-hoc explanations provide succinct reasons for why a...

Temporal Jump Point Search (JPST) is a recently introduced algorithm for grid-optimal pathfinding among dynamic temporal obstacles. In this work we consider JPST as a low-level planner in Multi-Agent Path Finding (MAPF). We investigate how the canonical ordering of JPST can negatively impact MAPF performance and we consider several strategies which...

Computing time-optimal shortest paths, in road networks, is one of the most popular applications of Artificial Intelligence. This problem is tricky to solve because road congestion affects travel times. The state-of-the-art in this area is an algorithm called Time-dependent Contraction Hierarchies (TCH). Although fast and optimal, TCH still suffers...

Discrete optimisation problems often reason about finite sets of objects. While the underlying solvers will represent these objects as integer values, most modelling languages include enumerated types that allow the objects to be expressed as a set of names. Data attached to an object is made accessible through given arrays or functions from object...

Block modeling algorithms are used to discover important latent structures in graphs. They are the graph equivalent of clustering algorithms. However, existing block modeling algorithms work directly on the given graphs, making them computationally expensive and less effective on large complex graphs. In this paper, we propose a FastMap-based algor...

Boolean satisfiability (SAT) solvers have dramatically improved their performance in the last twenty years, enabling them to solve large and complex problems. More recently MaxSAT solvers have appeared that efficiently solve optimisation problems based on SAT. This means that SAT solvers have become a competitive technology for tackling discrete op...

This paper explains the main principles and some of the technical details for auditing the scanning and digitisation of the Australian Senate ballot papers. We give a short summary of the motivation for auditing paper ballots, explain the necessary supporting steps for a rigorous and transparent audit, and suggest some statistical methods that woul...

Blockmodelling is the process of determining community structure in a graph. Real graphs contain noise and so it is up to the blockmodelling method to allow for this noise and reconstruct the most likely role memberships and role relationships. Relationships are encoded in a graph using the absence and presence of edges. Two objects are considered...

The Electric Vehicle Routing Problem with Time Windows, Piecewise-Linear Recharging and Capacitated Recharging Stations aims to design minimum-cost routes for a fleet of electric vehicles subject to intra-route and inter-route constraints. Every vehicle is equipped with a rechargeable battery that depletes while it transports goods along its route....

Risk-limiting audits (RLAs) are an increasingly important method for checking that the reported outcome of an election is, in fact, correct. Indeed, their use is increasingly being legislated. While effective methods for RLAs have been developed for many forms of election -- for example: first-past-the-post, instant-runoff voting, and D'Hondt elect...

Decision sets and decision lists are two of the most easily explainable machine learning models. Given the renewed emphasis on explainable machine learning decisions, both of these machine learning models are becoming increasingly attractive, as they combine small size and clear explainability. In this paper, we define size as the total number of l...

Non-termination is an unwanted program property (considered a bug) for some software systems, and a safety property for other systems. In either case, automated discovery of preconditions for non-termination is of interest. We introduce NtHorn, a fast lightweight non-termination analyser, able to deduce non-trivial sufficient conditions for non-ter...

We revisit disjunctive interval analysis based on the Boxes abstract domain. We propose the use of what we call range decision diagrams (RDDs) to implement Boxes, and we provide algorithms for the necessary RDD operations. RDDs tend to be more compact than the linear decision diagrams (LDDs) that have traditionally been used for Boxes. Representing...

We consider optimal and suboptimal algorithms for the Euclidean Shortest Path Problem (ESPP) in two dimensions. For optimal path planning, Our approach leverages ideas from two recent works: Polyanya, a mesh-based ESPP planner which we use to represent and reason about the environment, and Compressed Path Databases (CPD), a speedup technique for pa...

Zones and Octagons are popular abstract domains for static program analysis. They enable the automated discovery of simple numerical relations that hold between pairs of program variables. Both domains are well understood mathematically but the detailed implementation of static analyses based on these domains poses many interesting algorithmic chal...

