Answer Set Programming Solver Research Articles

CEGAR-Based Approach for Solving Combinatorial Optimization Modulo Quantified Linear Arithmetics Problems

Bioinformatics has always been a prolific domain for generating complex satisfiability and optimization problems. For instance, the synthesis of multi-scale models of biological networks has recently been associated with the resolution of optimization problems mixing Boolean logic and universally quantified linear constraints (OPT+qLP), which can be benchmarked on real-world models. In this paper, we introduce a Counter-Example-Guided Abstraction Refinement (CEGAR) to solve such problems efficiently. Our CEGAR exploits monotone properties inherent to linear optimization in order to generalize counter-examples of Boolean relaxations. We implemented our approach by extending Answer Set Programming (ASP) solver Clingo with a quantified linear constraints propagator. Our prototype enables exploiting independence of sub-formulas to further exploit the generalization of counter-examples. We evaluate the impact of refinement and partitioning on two sets of OPT+qLP problems inspired by system biology. Additionally, we conducted a comparison with the state-of-the-art ASP solver Clingo[lpx] that handles non-quantified linear constraints, showing the advantage of our CEGAR approach for solving large problems.

Solving an Industrial-Scale Warehouse Delivery Problem with Answer Set Programming Modulo Difference Constraints

A warehouse delivery problem consists of a set of robots that undertake delivery jobs within a warehouse. Items are moved around the warehouse in response to events. A solution to a warehouse delivery problem is a collision-free schedule of robot movements and actions that ensures that all delivery jobs are completed and each robot is returned to its docking station. While the warehouse delivery problem is related to existing research, such as the study of multi-agent path finding (MAPF), the specific industrial requirements necessitated a novel approach that diverges from these other approaches. For example, our problem description was more suited to formalizing the warehouse in terms of a weighted directed graph rather than the more common grid-based formalization. We formalize and encode the warehouse delivery problem in Answer Set Programming (ASP) extended with difference constraints. We systematically develop and study different encoding variants, with a view to computing good quality solutions in near real-time. In particular, application specific criteria are contrasted against the traditional notion of makespan minimization as a measure of solution quality. The encoding is tested against both crafted and industry data and experiments run using the Hybrid ASP solver clingo[dl].

ASP and subset minimality: Enumeration, cautious reasoning and MUSes

Answer Set Programming (ASP) is a well-known logic-based formalism that has been used to model and solve a variety of AI problems. For several years, ASP implementations primarily focused on the main computational task: the computation of one answer set of a (logic) program. Nonetheless, several AI problems, that can be conveniently modelled in ASP, require to enumerate solutions characterized by an optimality property that can be expressed in terms of subset-minimality with respect to some objective atoms. In this context, solutions are often either (i) answer sets that are subset-minimal w.r.t. the objective atoms or (ii) atoms that are contained in all subset-minimal answer sets, or (iii) sets of atoms that enforce the absence of answer sets on the ASP program at hand — such sets are referred to as minimal unsatisfiable subsets (MUSes). In all the above-mentioned cases, the corresponding computational task is currently not supported by plain state-of-the-art ASP solvers. In this paper, we study formally these tasks and fill the gap in current implementations by proposing several algorithms to enumerate MUSes and subset-minimal answer sets, as well as perform cautious reasoning on subset-minimal answer sets. We implement our algorithms on top of wasp and perform an experimental analysis on several hard benchmarks showing the good performance of our implementation.

Domain-Specific Heuristics in Answer Set Programming: A Declarative Non-Monotonic Approach

Domain-specific heuristics are an essential technique for solving combinatorial problems efficiently. Current approaches to integrate domain-specific heuristics with Answer Set Programming (ASP) are unsatisfactory when dealing with heuristics that are specified non-monotonically on the basis of partial assignments. Such heuristics frequently occur in practice, for example, when picking an item that has not yet been placed in bin packing. Therefore, we present novel syntax and semantics for declarative specifications of domain-specific heuristics in ASP. Our approach supports heuristic statements that depend on the partial assignment maintained during solving, which has not been possible before. We provide an implementation in Alpha that makes Alpha the first lazy-grounding ASP system to support declaratively specified domain-specific heuristics. Two practical example domains are used to demonstrate the benefits of our proposal. Additionally, we use our approach to implement informed search with A*, which is tackled within ASP for the first time. A* is applied to two further search problems. The experiments confirm that combining lazy-grounding ASP solving and our novel heuristics can be vital for solving industrial-size problems.

