Limit Crossing for Decision Problems

Limit crossing is a methodology in which modified versions of a problem are solved and compared, yielding useful information about the original problem. Pruning rules that are used to exclude portions of search trees are excellent examples of the limit-crossing technique. In our previous work, we examined limit crossing for optimization problems. In this paper, we extend this methodology to decision problems. We demonstrate the use of limit crossing in our design of a tool for identifying K-SAT backbones. This tool is guaranteed to identify all of the backbone variables by solving at most n+1 formulae, where n is the total number of variables. While previous 3-SAT backbone research was limited to 28 variables, we have computed backbones for 200 variables. In addition to being useful for identifying backbones, this code can be used directly to solve a special class of QBF problem

Proceedings of SAT Competition 2021 : Solver and Benchmark Descriptions

Non peer reviewe

Energy and Route Optimization of Moving Devices

This thesis highlights our efforts in energy and route optimization of moving devices. We have focused on three categories of such devices; industrial robots in a multi-robot environment, generic vehicles in a vehicle routing problem (VRP) context, automatedguided vehicles (AGVs) in a large-scale flexible manufacturing system (FMS). In the first category, the aim is to develop a non-intrusive energy optimization technique, based on a given set of paths and sequences of operations, such that the original cycle time is not exceeded. We develop an optimization procedure based on a mathematical programming model that aims to minimize the energy consumption and peak power. Our technique has several advantages. It is non-intrusive, i.e. it requires limited changes in the robot program and can be implemented easily. Moreover,it is model-free, in the sense that no particular, and perhaps secret, parameter or dynamic model is required. Furthermore, the optimization can be done offline, within seconds using a generic solver. Through careful experiments, we have shown that it is possible to reduce energy and peak-power up to about 30% and 50% respectively. The second category of moving devices comprises of generic vehicles in a VRP context. We have developed a hybrid optimization approach that integrates a distributed algorithm based on a gossip protocol with a column generation (CG) algorithm, which manages to solve the tested problems faster than the CG algorithm alone. The algorithm is developed for a VRP variation including time windows (VRPTW), which is meant to model the task of scheduling and routing of caregivers in the context of home healthcare routing and scheduling problems (HHRSPs). Moreover,the developed algorithm can easily be parallelized to further increase its efficiency. The last category deals with AGVs. The choice of AGVs was not arbitrary; by design, we decided to transfer our knowledge of energy optimization and routing algorithms to a class of moving devices in which both techniques are of interest. Initially, we improve an existing method of conflict-free AGV scheduling and routing, such that the new algorithm can manage larger problems. A heuristic version of the algorithm manages to solve the problem instances in a reasonable amount of time. Later, we develop strategies to reduce the energy consumption. The study is carried out using an AGV system installed at Volvo Cars. The results are promising; (1)the algorithm reduces performance measures such as makespan up to 50%, while reducing the total travelled distance of the vehicles about 14%, leading to an energy saving of roughly 14%, compared to the results obtained from the original traffic controller. (2) It is possible to reduce the cruise velocities such that more energy is saved, up to 20%, while the new makespan remains better than the original one

Exploiting Structure in Backtracking Algorithms for Propositional and Probabilistic Reasoning

Boolean propositional satisfiability (SAT) and probabilistic reasoning represent two core problems in AI. Backtracking based algorithms have been applied in both problems. In this thesis, I investigate structure-based techniques for solving real world SAT and Bayesian networks, such as software testing and medical diagnosis instances. When solving a SAT instance using backtracking search, a sequence of decisions must be made as to which variable to branch on or instantiate next. Real world problems are often amenable to a divide-and-conquer strategy where the original instance is decomposed into independent sub-problems. Existing decomposition techniques are based on pre-processing the static structure of the original problem. I propose a dynamic decomposition method based on hypergraph separators. Integrating this dynamic separator decomposition into the variable ordering of a modern SAT solver leads to speedups on large real world SAT problems. Encoding a Bayesian network into a CNF formula and then performing weighted model counting is an effective method for exact probabilistic inference. I present two encodings for improving this approach with noisy-OR and noisy-MAX relations. In our experiments, our new encodings are more space efficient and can speed up the previous best approaches over two orders of magnitude. The ability to solve similar problems incrementally is critical for many probabilistic reasoning problems. My aim is to exploit the similarity of these instances by forwarding structural knowledge learned during the analysis of one instance to the next instance in the sequence. I propose dynamic model counting and extend the dynamic decomposition and caching technique to multiple runs on a series of problems with similar structure. This allows us to perform Bayesian inference incrementally as the evidence, parameter, and structure of the network change. Experimental results show that my approach yields significant improvements over previous model counting approaches on multiple challenging Bayesian network instances