Precondition inference is a non-trivial problem with important applications in program analysis and verification. We present a novel iterative method for automatically deriving preconditions for the safety and unsafety of programs. Each iteration maintains over-approximations of the set of safe and unsafe initial states, which are used to partition...

Presidential primaries are a critical part of the United States Presidential electoral process, since they are used to select the candidates in the Presidential election. While methods differ by state and party, many primaries involve proportional delegate allocation using the so-called Hamilton method. In this paper we show how to conduct risk-lim...

Risk-limiting audits (RLAs), an ingredient in evidence-based elections, are increasingly common. They are a rigorous statistical means of ensuring that electoral results are correct, usually without having to perform an expensive full recount—at the cost of some controlled probability of error. A recently developed approach for conducting RLAs, SHA...

Conflict-Based Search (CBS) is a leading algorithm for optimal Multi-Agent Path Finding (MAPF) which features strong performance. In CBS, one conflict in a high-level node is resolved to generate two child nodes, until a node with no conflicts is found. Choosing the right conflict to resolve can greatly speed up the search. It is currently recommen...

Contraction hierarchies are graph-based data structure developed to speed up shortest path search in road networks. Built during an offline pre-processing step, contraction hierarchies are always paired with an online query algorithm which is a variation on bi-directional Dijkstra search. Though effective and highly popular this combination can som...

We consider two new types of pairwise path symmetries which appear in the context of Multi-Agent Path Finding (MAPF). The first of them, corridor symmetry, arises when two agents attempt to pass through the same narrow passage but in opposite directions. The second, target symmetry, arises when the shortest path of one agent requires the target loc...

We describe a new way of reasoning about symmetric collisions for Multi-Agent Path Finding (MAPF) on 4-neighbor grids. We also introduce a symmetry-breaking constraint to resolve these conflicts. This specialized technique allows us to identify and eliminate, in a single step, all permutations of two currently assigned but incompatible paths. Each...

We study prioritized planning for Multi-Agent Path Finding (MAPF). Existing prioritized MAPF algorithms depend on rule-of-thumb heuristics and random assignment to determine a fixed total priority ordering of all agents a priori. We instead explore the space of all possible partial priority orderings as part of a novel systematic and conflict-drive...

Precondition inference is a non-trivial problem with important applications in program analysis and verification. We present a novel iterative method for automatically deriving preconditions for the safety and unsafety of programs. Each iteration maintains over-approximations of the set of safe and unsafe initial states; which are used to partition...

This document provides a brief introduction to learned automated planning problem where the state transition function is in the form of a binarized neural network (BNN), presents a general MaxSAT encoding for this problem, and describes the four domains, namely: Navigation, Inventory Control, System Administrator and Cellda, that are submitted as b...

Multi-Agent Path Finding (MAPF) is a challenging combinatorial problem that asks us to plan collision-free paths for a team of cooperative agents. In this work, we show that one of the reasons why MAPF is so hard to solve is due to a phenomenon called pairwise symmetry, which occurs when two agents have many different paths to their target location...

Multi-Agent Path Finding (MAPF) is the challenging problem of computing collision-free paths for multiple agents. Algorithms for solving MAPF can be categorized on a spectrum. At one end are (bounded-sub)optimal algorithms that can find high-quality solutions for small problems. At the other end are unbounded-suboptimal algorithms that can solve la...

Artificial Intelligence (AI) is widely used in decision making procedures in myriads of real-world applications across important practical areas such as finance, healthcare, education, and safety critical systems. Due to its ubiquitous use in safety and privacy critical domains, it is often vital to understand the reasoning behind the AI decisions,...

Risk-limiting audits (RLAs), an ingredient in evidence-based elections, are increasingly common. They are a rigorous statistical means of ensuring that electoral results are correct, usually without having to perform an expensive full recount -- at the cost of some controlled probability of error. A recently developed approach for conducting RLAs,...

