EURO Journal on Computational Optimization最新文献

We investigate a location-allocation-routing problem where trucks deliver goods from a central production facility to a set of warehouses with fixed locations and known demands. Due to limited capacities congestion occurs and results in queueing problems. The location of the center is determined to maximize the utilization of the given resources (measured in throughput) and the minimal number of trucks is determined to satisfy the overall demand generated by the warehouses. Main results for this integrated decision problem on strategic and tactical/operational level are: (i) The location decision is reduced to a standard Weber problem with weighted distances. (ii) The joint decision for location and fleet size is separable. (iii) The location of the center is robust against perturbations of several system parameters on the operational/tactical level. Additionally, we consider minimization of travel times as optimization target. By numerical examples we demonstrate the consequences of neglecting available information on long-term (rough) demand structure.

Price differentiation is a common strategy in many markets. In this paper, we study a static multiproduct price optimization problem with demand given by a discrete mixed multinomial logit model. By considering a mixed logit model that includes customer specific variables and parameters in the utility specification, our pricing problem reflects well the discrete choice models used in practice. To solve this pricing problem, we design an efficient iterative optimization algorithm that asymptotically converges to the optimal solution. To this end, a linear optimization (LO) problem is formulated, based on the trust-region approach, to find a “good” feasible solution and approximate the problem from below. A convex optimization problem is designed using a convexification technique to approximate the optimization problem from above. Then, using a branching method, we tighten the optimality gap. The effectiveness of our algorithm is illustrated on several cases, and compared against solvers and existing state-of-the-art methods in the literature.

Graph Semi-Supervised learning is an important data analysis tool, where given a graph and a set of labeled nodes, the aim is to infer the labels to the remaining unlabeled nodes. In this paper, we start by considering an optimization-based formulation of the problem for an undirected graph, and then we extend this formulation to multilayer hypergraphs. We solve the problem using different coordinate descent approaches and compare the results with the ones obtained by the classic gradient descent method. Experiments on synthetic and real-world datasets show the potential of using coordinate descent methods with suitable selection rules.

A multilevel programming problem is an optimization problem that involves multiple decision makers, whose decisions are made in a sequential (or hierarchical) order. If all objective functions and constraints are linear and some decision variables in any level are restricted to take on integral or discrete values, then the problem is called a multilevel mixed integer linear programming problem (ML-MILP). Such problems are known to have disconnected feasible regions (called inducible regions), making the task of constructing an optimal solution challenging. Therefore, existing solution approaches are limited to some strict assumptions in the model formulations and lack universality. This paper presents a branch-and-cut (B&C) algorithm for the global solution of such problems with any finite number of hierarchical levels, and containing both continuous and discrete variables at each level of the decision-making hierarchy. Finite convergence of the proposed algorithm to a global solution is established. Numerical examples are used to illustrate the detailed procedure and to demonstrate the performance of the algorithm. Additionally, the computational performance of the proposed method is studied by comparing it with existing method through some selected numerical examples.

Consider an undirected graph with demands scattered over the edges and a homogeneous fleet of vehicles to service the demands. In the open capacitated arc routing problem (OCARP) the objective is to find a set of routes that collectively service all demands with the minimum cost. Each vehicle has limited capacity and it can start and finish the route at any node. The OCARP is NP-hard, and its applications include meter reading and cutting path determination problems. State-of-the-art solution methods developed for the OCARP are heuristics, which show good tradeoffs between solution quality and processing time, but do not provide optimality certificates of the obtained solutions. This work focuses on a lower bounding method for the OCARP which can be used to better assess the quality of heuristic solutions. We propose the Relaxed Flow method ($RF\left(k\right)$) which involves the resolution of a mixed integer linear formulation where all vehicles' capacities are modeled as flows on an augmented graph. A parameter k controls the model tightness and $RF\left(k\right)$ is shown to be at least as tight as the well-known Belenguer and Benavent's formulation for any $k⩾0$. To strengthen the model, capacity cuts were included in $RF\left(k\right)$ by means of a branch-and-cut framework. Extensive computational experiments conducted on a set of benchmark instances revealed that our method outperformed previous methods. Computational experiments also demonstrated the importance of the parameterization technique to obtain good results. The previously known lower bounds were improved substantially and optimality certificates were attained in 78.9% of the instances. As far as we know this is the first parameterized lower bounding method proposed for an arc routing problem, and we argue it can be generalized to other variants of arc routing problems and general routing problems.

Multiple Instance Learning (MIL) is a kind of weak supervised learning, where each sample is represented by a bag of instances. The main characteristic of such problems resides in the training phase, since the class labels are provided only for each bag, whereas the instance labels are unknown.

We focus on binary MIL problems characterized by two types of instances (positive and negative): based on the standard MIL assumption, a bag is considered positive if at least one of its instances is positive and it is considered negative otherwise. Then our idea is to generate a maximum-margin polyhedral separation surface such that, for each positive bag, at least one of its instances is inside the polyhedron and all the instances of the negative bags are outside. The resulting optimization problem is a nonlinear, nonconvex and nonsmooth mixed integer program, that we heuristically solve by a Block Coordinate Descent type method, based on repeatedly applying the DC (Difference of Convex) Algorithm.

Numerical results are presented on a set of benchmark datasets.

In this paper, two new algorithms for dual decomposition-based distributed optimization are presented. Both algorithms rely on the quadratic approximation of the dual function of the primal optimization problem. The dual variables are updated in each iteration through a maximization of the approximated dual function. The first algorithm approximates the dual function by solving a regression problem, based on the values of the dual function collected from previous iterations. The second algorithm updates the parameters of the quadratic approximation via a quasi-Newton scheme. Both algorithms employ step size constraints for the update of the dual variables. Furthermore, the subgradients from previous iterations are stored in order to construct cutting planes, similar to bundle methods for nonsmooth optimization. However, instead of using the cutting planes to formulate a piece-wise linear over-approximation of the dual function, they are used to construct valid inequalities for the update step. In order to demonstrate the efficiency of the algorithms, they are evaluated on a large set of constrained quadratic, convex and mixed-integer benchmark problems and compared to the subgradient method, the bundle trust method, the alternating direction method of multipliers and the quadratic approximation coordination algorithm. The results show that the proposed algorithms perform better than the compared algorithms both in terms of the required number of iterations and in the number of solved benchmark problems in most cases.

Logistic regression is one of the widely-used classification tools to construct prediction models. For datasets with a large number of features, feature subset selection methods are considered to obtain accurate and interpretable prediction models, in which irrelevant and redundant features are removed. In this paper, we address the problem of feature subset selection in logistic regression using modern optimization techniques. To this end, we formulate this problem as a mixed-integer exponential cone program (MIEXP). To the best of our knowledge, this is the first time both nonlinear and discrete aspects of the underlying problem are fully considered within an exact optimization framework. We derive different versions of the MIEXP model by the means of regularization and goodness of fit measures including Akaike Information Criterion and Bayesian Information Criterion. Finally, we solve our MIEXP models using the solver MOSEK and evaluate the performance of our different versions over a set of toy examples and benchmark datasets. The results show that our approach is quite successful in obtaining accurate and interpretable prediction models compared to other methods from the literature.