Proceedings of the Workshop on Change of Representation and Problem Reformulation

The proceedings of the third Workshop on Change of representation and Problem Reformulation is presented. In contrast to the first two workshops, this workshop was focused on analytic or knowledge-based approaches, as opposed to statistical or empirical approaches called 'constructive induction'. The organizing committee believes that there is a potential for combining analytic and inductive approaches at a future date. However, it became apparent at the previous two workshops that the communities pursuing these different approaches are currently interested in largely non-overlapping issues. The constructive induction community has been holding its own workshops, principally in conjunction with the machine learning conference. While this workshop is more focused on analytic approaches, the organizing committee has made an effort to include more application domains. We have greatly expanded from the origins in the machine learning community. Participants in this workshop come from the full spectrum of AI application domains including planning, qualitative physics, software engineering, knowledge representation, and machine learning

A Unified Framework for Solving Multiagent Task Assignment Problems

Multiagent task assignment problem descriptors do not fully represent the complex interactions in a multiagent domain, and algorithmic solutions vary widely depending on how the domain is represented. This issue is compounded as related research fields contain descriptors that similarly describe multiagent task assignment problems, including complex domain interactions, but generally do not provide the mechanisms needed to solve the multiagent aspect of task assignment. This research presents a unified approach to representing and solving the multiagent task assignment problem for complex problem domains. Ideas central to multiagent task allocation, project scheduling, constraint satisfaction, and coalition formation are combined to form the basis of the constrained multiagent task scheduling (CMTS) problem. Basic analysis reveals the exponential size of the solution space for a CMTS problem, approximated by O(2n(m+n)) based on the number of agents and tasks involved in a problem. The shape of the solution space is shown to contain numerous discontinuous regions due to the complexities involved in relational constraints defined between agents and tasks. The CMTS descriptor represents a wide range of classical and modern problems, such as job shop scheduling, the traveling salesman problem, vehicle routing, and cooperative multi-object tracking. Problems using the CMTS representation are solvable by a suite of algorithms, with varying degrees of suitability. Solution generating methods range from simple random scheduling to state-of-the-art biologically inspired approaches. Techniques from classical task assignment solvers are extended to handle multiagent task problems where agents can also multitask. Additional ideas are incorporated from constraint satisfaction, project scheduling, evolutionary algorithms, dynamic coalition formation, auctioning, and behavior-based robotics to highlight how different solution generation strategies apply to the complex problem space

Sequential matching problem

Kurzfassung in englisch We present sequential matching problem (SMP) as the problem of finding maximal matchings in a sequence of bipartite graphs, with a strategy of making maximum number of common edges in two consecutive matchings. One application of SMP is the problem of assigning workers to jobs in different time shifts with a goal of minimizing total number of unnecessary switches between jobs. We analyze various algorithmic techniques for this NP-complete problem. We also analyze the Mixed Integer Programming (MIP)problem formulation with huge number of variables and their solution by branch and price method, a column generation scheme with branch and bound, of implicit pricing of nonbasic variables to generate new columns. We then discuss special branching rules, pricing problems, implementation issues, and computational results. Finally we analyze a simpler version of SMP with only two bipartite graphs which is still NP-complete, and an algorithm to augment the common edges in the maximum matchings