EURO Journal on Computational Optimization最新文献

We tackle a new single-machine scheduling problem, whose objective is to balance the average weighted completion times of two classes of jobs. Because both the job sets contribute to the same objective function, this problem can be interpreted as a cooperative two-agent scheduling problem, in contraposition to the standard multiagent problems, which are of the competitive type since each class of job is involved only in optimizing its agent's criterion. Balancing the completion times of different sets of tasks finds application in many fields, such as in logistics for balancing the delivery times, in manufacturing for balancing the assembly lines and in services for balancing the waiting times of groups of people.

To solve the problem, for which we show the NP-hardness, a Lagrangian heuristic algorithm is proposed. In particular, starting from a nonsmooth variant of the quadratic assignment problem, our approach is based on the Lagrangian relaxation of a linearized model and reduces to solve a finite sequence of successive linear assignment problems.

Numerical results are presented on a set of randomly generated test problems, showing the efficiency of the proposed technique.

In distributed learning, a central server trains a model according to updates provided by nodes holding local data samples. In the presence of one or more malicious servers sending incorrect information (a Byzantine adversary), standard algorithms for model training such as stochastic gradient descent (SGD) fail to converge. In this paper, we present a simplified convergence theory for the generic Byzantine Resilient SGD method originally proposed by Blanchard et al. (2017) [3]. Compared to the existing analysis, we shown convergence to a stationary point in expectation under standard assumptions on the (possibly nonconvex) objective function and flexible assumptions on the stochastic gradients.

Tabu search is a well-established metaheuristic framework for solving hard combinatorial optimization problems. At its core, the method uses different forms of memory to guide a local search through the solution space so as to identify high-quality local optima while avoiding getting stuck in the vicinity of any particular local optimum. This paper examines characteristics of moves that can be exploited to make good decisions about steps that lead away from recently visited local optima and towards a new local optimum. Our approach uses a new type of adaptive memory based on a construction called exponential extrapolation. The memory operates by means of threshold inequalities that ensure selected moves will not lead to a specified number of most recently encountered local optima. Computational experiments on a set of one hundred different benchmark instances for the binary integer programming problem suggest that exponential extrapolation is a useful type of memory to incorporate into a tabu search.

We propose a formulation of the stochastic cutting stock problem as a discounted infinite-horizon Markov decision process. At each decision epoch, given current inventory of items, an agent chooses in which patterns to cut objects in stock in anticipation of the unknown demand. An optimal solution corresponds to a policy that associates each state with a decision and minimizes the expected total cost. Since exact algorithms scale exponentially with the state-space dimension, we develop a heuristic solution approach based on reinforcement learning. We propose an approximate policy iteration algorithm in which we apply a linear model to approximate the action-value function of a policy. Policy evaluation is performed by solving the projected Bellman equation from a sample of state transitions, decisions and costs obtained by simulation. Due to the large decision space, policy improvement is performed via the cross-entropy method. Computational experiments are carried out with the use of realistic data to illustrate the application of the algorithm. Heuristic policies obtained with polynomial and Fourier basis functions are compared with myopic and random policies. Results indicate the possibility of obtaining policies capable of adequately controlling inventories with an average cost up to 80% lower than the cost obtained by a myopic policy.

This paper considers the problem of decentralized, personalized federated learning. For centralized personalized federated learning, a penalty that measures the deviation from the local model and its average, is often added to the objective function. However, in a decentralized setting this penalty is expensive in terms of communication costs, so here, a different penalty — one that is built to respect the structure of the underlying computational network — is used instead. We present lower bounds on the communication and local computation costs for this problem formulation and we also present provably optimal methods for decentralized personalized federated learning. Numerical experiments are presented to demonstrate the practical performance of our methods.

EUROPT, the Continuous Optimization working group of EURO, celebrated its 20 years of activity in 2020. We trace the history of this working group by presenting the major milestones that have led to its current structure and organization and its major trademarks, such as the annual EUROPT workshop and the EUROPT Fellow recognition.

For a given graph with a vertex set that is partitioned into clusters, the generalized traveling salesman problem (GTSP) is the problem of finding a cost-minimal cycle that contains exactly one vertex of every cluster. We introduce three new GTSP neighborhoods that allow the simultaneous permutation of the sequence of the clusters and the selection of vertices from each cluster. The three neighborhoods and some known neighborhoods from the literature are combined into an effective iterated local search (ILS) for the GTSP. The ILS performs a straightforward random neighborhood selection within the local search and applies an ordinary record-to-record ILS acceptance criterion. The computational experiments on four symmetric standard GTSP libraries show that, with some purposeful refinements, the ILS can compete with state-of-the-art GTSP algorithms.

Chance-constrained programming (CCP) is one of the most difficult classes of optimization problems that has attracted the attention of researchers since the 1950s. In this survey, we focus on cases when only limited information on the distribution is available, such as a sample from the distribution, or the moments of the distribution. We first review recent developments in mixed-integer linear formulations of chance-constrained programs that arise from finite discrete distributions (or sample average approximation). We highlight successful reformulations and decomposition techniques that enable the solution of large-scale instances. We then review active research in distributionally robust CCP, which is a framework to address the ambiguity in the distribution of the random data. The focal point of our review is on scalable formulations that can be readily implemented with state-of-the-art optimization software. Furthermore, we highlight the prevalence of CCPs with a review of applications across multiple domains.

Optimization acceleration techniques such as momentum play a key role in state-of-the-art machine learning algorithms. Recently, generic vector sequence extrapolation techniques, such as regularized nonlinear acceleration (RNA) of Scieur et al. [22], were proposed and shown to accelerate fixed point iterations. In contrast to RNA which computes extrapolation coefficients by (approximately) setting the gradient of the objective function to zero at the extrapolated point, we propose a more direct approach, which we call direct nonlinear acceleration (DNA). In DNA, we aim to minimize (an approximation of) the function value at the extrapolated point instead. We adopt a regularized approach with regularizers designed to prevent the model from entering a region in which the functional approximation is less precise. While the computational cost of DNA is comparable to that of RNA, our direct approach significantly outperforms RNA on both synthetic and real-world datasets. While the focus of this paper is on convex problems, we obtain very encouraging results in accelerating the training of neural networks.

First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories reported in various applications, including most importantly machine learning, signal processing, imaging and control theory. First-order methods have the potential to provide low accuracy solutions at low computational complexity which makes them an attractive set of tools in large-scale optimization problems. In this survey, we cover a number of key developments in gradient-based optimization methods. This includes non-Euclidean extensions of the classical proximal gradient method, and its accelerated versions. Additionally we survey recent developments within the class of projection-free methods, and proximal versions of primal-dual schemes. We give complete proofs for various key results, and highlight the unifying aspects of several optimization algorithms.