Multi-genome metabolic modeling predicts functional inter-dependencies in the Arabidopsis root microbiome

From a theoretical ecology point of view, microbiomes are far more complex than expected. Besides competition and competitive exclusion, cooperative microbe-microbe interactions have to be carefully considered. Metabolic dependencies among microbes likely explain co-existence in microbiota. In this in silico study, we explored genome-scale metabolic models (GEMs) of 193 bacteria isolated from Arabidopsis thaliana roots. We analyzed their predicted producible metabolites under simulated nutritional constraints including "root exudate-mimicking growth media" and assessed the potential of putative metabolic exchanges of by- and end-products to avoid those constraints. We found that the genome-encoded metabolic potential is quantitatively and qualitatively clustered by phylogeny, highlighting metabolic differentiation between taxonomic groups. Random, synthetic combinations of increasing numbers of strains (SynComs) indicated that the number of producible compounds by GEMs increased with average phylogenetic distance, but that most SynComs were centered around an optimal phylogenetic distance. Moreover, relatively small SynComs could reflect the capacity of the whole community due to metabolic redundancy. Inspection of 30 specific end-product metabolites (i.e., target metabolites: amino acids, vitamins, phytohormones) indicated that the majority of the strains had the genetic potential to produce almost all the targeted compounds. Their production was predicted (1) to depend on external nutritional constraints and (2) to be facilitated by nutritional constraints mimicking root exudates, suggesting nutrient availability and root exudates play a key role in determining the number of producible metabolites. An answer set programming solver enabled the identification of numerous combinations of strains predicted to depend on each other to produce these targeted compounds under severe nutritional constraints thus indicating a putative sub-community level of functional redundancy. This study predicts metabolic restrictions caused by available nutrients in the environment. By extension, it highlights the importance of the environment for niche potential, realization, partitioning, and overlap. Our results also suggest that metabolic dependencies and cooperation among root microbiota members compensate for environmental constraints and help maintain co-existence in complex microbial communities. Video Abstract.

A Neuro-Symbolic ASP Pipeline for Visual Question Answering

AbstractWe present a neuro-symbolic visual question answering (VQA) pipeline for CLEVR, which is a well-known dataset that consists of pictures showing scenes with objects and questions related to them. Our pipeline covers (i) training neural networks for object classification and bounding-box prediction of the CLEVR scenes, (ii) statistical analysis on the distribution of prediction values of the neural networks to determine a threshold for high-confidence predictions, and (iii) a translation of CLEVR questions and network predictions that pass confidence thresholds into logic programmes so that we can compute the answers using an answer-set programming solver. By exploiting choice rules, we consider deterministic and non-deterministic scene encodings. Our experiments show that the non-deterministic scene encoding achieves good results even if the neural networks are trained rather poorly in comparison with the deterministic approach. This is important for building robust VQA systems if network predictions are less-than perfect. Furthermore, we show that restricting non-determinism to reasonable choices allows for more efficient implementations in comparison with related neuro-symbolic approaches without losing much accuracy.

Problem Decomposition and Multi-shot ASP Solving for Job-shop Scheduling

AbstractScheduling methods are important for effective production and logistics management, where tasks need to be allocated and performed with limited resources. In particular, the Job-shop Scheduling Problem (JSP) is a well known and challenging combinatorial optimization problem in which tasks sharing a machine are to be arranged in a sequence such that encompassing jobs can be completed as early as possible. Given that already moderately sized JSP instances can be highly combinatorial, and neither optimal schedules nor the runtime to termination of complete optimization methods is known, efficient approaches to approximate good-quality schedules are of interest. In this paper, we propose problem decomposition into time windows whose operations can be successively scheduled and optimized by means of multi-shot Answer Set Programming (ASP) solving. From a computational perspective, decomposition aims to split highly complex scheduling tasks into better manageable subproblems with a balanced number of operations so that good-quality or even optimal partial solutions can be reliably found in a small fraction of runtime. Regarding the feasibility and quality of solutions, problem decomposition must respect the precedence of operations within their jobs and partial schedules optimized by time windows should yield better global solutions than obtainable in similar runtime on the entire instance. We devise and investigate a variety of decomposition strategies in terms of the number and size of time windows as well as heuristics for choosing their operations. Moreover, we incorporate time window overlapping and compression techniques into the iterative scheduling process to counteract window-wise optimization limitations restricted to partial schedules. Our experiments on JSP benchmark sets of several sizes show that successive optimization by multi-shot ASP solving leads to substantially better schedules within the runtime limit than global optimization on the full problem, where the gap increases with the number of operations to schedule. While the obtained solution quality still remains behind a state-of-the-art Constraint Programming system, our multi-shot solving approach comes closer the larger the instance size, demonstrating good scalability by problem decomposition.

