Dynamic Resource Allocation

Computer systems are subject to continuously increasing performance demands. However, energy consumption has become a critical issue, both for high-end large-scale parallel systems [12], as well as for portable devices [34]. In other words, more work needs to be done in less time, preferably with the same or smaller energy budget. Future performance and efficiency goals of computer systems can only be reached with large-scale, heterogeneous architectures [6]. Due to their distributed nature, control software is required to coordinate the parallel execution of applications on such platforms. Abstraction, arbitration and multi-objective optimization are only a subset of the tasks this software has to fulfill [6, 31]. The essential problem in all this is the allocation of platform resources to satisfy the needs of an application.\ud \ud This work considers the dynamic resource allocation problem, also known as the run-time mapping problem. This problem consists of task assignment to (processing) elements and communication routing through the interconnect between the elements. In mathematical terms, the combined problem is defined as the multi-resource quadratic assignment and routing problem (MRQARP). An integer linear programming formulation is provided, as well as complexity proofs on the N P-hardness of the problem.\ud \ud This work builds upon state-of-the-art work of Yagiura et al. [39, 40, 42] on metaheuristics for various generalizations of the generalized assignment problem. Specifically, we focus on the guided local search (GLS) approach for the multi-resource quadratic assignment problem (MRQAP). The quadratic assignment problem defines a cost relation between tasks and between elements. We generalize the multi-resource quadratic assignment problem with the addition of a capacitated interconnect and a communication topology between tasks. Numerical experiments show that the performance of the approach is comparable with commercial solvers. The footprint, the time versus quality trade-off and available metadata make guided local search a suitable candidate for run-time mapping

Q-{M}atch: {I}terative Shape Matching via Quantum Annealing

Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) that becomes infeasible for shapes with high sampling density. A promising research direction is to tackle such quadratic optimization problems over binary variables with quantum annealing, which allows for some problems a more efficient search in the solution space. Unfortunately, enforcing the linear equality constraints in QAPs via a penalty significantly limits the success probability of such methods on currently available quantum hardware. To address this limitation, this paper proposes Q-Match, i.e., a new iterative quantum method for QAPs inspired by the alpha-expansion algorithm, which allows solving problems of an order of magnitude larger than current quantum methods. It implicitly enforces the QAP constraints by updating the current estimates in a cyclic fashion. Further, Q-Match can be applied iteratively, on a subset of well-chosen correspondences, allowing us to scale to real-world problems. Using the latest quantum annealer, the D-Wave Advantage, we evaluate the proposed method on a subset of QAPLIB as well as on isometric shape matching problems from the FAUST dataset

PasMoQAP: A Parallel Asynchronous Memetic Algorithm for solving the Multi-Objective Quadratic Assignment Problem

Multi-Objective Optimization Problems (MOPs) have attracted growing attention during the last decades. Multi-Objective Evolutionary Algorithms (MOEAs) have been extensively used to address MOPs because are able to approximate a set of non-dominated high-quality solutions. The Multi-Objective Quadratic Assignment Problem (mQAP) is a MOP. The mQAP is a generalization of the classical QAP which has been extensively studied, and used in several real-life applications. The mQAP is defined as having as input several flows between the facilities which generate multiple cost functions that must be optimized simultaneously. In this study, we propose PasMoQAP, a parallel asynchronous memetic algorithm to solve the Multi-Objective Quadratic Assignment Problem. PasMoQAP is based on an island model that structures the population by creating sub-populations. The memetic algorithm on each island individually evolve a reduced population of solutions, and they asynchronously cooperate by sending selected solutions to the neighboring islands. The experimental results show that our approach significatively outperforms all the island-based variants of the multi-objective evolutionary algorithm NSGA-II. We show that PasMoQAP is a suitable alternative to solve the Multi-Objective Quadratic Assignment Problem.Comment: 8 pages, 3 figures, 2 tables. Accepted at Conference on Evolutionary Computation 2017 (CEC 2017