Researchers have used distributed constraint optimization problems (DCOPs) to model various multi-agent coordination and resource allocation problems. Very recently, Ottens et al. proposed a promising new approach to solve DCOPs that is based on confidence bounds via their Distributed UCT (DUCT) sampling-based algorithm. Unfortunately, its memory requirement per agent is exponential in the number of agents in the problem, which prohibits it from scaling up to large problems. Thus, in this article, we introduce two new sampling-based DCOP algorithms called Sequential Distributed Gibbs (SD-Gibbs) and Parallel Distributed Gibbs (PD-Gibbs). Both algorithms have memory requirements per agent that is linear in the number of agents in the problem. Our empirical results show that our algorithms can find solutions that are better than DUCT, run faster than DUCT, and solve some large problems that DUCT failed to solve due to memory limitations.

When creating benchmarks for SAT solvers, we need SAT instances that are easy to build but hard to solve. A recent development in the search for such methods has led to the Balanced SAT algorithm, which can create k-SAT instances with m clauses of high difficulty, for arbitrary k and m. In this paper we introduce the No-Triangle SAT algorithm, a SAT instance generator based on the cluster coefficient graph statistic. We empirically compare the two algorithms by fixing the arity and the number of variables, but varying the number of clauses. The hardest instances that we find are produced by No-Triangle SAT. Furthermore, difficult instances from No-Triangle SAT have a different number of clauses than difficult instances from Balanced SAT, potentially allowing a combination of the two methods to find hard SAT instances for a larger array of parameters.

This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the sum of local convex constraint functions. A distributed online primal-dual dynamic mirror descent algorithm is proposed to solve this problem, where the local cost, regularization, and constraint functions are held privately and revealed only after each time slot. We first derive regret and cumulative constraint violation bounds for the algorithm and show how they depend on the stepsize sequences, the accumulated dynamic variation of the comparator sequence, the number of agents, and the network connectivity. As a result, under some natural decreasing stepsize sequences, we prove that the algorithm achieves sublinear dynamic regret and cumulative constraint violation if the accumulated dynamic variation of the optimal sequence also grows sublinearly. We also prove that the algorithm achieves sublinear static regret and cumulative constraint violation under mild conditions. In addition, smaller bounds on the static regret are achieved when the objective functions are strongly convex. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

There have been recent efforts for incorporating Graph Neural Network models for learning full-stack solvers for constraint satisfaction problems (CSP) and particularly Boolean satisfiability (SAT). Despite the unique representational power of these neural embedding models, it is not clear how the search strategy in the learned models actually works. On the other hand, by fixing the search strategy (e.g. greedy search), we would effectively deprive the neural models of learning better strategies than those given. In this paper, we propose a generic neural framework for learning CSP solvers that can be described in terms of probabilistic inference and yet learn search strategies beyond greedy search. Our framework is based on the idea of propagation, decimation and prediction (and hence the name PDP) in graphical models, and can be trained directly toward solving CSP in a fully unsupervised manner via energy minimization, as shown in the paper. Our experimental results demonstrate the effectiveness of our framework for SAT solving compared to both neural and the state-of-the-art baselines.

Dynamic Controllability (DC) of a Simple Temporal Problem with Uncertainty (STPU) uses a dynamic decision strategy, rather than a fixed schedule, to tackle temporal uncertainty. We extend this concept to the Controllable Conditional Temporal Problem with Uncertainty (CCTPU), which extends the STPU by conditioning temporal constraints on the assignment of controllable discrete variables. We define dynamic controllability of a CCTPU as the existence of a strategy that decides on both the values of discrete choice variables and the scheduling of controllable time points dynamically. This contrasts with previous work, which made a static assignment of choice variables and dynamic decisions over time points only. We propose an algorithm to find such a fully dynamic strategy. The algorithm computes the "envelope" of outcomes of temporal uncertainty in which a particular assignment of discrete variables is feasible, and aggregates these over all choices. When an aggregated envelope covers all uncertain situations of the CCTPU, the problem is dynamically controllable. However, the algorithm is complete only under certain assumptions. Experiments on an existing set of CCTPU benchmarks show that there are cases in which making both discrete and temporal decisions dynamically it is feasible to satisfy the problem constraints while assigning the discrete variables statically it is not.