The shortest path problem (SPP) asks us to find a minimum length path between two points, usually on a graph. In a Euclidean environment the points are in a 2D plane and here the path must avoid a set of polygonal obstacles. Solution methods for this Euclidean SPP (ESPP) typically convert the continuous 2D map into a discretised representation, lik...

Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths for multiple agents. CBS is a leading optimal two-level MAPF solver whose low level plans optimal paths for single agents and whose high level runs a best-first search on a Constraint Tree (CT) to resolve the collisions between the paths. ECBS, a bounded-suboptimal varia...

Multi-Agent Path Finding (MAPF) is the combinatorial problem of finding collision-free paths for multiple agents on a graph. This paper describes MAPF-based software for solving train planning and replanning problems on large-scale railway networks under uncertainty. The software recently won the 2020 Flatland Challenge, a NeurIPS competition tryin...

Conflict-Based Search (CBS) is a leading two-level algorithm for optimal Multi-Agent Path Finding (MAPF). At its high level, CBS expands nodes by resolving conflicts. In recent years, admissible heuristics were added to the high level of CBS. We enhance all known heuristic functions for CBS by using information about the cost of resolving certain c...

We consider the design and implementation of a centralised oracle that provides commuters with customised and congestion-aware driving directions. Computing directions for a single journey is straightforward, but doing so at city-scale, in real-time, and under changing conditions is extremely challenging. In this work we describe a new type of cent...

Path planning on gridmaps is a common problem in AI and a popular topic in application areas such as computer games. Compressed Path Databases (CPDs) represent a state-of-theart approach to the problem, in terms of the speed of computing full optimal paths and also individual optimal moves. Despite significant improvements in recent years, the memo...

Conflict-based Search (CBS) is a effective approach to optimal multi-agent path finding. However, performance of CBS approaches degrade rapidly in highly-contended graphs with many agents. One of the reasons this occurs is that CBS does not detect independent subproblems; i.e. it can re-solve the same conflicts between the same pairs of agents up t...

Multi-Agent Path Finding (MAPF) is the planning problem of finding collision-free paths for a team of agents. We focus on Conflict-Based Search (CBS), a two-level tree-search state-of-the-art MAPF algorithm. The standard splitting strategy used by CBS is not disjoint, i.e., when it splits a problem into two subproblems, some solutions are shared by...

Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI. Rule-based models, such as decision trees, decision lists, and decision sets, are conventionally deemed to be...

Core-guided techniques have revolutionized Boolean satisfiability approaches to optimization problems (MaxSAT), but the process at the heart of these methods, strengthening bounds on solutions by repeatedly adding cardinality constraints, remains a bottleneck. Cardinality constraints require significant work to be re-encoded to SAT, and SAT solvers...

Nonlinear metrics, such as the F1-score, Matthews correlation coefficient, and Fowlkes–Mallows index, are often used to evaluate the performance of machine learning models, in particular, when facing imbalanced datasets that contain more samples of one class than the other. Recent optimal decision tree algorithms have shown remarkable progress in p...

During Multi-Agent Path Finding (MAPF) problems, agentscan be delayed by unexpected events. To address suchsituations recent work describes k-Robust Conflict-BasedSearch (k-CBS): an algorithm that produces coordinated andcollision-free plan that is robust for up tokdelays. In thiswork we introducing a variety of pairwise symmetry break-ing constrai...

Conflict-Based Search (CBS) is a leading two-level algorithm for optimal Multi-Agent Path Finding (MAPF). The main step of CBS is to expand nodes by resolving conflicts (where two agents collide). Choosing the ‘right’ conflict to resolve can greatly speed up the search. CBS first resolves conflicts where the costs (g-values) of the resulting child...

Compressed Path Databases (CPD) are powerful database-driven methods for shortest path extraction in grids and in spatial networks. Yet CPDs have two main drawbacks: (1) constructing the database requires an offline all-pairs precompute, which can sometimes be prohibitive and; (2) extracting a path requires a number of database lookups equal to its...

