Piecewise Linear Valued CSPs Solvable by Linear Programming Relaxation

Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. The computational complexity of VCSPs depends on the set of allowed cost functions in the input. Recently, the computational complexity of all VCSPs for finite sets of cost functions over finite domains has been classified. Many natural optimisation problems, however, cannot be formulated as VCSPs over a finite domain. We initiate the systematic investigation of the complexity of infinite-domain VCSPs with piecewise linear homogeneous cost functions. Such VCSPs can be solved in polynomial time if the cost functions are improved by fully symmetric fractional operations of all arities. We show this by reducing the problem to a finite-domain VCSP which can be solved using the basic linear program relaxation. It follows that VCSPs for submodular PLH cost functions can be solved in polynomial time; in fact, we show that submodular PLH functions form a maximally tractable class of PLH cost functions.

Adapting k-means for graph clustering

We propose two new algorithms for clustering graphs and networks. The first, called K‑algorithm, is derived directly from the k-means algorithm. It applies similar iterative local optimization but without the need to calculate the means. It inherits the properties of k-means clustering in terms of both good local optimization capability and the tendency to get stuck at a local optimum. The second algorithm, called the M-algorithm, gradually improves on the results of the K-algorithm to find new and potentially better local optima. It repeatedly merges and splits random clusters and tunes the results with the K-algorithm. Both algorithms are general in the sense that they can be used with different cost functions. We consider the conductance cost function and also introduce two new cost functions, called inverse internal weight and mean internal weight. According to our experiments, the M-algorithm outperforms eight other state-of-the-art methods. We also perform a case study by analyzing clustering results of a disease co-occurrence network, which demonstrate the usefulness of the algorithms in an important real-life application.

Data-Driven Robust Resource Allocation with Monotonic Cost Functions

Using Data to Allocate Resources Efficiently In city logistics systems, a fleet of vehicles is divided between service regions that function autonomously. Each region finds optimal routes for its own fleet and incurs costs accordingly. More vehicles lead to lower costs, but the trade-off is that fewer vehicles are left for other regions. Costs are difficult to quantify precisely because of demand uncertainty but can be estimated using data. The paper “Data-driven robust resource allocation with monotonic cost functions” by Chen, Marković, Ryzhov, and Schonfeld develops a principled risk-averse approach for two-stage resource allocation. The authors propose a new uncertainty model for decreasing cost functions and show how it can be leveraged to efficiently find resource allocations that demonstrably reduce the frequency of high-cost scenarios. This framework combines statistics and optimization in a novel way and is applicable to a general class of resource allocation problems, encompassing facility location, vehicle routing, and discrete-event simulation.

Integrated Lateral and Longitudinal Control with Optimization-Based Allocation Strategy for Autonomous Electric Vehicles

This paper presents a novel approach for path-following control of a four-wheeled autonomous vehicle. The rear wheels of the vehicle are driven independently, all four wheels can be braked independently, and the front wheels are steered together. The proposed cascade structure consists of two convex optimization-based parts: one for path-following and another for the control allocation problem of the actuators. The control algorithm presents cost functions for the allocation problem focusing on safety. The proposed cost functions were examined and compared to former ones in a simulation environment. After all, the controller was tested in real-time test on a Lotus Evora test vehicle developed by ThyssenKrupp.