Real-world project scheduling often requires flexibility in terms of the selection and the exact length of alternative production activities. Moreover, the simultaneous scheduling of multiple lots is mandatory in many production planning applications. To meet these requirements, a new flexible resource-constrained multi-project scheduling problem is introduced where both decisions (activity selection flexibility and time flexibility) are integrated. Besides the minimization of makespan, two alternative objectives inspired by a steel industry application case are presented: maximization of balanced length of selected activities (time balance) and maximization of balanced resource utilization (resource balance). New mixed integer and constraint programming (CP) models are proposed for the developed integrated flexible project scheduling problem. The real-world applicability of the suggested CP models is shown by solving large steel industry instances with the CP Optimizer of IBM ILOG CPLEX. Furthermore, benchmark instances on flexible resource-constrained project scheduling problems (RCPSP) are solved to optimality.

In real-world project scheduling applications, activity durations are often uncertain. Proactive scheduling can effectively cope with the duration uncertainties, by generating robust baseline solutions according to a priori stochastic knowledge. However, most of the existing proactive approaches assume that the duration uncertainty of an activity is not related to its scheduled start time, which may not hold in many real-world scenarios. In this paper, we relax this assumption by allowing the duration uncertainty to be time-dependent, which is caused by the uncertainty of whether the activity can be executed on each time slot. We propose a stochastic optimization model to find an optimal Partial-order Schedule (POS) that minimizes the expected makespan. This model can cover both the time-dependent uncertainty studied in this paper and the traditional time-independent duration uncertainty. To circumvent the underlying complexity in evaluating a given solution, we approximate the stochastic optimization model based on Sample Average Approximation (SAA). Finally, we design two efficient branch-and-bound algorithms to solve the NP-hard SAA problem. Empirical evaluation confirms that our approach can generate high-quality proactive solutions for a variety of uncertainty distributions.

There exists a solution universe of all the possible solutions to this set of constraints. If the solution universe contains a single possible solution, then the published statistics completely reveal the underlying confidential data--provided that noise was not added to either the microdata or the tabulations as a disclosure-avoidance mechanism. If there are multiple satisfying solutions, then any element (person) in common among all of the solutions is revealed. If the equations have no solution, either the set of published statistics is inconsistent with the fictional statistical agency's claim that it is tabulated from a real confidential database or an error was made in that tabulation. This doesn't mean that a high-quality reconstruction is not possible.

Here we identify a type of privacy concern in Distributed Constraint Optimization (DCOPs) not previously addressed in literature, despite its importance and impact on the application field: the privacy of existence of secrets. Science only starts where metrics and assumptions are clearly defined. The area of Distributed Constraint Optimization has emerged at the intersection of the multi-agent system community and constraint programming. For the multi-agent community, the constraint optimization problems are an elegant way to express many of the problems occurring in trading and distributed robotics. For the theoretical constraint programming community the DCOPs are a natural extension of their main object of study, the constraint satisfaction problem. As such, the understanding of the DCOP framework has been refined with the needs of the two communities, but sometimes without spelling the new assumptions formally and therefore making it difficult to compare techniques. Here we give a direction to the efforts for structuring concepts in this area.

Testing cyber-physical systems involves the execution of test cases on target-machines equipped with the latest release of a software control system. When testing industrial robots, it is common that the target machines need to share some common resources, e.g., costly hardware devices, and so there is a need to schedule test case execution on the target machines, accounting for these shared resources. With a large number of such tests executed on a regular basis, this scheduling becomes difficult to manage manually. In fact, with manual test execution planning and scheduling, some robots may remain unoccupied for long periods of time and some test cases may not be executed. This paper introduces TC-Sched, a time-aware method for automated test case execution scheduling. TC-Sched uses Constraint Programming to schedule tests to run on multiple machines constrained by the tests' access to shared resources, such as measurement or networking devices. The CP model is written in SICStus Prolog and uses the Cumulatives global constraint. Given a set of test cases, a set of machines, and a set of shared resources, TC-Sched produces an execution schedule where each test is executed once with minimal time between when a source code change is committed and the test results are reported to the developer. Experiments reveal that TC-Sched can schedule 500 test cases over 100 machines in less than 4 minutes for 99.5% of the instances. In addition, TC-Sched largely outperforms simpler methods based on a greedy algorithm and is suitable for deployment on industrial robot testing.