In 4-connected grid-based path planning one often needs to account for temporal and moving obstacles: ones that appear, disappear and which can prevent the agent from reaching its target. Such problems are common in a variety of settings (games, robotics etc.) and they can be surprisingly challenging to solve. First, because the temporal aspect inc...

Multi-Agent Path Finding (MAPF) is the combinatorial problem of finding collision-free paths for multiple agents on a graph. This paper describes MAPF-based software for solving train planning and replanning problems on large-scale rail networks under uncertainty. The software recently won the 2020 Flatland Challenge, a NeurIPS competition trying t...

What is the architectural “basis set” of the observed universe of protein structures? Using information-theoretic inference, we answer this question with a dictionary of 1,493 substructures—called concepts—typically at a subdomain level, based on an unbiased subset of known protein structures. Each concept represents a topologically conserved assem...

Multi-agent Pickup and Delivery (MAPD) is a challenging industrial problem where a team of robots is tasked with transporting a set of tasks, each from an initial location and each to a specified target location. Appearing in the context of automated warehouse logistics and automated mail sortation, MAPD requires first deciding which robot is assig...

Multi-Agent Path Finding (MAPF) is a challenging combinatorial problem that asks us to plan collision-free paths for a team of cooperative agents. In this work, we show that one of the reasons why MAPF is so hard to solve is due to a phenomenon called pairwise symmetry, which occurs when two agents have many different paths to their target location...

During Multi-Agent Path Finding (MAPF) problems, agents can be delayed by unexpected events. To address such situations recent work describes k-Robust Conflict-BasedSearch (k-CBS): an algorithm that produces coordinated and collision-free plan that is robust for up to k delays. In this work we introducing a variety of pairwise symmetry breaking con...

Presidential primaries are a critical part of the United States Presidential electoral process, since they are used to select the candidates in the Presidential election. While methods differ by state and party, many primaries involve proportional delegate allocation using the so-called Hamilton method. In this paper we show how to conduct risk-lim...

Given a portfolio of algorithms, the goal of Algorithm Selection (AS) is to select the best algorithm(s) for a new, unseen problem instance. Dynamic Symbolic Execution (DSE) brings together concrete and symbolic execution to maximise the program coverage. DSE uses a constraint solver to solve the path conditions and generate new inputs to explore....

Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI. Rule-based models, such as decision trees, decision lists, and decision sets, are conventionally deemed to be...

The predict+optimize problem combines machine learning ofproblem coefficients with a combinatorial optimization prob-lem that uses the predicted coefficients. While this problemcan be solved in two separate stages, it is better to directlyminimize the optimization loss. However, this requires dif-ferentiating through a discrete, non-differentiable...

String processing is ubiquitous across computer science, and arguably more so in web programming — where it is also a critical part of security issues such as injection attacks. In recent years, a number of string solvers have been developed to solve combinatorial problems involving string variables and constraints. We examine the dashed string app...

Decision lists are one of the most easily explainable machine learning models. Given the renewed emphasis on explainable machine learning decisions, this machine learning model is increasingly attractive, combining small size and clear explainability. In this paper, we show for the first time how to construct optimal "perfect" decision lists which...

In the context of increasing automation of Australian electoral processes, and accusations of deliberate interference in elections in Europe and the USA, it is worthwhile understanding how little a change in the recorded ballots could change an election result. In this paper we construct manipulations of the ballots in order to change the overall b...

Errors are inevitable in the implementation of any complex process. Here we examine the effect of random errors on Single Transferable Vote (STV) elections, a common approach to deciding multi-seat elections. It is usually expected that random errors should have nearly equal effects on all candidates, and thus be fair. We find to the contrary that...

Nonlinear metrics, such as the F1-score, Matthews correlation coefficient, and Fowlkes-Mallows index, are often used to evaluate the performance of machine learning models, in particular, when facing imbalanced datasets that contain more samples of one class than the other. Recent optimal decision tree algorithms have shown remarkable progress in p...