ApproxASP – a Scalable Approximate Answer Set Counter

Answer Set Programming (ASP) is a framework in artificial intelligence and knowledge representation for declarative modeling and problem solving. Modern ASP solvers focus on the computation or enumeration of answer sets. However, a variety of probabilistic applications in reasoning or logic programming require counting answer sets. While counting can be done by enumeration, simple enumeration becomes immediately infeasible if the number of solutions is high. On the other hand, approaches to exact counting are of high worst-case complexity. In fact, in propositional model counting, exact counting becomes impractical. In this work, we present a scalable approach to approximate counting for answer set programming. Our approach is based on systematically adding XOR constraints to ASP programs, which divide the search space. We prove that adding random XOR constraints partitions the answer sets of an ASP program. In practice, we use a Gaussian elimination-based approach by lifting ideas from SAT to ASP and integrating it into a state of the art ASP solver, which we call ApproxASP. Finally, our experimental evaluation shows the scalability of our approach over the existing ASP systems.

Large-Neighbourhood Search for Optimisation in Answer-Set Solving

While Answer-Set Programming (ASP) is a prominent approach to declarative problem solving, optimisation problems can still be a challenge for it. Large-Neighbourhood Search (LNS) is a metaheuristic for optimisation where parts of a solution are alternately destroyed and reconstructed that has high but untapped potential for ASP solving. We present a framework for LNS optimisation in answer-set solving, in which neighbourhoods can be specified either declaratively as part of the ASP encoding, or automatically generated by code. To effectively explore different neighbourhoods, we focus on multi-shot solving as it allows to avoid program regrounding. We illustrate the framework on different optimisation problems, some of which are notoriously difficult, including shift planning and a parallel machine scheduling problem from semi-conductor production which demonstrate the effectiveness of the LNS approach.

Benchmarking Answer Set Programming systems for resource allocation in business processes

Declarative logic programming formalisms are well-suited to model various optimization and configuration problems. In particular, Answer Set Programming (ASP) systems have gained popularity, for example, to deal with scheduling problems present in several domains. The main goal of this paper is to devise a benchmark for ASP systems to assess their performance when dealing with complex and realistic resource allocation with objective optimization. To this end, we provide (i) a declarative and compact encoding of the resource allocation problem in ASP (compliant with the ASP Core-2 standard), (ii) a configurable ASP systems benchmark named BRANCH that is equipped with resource allocation instance generators that produce problem instances of different sizes with adjustable parameters (e.g., in terms of process complexity, organizational and temporal constraints), and (iii) an evaluation of four state-of-the-art ASP systems using BRANCH. This solid application-oriented benchmark serves the ASP community with a tool that leads to potential optimizations and improvements in encodings and further drives the development of ASP solvers. On the other hand, resource allocation is an important problem that still lacks adequate automated tool support in the context of Business Process Management (BPM). The ASP problem encoding, ready-to-use ASP systems and problem instance generators benefit the BPM community to tackle the problem at scale and mitigate the lack of openly available problem instance data.

Linear-Time Temporal Answer Set Programming

AbstractIn this survey, we present an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving. The syntax of this extension of logic programs is the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). In the paper, we focus on the main recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL but involves a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). As a result, we obtain a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between finite and infinite trace length. We also provide further useful results, such as the translation into other formalisms like Quantified Equilibrium Logic and Second-order LTL, and some techniques for computing temporal stable models based on automata constructions. In the remainder of the paper, we focus on practical aspects, defining a syntactic fragment called (modal) temporal logic programs closer to ASP, and explaining how this has been exploited in the construction of the solver telingo, a temporal extension of the well-known ASP solver clingo that uses its incremental solving capabilities.

