Combinatorial problems are ubiquitous in the world around us. Actually, they are found in all fields of human activity. As illustrations, it may be a question of scheduling the operations to be carried out within an industrial process (production line of a vehicle, an airplane or a satellite), of extracting the recurring patterns in a transaction database (data mining), of organizing the roster of a service (in a hospital, university or industrial environment), of generating molecular structures with good properties (in chemistry or bioinformatics), etc. Solving optimization problems remains a difficult task, especially when the size of the instances of the problems to be solved is large and/or when optimality is desired. In reality, the difficulty is twofold: being able to appropriately write models for encountered problems and being able to effectively solve the different instances of these problems. The main paradigms for optimization, namely mathematical programming, metaheuristics and Constraint Programming (CP), including the Boolean SAT framework, offer varied and interesting tools (languages, libraries, software), and are in a way, quite complementary; each paradigm having its own success stories.

Combinatorics math problems are often used as a benchmark to test human cognitive and logical problem-solving skills. These problems are concerned with counting the number of solutions that exist in a specific scenario that is sketched in natural language. Humans are adept at solving such problems as they can identify commonly occurring structures in the questions for which a closed-form formula exists for computing the answer. These formulas exploit the exchangeability of objects and symmetries to avoid a brute-force enumeration of all possible solutions. Unfortunately, current AI approaches are still unable to solve combinatorial problems in this way. This paper aims to fill this gap by developing novel AI techniques for representing and solving such problems. It makes the following five contributions. First, we identify a class of combinatorics math problems which traditional lifted counting techniques fail to model or solve efficiently. Second, we propose a novel declarative language for this class of problems. Third, we propose novel lifted solving algorithms bridging probabilistic inference techniques and constraint programming. Fourth, we implement them in a lifted solver that solves efficiently the class of problems under investigation. Finally, we evaluate our contributions on a real-world combinatorics math problems dataset and synthetic benchmarks.

Robin Hirsch posed in 1996 the Really Big Complexity Problem: classify the computational complexity of the network satisfaction problem for all finite relation algebras A. We provide a complete classification for the case that A is symmetric and has a flexible atom; in this case, the problem is NP-complete or in P. The classification task can be reduced to the case where A is integral. If a finite integral relation algebra has a flexible atom, then it has a normal representation B. We can then study the computational complexity of the network satisfaction problem of A using the universal-algebraic approach, via an analysis of the polymorphisms of B. We also use a Ramsey-type result of Nešetřil and Rödl and a complexity dichotomy result of Bulatov for conservative finite-domain constraint satisfaction problems.

The LM-cut heuristic, both alone and as part of the operator counting framework, represents one of the most successful heuristics for classical planning. In this paper, we generalize LM-cut and its use in operator counting to optimal numeric planning with simple conditions and simple numeric effects, i.e., linear expressions over numeric state variables and actions that increase or decrease such variables by constant quantities. We introduce a variant of hmaxhbd (a previously proposed numeric hmax heuristic) based on the delete-relaxed version of such planning tasks and show that, although inadmissible by itself, our variant yields a numeric version of the classical LM-cut heuristic which is admissible. We classify the three existing families of heuristics for this class of numeric planning tasks and introduce the LM-cut family, proving dominance or incomparability between all pairs of existing max and LM-cut heuristics for numeric planning with simple conditions. Our extensive empirical evaluation shows that the new LM-cut heuristic, both on its own and as part of the operator counting framework, is the state-of-the-art for this class of numeric planning problem.

This paper considers the distributed online convex optimization problem with time-varying constraints over a network of agents. This is a sequential decision making problem with two sequences of arbitrarily varying convex loss and constraint functions. At each round, each agent selects a decision from the decision set, and then only a portion of the loss function and a coordinate block of the constraint function at this round are privately revealed to this agent. The goal of the network is to minimize the network-wide loss accumulated over time. Two distributed online algorithms with full-information and bandit feedback are proposed. Both dynamic and static network regret bounds are analyzed for the proposed algorithms, and network cumulative constraint violation is used to measure constraint violation, which excludes the situation that strictly feasible constraints can compensate the effects of violated constraints. In particular, we show that the proposed algorithms achieve $\mathcal{O}(T^{\max\{\kappa,1-\kappa\}})$ static network regret and $\mathcal{O}(T^{1-\kappa/2})$ network cumulative constraint violation, where $T$ is the time horizon and $\kappa\in(0,1)$ is a user-defined trade-off parameter. Moreover, if the loss functions are strongly convex, then the static network regret bound can be reduced to $\mathcal{O}(T^{\kappa})$. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