Online optimization approaches are popular for solving optimization problems where not all data is considered at once, because it is computationally prohibitive, or because new data arrives in an ongoing fashion. Online approaches solve the problem iteratively, with the amount of data growing in each iteration. Over time, many problem variables pro...

This paper describes the implementation of Nutmeg, a solver that hybridizes mixed integer linear programming and constraint programming using the branch-and-cut style of logic-based Benders decomposition known as branch-and-check. Given a high-level constraint programming model, Nutmeg automatically derives a mixed integer programming master proble...

Dashed strings are a formalism for modelling the domain of string variables when solving combinatorial problems with string constraints. In this work we focus on (variants of) the Replace constraint, which aims to find the first occurrence of a query string in a target string, and (possibly) replaces it with a new string. We define a Replace propag...

We study planning problems where the transition function is described by a learned binarized neural network (BNN). Theoretically, we show that feasible planning with a learned BNN model is NP-complete, and present two new constraint programming models of this task as a mathematical optimization problem. Experimentally, we run solvers for constraint...

The multi-agent collective construction problem tasks agents to construct any given three-dimensional structure on a grid by repositioning blocks. Agents are required to also use the blocks to build ramps in order to access the higher levels necessary to construct the building, and then remove the ramps upon completion of the building. This paper p...

Large-neighbourhood search (LNS) improves an initial solution, hence it is not directly applicable to satisfaction problems. In order to use LNS in a constraint programming (CP) framework to solve satisfaction problems, we usually soften some hard-to-satisfy constraints by replacing them with penalty-function constraints. LNS is then used to reduce...

Demand response is a control problem that optimizes the operation of electrical loads subject to limits on power consumption during times of low power supply or extreme power demand. This paper studies the demand response problem for centrally controlling the space conditioning systems of several buildings connected to a microgrid. The paper develo...

The argmax function returns the index of the (first copy of the) maximum value occuring in a list of values. argmax is important in models where we choose a characteristic value based on a seperate criteria, and for modelling neural networks which make use of argmax in their definition. The argmax constraint has been studied for the special case of...

As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type of model with unordered rules, which explains each prediction with a single rule. In order to be easy for hum...

Aircraft turnaround scheduling and airport ground services team/equipment planning directly concern both the airport operator and service providers. We first ensure airport-wide global optimality by solving a resource-constrained project scheduling problem (RCPSP) for minimal overall delays. We then support decentralized allocation of teams/vehicle...

Core-guided search has proven to be the state-of-the-art in finding optimal solutions for maximum Boolean satisfiability and these techniques have recently been successfully imported in constraint programming. While effective on a wide range of problems, the methods are direct translations of their propositional logic counterparts. We propose two r...

As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type of model with unordered rules, which explains each prediction with a single rule. In order to be easy for hum...

Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy. A commonly criticised point, however, is that the resulting trees may not necessarily be the best representati...

We have modelled modifications of a known ligand to the SARS‐CoV‐2 (COVID‐19) protease, that can form a covalent adduct, plus additional ligand‐protein hydrogen bonds. This article is protected by copyright. All rights reserved.

Errors are inevitable in the implementation of any complex process. Here we examine the effect of random errors on Single Transferable Vote (STV) elections, a common approach to deciding multi-seat elections. It is usually expected that random errors should have nearly equal effects on all candidates, and thus be fair. We find to the contrary that...

Conflict-Based Search (CBS) is a leading algorithm for optimal Multi-Agent Path Finding (MAPF). CBS variants typically compute MAPF solutions using some form of A* search. However, they often do so under strict time limits so as to avoid exhausting the available memory. In this paper, we present IDCBS, an iterative-deepening variant of CBS which ca...

We consider optimal and anytime algorithms for the Euclidean Shortest Path Problem (ESPP) in two dimensions. Our approach leverages ideas from two recent works: Polyanya, a mesh-based ESPP planner which we use to represent and reason about the environment, and Compressed Path Databases, a speedup technique for pathfinding on grids and spatial netwo...