FOLASP: FO(·) as Input Language for Answer Set Solvers

AbstractTechnological progress in Answer Set Programming (ASP) has been stimulated by the use of common standards, such as the ASP-Core-2 language. While ASP has its roots in nonmonotonic reasoning, efforts have also been made to reconcile ASP with classical first-order (FO) logic. This has resulted in the development of FO(·), an expressive extension of FO, which allows ASP-like problem solving in a purely classical setting. This language may be more accessible to domain experts already familiar with FO and may be easier to combine with other formalisms that are based on classical logic. It is supported by the IDP inference system, which has successfully competed in a number of ASP competitions. Here, however, technological progress has been hampered by the limited number of systems that are available for FO(·). In this paper, we aim to address this gap by means of a translation tool that transforms an FO(·) specification into ASP-Core-2, thereby allowing ASP-Core-2 solvers to be used as solvers for FO(·) as well. We present experimental results to show that the resulting combination of our translation with an off-the-shelf ASP solver is competitive with the IDP system as a way of solving problems formulated in FO(·).

Graph Based Answer Set Programming Solver Systems

Answer set programming (ASP) is a popular nonmonotonic-logic based paradigm for knowledge representation and solving combinatorial problems. Computing the answer set of an ASP program is NP-hard in general, and researchers have been investing significant effort to speed it up. The majority of current ASP solvers employ SAT solver-like technology to find these answer sets. As a result, justification for why a literal is in the answer set is hard to produce. There are dependency graph based approaches to find answer sets, but due to the representational limitations of dependency graphs, such approaches are limited. This paper proposes a novel dependency graph-based approach for finding answer sets in which conjunction of goals is explicitly represented as a node which allows arbitrary answer set programs to be uniformly represented. Our representation preserves causal relationships allowing for justification for each literal in the answer set to be elegantly found. In this paper, we explore two different approaches based on the graph representation: bottom-up and top-down. The bottom-up approach finds models by assigning truth values along with the topological order, while the top-down approach generates models starting from the constraints.

Compilation of Aggregates in ASP

Answer Set Programming (ASP) is a well-known problem-solving formalism in computational logic. Nowadays, ASP is used in many real world scenarios thanks to ASP solvers. Standard evaluation of ASP programs suffers from an intrinsic limitation, knows as Grounding Bottleneck, due to the grounding of some rules that could fit all the available memory. As a result, there exist instances of real world problems that are untractable using the standard Ground and Solve approach. In order to tackle this problem, different strategies have been proposed. Among them we focus on a recent approach based on compilation of problematic constraints as propagators, which revealed to be very promising but is currently limited to constraints without aggregates. Since aggregates are widely used in ASP, in this paper we extend such an approach also to constraints containing aggregates. Good results, that proof the effectiveness of the proposed approach, have been reached.

Automata Techniques for Temporal Answer Set Programming

Temporal and dynamic extensions of Answer Set Programming (ASP) have played an important role in addressing dynamic problems, as they allow the use of temporal operators to reason with dynamic scenarios in a very effective way. In my Ph.D. research, I intend to exploit the relationship between automata theory and dynamic logic to add automata-based techniques to the ASP solver CLINGO helping us to deal with theses type of problems.

How to Split a Logic Program

Answer Set Programming (ASP) is a successful method for solving a range of real-world applications. Despite the availability of fast ASP solvers, computing answer sets demands a very large computational power, since the problem tackled is in the second level of the polynomial hierarchy. A speed-up in answer set computation may be attained, if the program can be split into two disjoint parts, bottom and top. Thus, the bottom part is evaluated independently of the top part, and the results of the bottom part evaluation are used to simplify the top part. Lifschitz and Turner have introduced the concept of a splitting set, i.e., a set of atoms that defines the splitting. In this paper, We show that the problem of computing a splitting set with some desirable properties can be reduced to a classic Search Problem and solved in polynomial time. This allows us to conduct experiments on the size of the splitting set in various programs and lead to an interesting discovery of a source of complication in stable model computation. We also show that for Head-Cycle-Free programs, the definition of splitting sets can be adjusted to allow splitting of a broader class of programs.