We deal with a challenging scheduling problem on parallel machines with sequence-dependent setup times and release dates from a real-world application of semiconductor work-shop production. There, jobs can only be processed by dedicated machines, thus few machines can determine the makespan almost regardless of how jobs are scheduled on the remaining ones. This causes problems when machines fail and jobs need to be rescheduled. Instead of optimising only the makespan, we put the individual machine spans in non-ascending order and lexicographically minimise the resulting tuples. This achieves that all machines complete as early as possible and increases the robustness of the schedule. We study the application of Answer-Set Programming (ASP) to solve this problem. While ASP eases modelling, the combination of timing constraints and the considered objective function challenges current solving technology. The former issue is addressed by using an extension of ASP by difference logic. For the latter, we devise different algorithms that use multi-shot solving. To tackle industrial-sized instances, we study different approximations and heuristics. Our experimental results show that ASP is indeed a promising KRR paradigm for this problem and is competitive with state-of-the-art CP and MIP solvers. Under consideration in Theory and Practice of Logic Programming (TPLP).

In prior work, learning from demonstration (LfD) [1, 2] has successfully enabled robots to accomplish multi-step tasks by segmenting demonstrations (primarily of robot end-effector or tool trajectories) into sub-tasks/goals [3, 4, 5, 6, 7, 8], phases [9, 10], keyframes [11, 12], or skills/primitives/options [13, 14, 15, 16]. Most of these abstractions assume reaching subgoals sequentially will deliver the desired outcomes; however, successful imitation of many manipulation tasks with spatial/temporal constraints cannot be reduced to imitation at the motion level unless the learned motion policy also satisfies these constraints. This becomes highly relevant if we want robots to not only imitate but also generalize, adapt and be robust to perturbations imposed by humans, who are in the loop of task learning and execution. LfD techniques that learn stable motion policies with convergence guarantees (e.g., Dynamic Movement Primitives (DMP) [17], Dynamical Systems (DS) [18]) are capable of providing such desired properties but only at the motion level. As shown in Figure 1 (a-b) a robot can successfully replay a soup-scooping task while being robust to physical perturbations with a learned DS. Nevertheless, if the spoon orientation is perturbed to a state where all material is dropped, as seen in Figure 1 (c), the motion policy will still lead the robot to the target, unaware of the task-level failure or how to recover from it.

Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating the marginals of the probability distribution which is uniform over satisfying configurations). This paper presents new algorithms for the latter framework, ultimately producing estimates for satisfying configurations using methods from Boolean Fourier analysis. The approach is broadly inspired by the quantum amplitude amplification algorithm in that it maximally increases the amplitude of the approximation function over satisfying configurations given sequential refinements. We demonstrate that satisfying solutions may be retrieved in a process analogous to quantum measurement made efficient by sparsity in the Fourier domain, and present a complete solver construction using this novel approximation. Freedom in the refinement strategy invites further opportunities to design solvers in an evolutionary computing framework. Results demonstrate competitive performance against local solvers for the Boolean satisfiability (SAT) problem, encouraging future work in understanding the connections between Boolean Fourier analysis and constraint satisfaction.

We present a way to create small yet difficult model counting instances. Our generator is highly parameterizable: the number of variables of the instances it produces, as well as their number of clauses and the number of literals in each clause, can all be set to any value. Our instances have been tested on state of the art model counters, against other difficult model counting instances, in the Model Counting Competition. The smallest unsolved instances of the competition, both in terms of number of variables and number of clauses, were ours. We also observe a peak of difficulty when fixing the number of variables and varying the number of clauses, in both random instances and instances built by our generator. Using these results, we predict the parameter values for which the hardest to count instances will occur.

Side-channel attacks impose a serious threat to cryptographic algorithms, including widely employed ones, such as AES and RSA. These attacks take advantage of the algorithm implementation in hardware or software to extract secret information via side channels. Software masking is a mitigation approach against power side-channel attacks aiming at hiding the secret-revealing dependencies from the power footprint of a vulnerable implementation. However, this type of software mitigation often depends on general-purpose compilers, which do not preserve non-functional properties. Moreover, microarchitectural features, such as the memory bus and register reuse, may also leak secret information. These abstractions are not visible at the high-level implementation of the program. Instead, they are decided at compile time. To remedy these problems, security engineers often sacrifice code efficiency by turning off compiler optimization and/or performing local, post-compilation transformations. This paper proposes Secure by Construction Code Generation (SecCG), a constraint-based compiler approach that generates optimized yet secure against power side channels code. SecCG controls the quality of the mitigated program by efficiently searching the best possible low-level implementation according to a processor cost model. In our experiments with twelve masked cryptographic functions up to 100 lines of code on Mips32 and ARM Thumb, SecCG speeds up the generated code from 75% to 8 times compared to non-optimized secure code with an overhead of up to 7% compared to non-secure optimized code at the expense of a high compilation cost. In summary, this paper proposes a formal model to generate power side channel free low-level code.