Automated planning, a core area of artificial intelligence, aims to generate action sequences that achieve specified goals based on a formal model. In classical planning, where only Boolean state variables are allowed, conditional effects are the standard approach for modelling actions with state-dependent outcomes. However, unlike in the classical setting, relatively little research has focused on developing planning methods for numeric problems with conditional effects. To address this gap in the literature, this work studies numeric planning with conditional effects. We formalise its semantics and revise existing classical planning compilations for conditional effects to account for the specific features of numeric planning. This results in three encodings: two are designed for the full class of numeric planning problems, while the third is specific to tasks with conditional effects that increase or decrease variables by a constant, transforming such problems into instances of Simple Numeric Planning, a well-known and practically significant subclass of numeric tasks. The experimental evaluation compares these compilations across both newly designed and compelling benchmarks as well as existing domains featuring conditional effects. Our empirical findings reveal complementary behaviour among the approaches, highlighting the practical impact of selecting the appropriate compilation for different problem structures.

Puzznic is a tile-matching video game published by Taito in 1989 and ported to many platforms. The player manipulates blocks in a given grid until they match when two or more blocks of the same pattern are adjacent and are removed from play. The goal is to match all patterned blocks in the grid. Puzznic is rich in structure: levels have internal platforms and the blocks are affected by gravity, leading to complex state changes and the possibility of a cascaded series of matches following each move by the player. The puzzle is therefore a significant challenge to model, motivating our study. We study Puzznic from both constraint modelling and AI Planning perspectives, identifying their complementary strengths and weaknesses for this problem. We further exploit our constraint model to produce an automated tool for instance generation, parameterised on the grid, the combination of patterned blocks, and the steps required.

Benchmarking is an important tool for assessing the relative performance of alternative solving approaches. However, the utility of benchmarking is limited by the quantity and quality of the available problem instances. Modern constraint programming languages typically allow the specification of a class-level model that is parameterised over instance data. This separation presents an opportunity for automated approaches to generate instance data that define instances that are graded (solvable at a certain difficulty level for a solver) or can discriminate between two solving approaches. In this paper, we introduce a framework that combines these two properties to generate a large number of benchmark instances, purposely generated for effective and informative benchmarking. We use five problems that were used in the MiniZinc competition to demonstrate the usage of our framework. In addition to producing a ranking among solvers, our framework gives a broader understanding of the behaviour of each solver for the whole instance space; for example by finding subsets of instances where the solver performance significantly varies from its average performance.

We focus on a planning problem based on Plotting, a tile-matching puzzle video game published by Taito. The objective of the game is to remove at least a certain number of coloured blocks from a grid by sequentially shooting blocks into the same grid. The interest and difficulty of Plotting is due to the complex transitions after every shot: various blocks are affected directly, while others can be indirectly affected by gravity. We highlight the difficulties and inefficiencies of modelling and solving Plotting using PDDL, the de-facto standard language for AI planners. We also provide two constraint models that are able to capture the inherent complexities of the problem. In addition, we provide a set of benchmark instances, an instance generator and an extensive experimental comparison demonstrating solving performance with SAT, CP, MIP and a state-of-the-art AI planner.

Planning Modulo Theories (PMT), inspired by Satisfiability Modulo Theories (SMT), allows the integration of arbitrary first order theories, such as linear arithmetic, with propositional planning. Under this setting, planning as SAT is generalized to planning as SMT. In this paper we introduce a new encoding for planning as SMT, which adheres to the relaxed relaxed ∃-step (R 2 ∃-step) semantics for parallel plans. We show the benefits of relaxing the requirements on the set of actions eligible to be executed at the same time, even though many redundant actions can be introduced. We also show how, by a MaxSMT based post-processing step, redundant actions can be efficiently removed, and provide experimental results showing the benefits of this approach.