A New Boolean Encoding for MAPF and its Performance with ASP and MaxSAT Solvers

Multi-agent pathfinding (MAPF) is an NP-hard problem. As such, dense maps may be very hard to solve optimally. In such scenarios, compilation-based approaches, via Boolean satisfiability (SAT) and answer set programming (ASP), have proven to be most effective. In this paper, we propose a new encoding for MAPF, which we implement and solve using both ASP and MaxSAT solvers. Our encoding builds on a recent ASP encoding for MAPF but changes the way agent moves are encoded. This allows to represent swap and follow conflicts with binary clauses, which are known to work well along with conflict-based clause learning. For MaxSAT, we study different ways in which we may combine the MSU3 and LSU algorithms for maximum performance. Our results, over grid and warehouse maps, show that the ASP solver scales better when the number of agents is increased on grids with few obstacles, while the MaxSAT solver performs better in scenarios with more obstacles and fewer agents.

DynASP2.5: Dynamic Programming on Tree Decompositions in Action

Efficient exact parameterized algorithms are an active research area. Such algorithms exhibit a broad interest in the theoretical community. In the last few years, implementations for computing various parameters (parameter detection) have been established in parameterized challenges, such as treewidth, treedepth, hypertree width, feedback vertex set, or vertex cover. In theory, instances, for which the considered parameter is small, can be solved fast (problem evaluation), i.e., the runtime is bounded exponential in the parameter. While such favorable theoretical guarantees exists, it is often unclear whether one can successfully implement these algorithms under practical considerations. In other words, can we design and construct implementations of parameterized algorithms such that they perform similar or even better than well-established problem solvers on instances where the parameter is small. Indeed, we can build an implementation that performs well under the theoretical assumptions. However, it could also well be that an existing solver implicitly takes advantage of a structure, which is often claimed for solvers that build on Sat-solving. In this paper, we consider finding one solution to instances of answer set programming (ASP), which is a logic-based declarative modeling and solving framework. Solutions for ASP instances are so-called answer sets. Interestingly, the problem of deciding whether an instance has an answer set is already located on the second level of the polynomial hierarchy. An ASP solver that employs treewidth as parameter and runs dynamic programming on tree decompositions is DynASP2. Empirical experiments show that this solver is fast on instances of small treewidth and can outperform modern ASP when one counts answer sets. It remains open, whether one can improve the solver such that it also finds one answer set fast and shows competitive behavior to modern ASP solvers on instances of low treewidth. Unfortunately, theoretical models of modern ASP solvers already indicate that these solvers can solve instances of low treewidth fast, since they are based on Sat-solving algorithms. In this paper, we improve DynASP2 and construct the solver DynASP2.5, which uses a different approach. The new solver shows competitive behavior to state-of-the-art ASP solvers even for finding just one solution. We present empirical experiments where one can see that our new implementation solves ASP instances, which encode the Steiner tree problem on graphs with low treewidth, fast. Our implementation is based on a novel approach that we call multi-pass dynamic programming (M-DPSINC). In the paper, we describe the underlying concepts of our implementation (DynASP2.5) and we argue why the techniques still yield correct algorithms.

Semantic Task Planning for Service Robots in Open Worlds

This paper presents a planning system based on semantic reasoning for a general-purpose service robot, which is aimed at behaving more intelligently in domains that contain incomplete information, under-specified goals, and dynamic changes. First, Two kinds of data are generated by Natural Language Processing module from the speech: (i) action frames and their relationships; (ii) the modifier used to indicate some property or characteristic of a variable in the action frame. Next, the task’s goals are generated from these action frames and modifiers. These goals are represented as AI symbols, combining world state and domain knowledge, which are used to generate plans by an Answer Set Programming solver. Finally, the plan’s actions are executed one by one, and continuous sensing grounds useful information, which makes the robot use contingent knowledge to adapt to dynamic changes and faults. For each action in the plan, the planner gets its preconditions and effects from domain knowledge, so during the execution of the task, the environmental changes, especially those conflict with the actions, not only the action being performed but also the subsequent actions, can be detected and handled as early as possible. A series of case studies are used to evaluate the system and verify its ability to acquire knowledge through dialogue with users, solve problems with the acquired causal knowledge, and plan for complex tasks autonomously in the open world.

Answer Set Programming for Regular Inference

We propose an approach to non-deterministic finite automaton (NFA) inductive synthesis that is based on answer set programming (ASP) solvers. To that end, we explain how an NFA and its response to input samples can be encoded as rules in a logic program. We then ask an ASP solver to find an answer set for the program, which we use to extract the automaton of the required size. We conduct a series of experiments on some benchmark sets, using the implementation of our approach. The results show that our method outperforms, in terms of CPU time, a SAT approach and other exact algorithms on all benchmarks.