EURO Journal on Computational Optimization最新文献

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.

Nowadays, the supply chain networks, consisting of different tiers of decision-makers, provide an effective framework for the production, the distribution, and the consumption of goods. In this paper we propose a supply chain network optimization model where manufacturers, retailers and consumers in the demand markets have a degree of interest in environmental sustainability. The manufacturers can improve their energy level (assumed as variables), aim to minimize their environmental emissions (for production and transport) and can also establish the amount of quantity of the production waste to dispose in a eco-sustainable way. The retailers, who are also profit-maximizers, aim to minimize their environmental emissions (which depend on the chosen shipping methods). The consumers at demand markets make their own choices according to the prices and to their degree of aversion to the environmental emissions. We describe the behavior of each decision-maker and we present the mathematical model for each of them, deriving the variational inequality problems. Furthermore, we derive a unique variational inequality formulation for the entire network for whose solution an existence and uniqueness result is obtained. Finally, we illustrate some numerical simulations that highlight how the use of UAVs and the presence of waste sorting centers in the supply chain reduce environmental emissions and related costs.

The Dai-Kou method Dai and Kou (2013), [12] is efficient for solving unconstrained optimization problems. However, its modified variants are quite rare for constrained nonlinear monotone equations. In an attempt to address this, two adaptive versions of the scheme with new and efficient parameter choices are presented in this paper. The schemes are obtained by analyzing eigenvalues of a modified Dai-Kou iteration matrix and constructing two new directions, which are used in the scheme's algorithms. The new methods are derivative-free, which is an attribute required for handling problems with very large dimensions. Both methods also satisfy the required condition for analyzing global convergence in the literature. By applying mild conditions, it is shown that the schemes are globally convergent and description of their effectiveness is achieved through experiments with four effective schemes for solving constrained nonlinear monotone equations. Furthermore, the methods are applied to recover images that are contaminated by impulse noise in compressed sensing.

Stochastic optimization algorithms such as genetic algorithm (GA), particle swarm optimization (PSO), estimation of distribution algorithms (EDAs), and nested partitions algorithm (NPA) are used in many problems including nonlinear model predictive control and task assignment. Some of these algorithms, however, lack global convergence guarantee such as PSO, or require strict convergence assumptions such as NPA. To enhance these methods in terms of convergence, a common underlying framework towards representing the seemingly unrelated methods is established as the updating of the distribution of the population through iterative sampling, and the methods that fit into this framework are called population distribution-based methods. Global convergence conditions for this framework are innovatively developed by building a shadow NPA structure for the population evolution process. The result is generic and is capable of analyzing convergence of many methods including GA, PSO, EDA, and NPA. It can be further exploited to improve convergence by modifying these methods. The existing and modified variants of these methods are then applied to case studies to show the improvement.

We introduce a new predictor-corrector interior-point algorithm for solving $P_{⁎}\left(\kappa \right)$-linear complementarity problems which works in a wide neighbourhood of the central path. We use the technique of algebraic equivalent transformation of the centering equations of the central path system. In this technique, we apply the function $\phi \left(t\right)=\sqrt{t}$ in order to obtain the new search directions. We define the new wide neighbourhood $D_{\phi }$. In this way, we obtain the first interior-point method, where not only the central path system is transformed, but the definition of the neighbourhood is also modified taking into consideration the algebraic equivalent transformation technique. This gives a new direction in the research of interior-point algorithms. We prove that the interior-point method has $O\left(\right(1+\kappa )n\log \left(\frac{{\left(x^0\right)}^T{s}^0}{ϵ}\right))$ iteration complexity. Furthermore, we show the efficiency of the proposed predictor-corrector algorithm by providing numerical results. To our best knowledge, this is the first predictor-corrector interior-point algorithm which works in the $D_{\phi }$ neighbourhood using $\phi \left(t\right)=\sqrt{t}$.

Location-routing problems (LRPs) jointly optimize the location of depots and the routing of vehicles. The most studied LRP variant, the capacitated LRP (CLRP), has been addressed by a large number of metaheuristic approaches. These methods often decompose the problem into a location stage to determine a promising depot configuration and a routing stage, in which a vehicle-routing problem is solved to assess the quality of the previously determined depot configuration. Unfortunately, the CLRP literature does not shed much light on the important question which algorithmic features have the biggest influence on the solution quality and runtime of such heuristics. The purpose of this paper is to propose a conceptually simple (yet reasonably effective) heuristic for the CLRP and to provide some insights on the design of successful metaheuristics for this problem. Our algorithm is a hybrid combining (i) a GRASP phase that uses a variable neighborhood descent for local improvement in the location stage, and (ii) a variable neighborhood search in the routing stage. We analyze the impact of the algorithmic components on solution quality and runtime. In addition, we find that the suboptimal routing solutions used to assess the quality of the investigated depot configurations in tendency lead to depot configurations with too many open depots. We propose a depot configuration refinement phase that alleviates this drawback, and we show that this algorithmic component significantly contributes to the solution quality of our method, enabling it to provide reasonable results in comparison to the state-of-the-art methods from the literature.

In this paper, we consider policy interventions for international migrant flows and quantify their ramifications. In particular, we further develop a recent equilibrium model of international human migration in which some of the destination countries form coalitions to establish a common upper bound on the migratory flows that they agree to accept jointly. We also consider here a scenario where some countries can leave or join an initial coalition and investigate the problem of finding the coalitions that maximize the overall social welfare. Moreover, we compare the social welfare at equilibrium with the one that a supranational organization might suggest in an ideal scenario. This research adds to the literature on the development of mathematical models to address pressing issues associated with problems of human migration with insights for policy and decision-makers.

The main purpose of solving a classical generation capacity expansion problem is to ensure that, in the medium- to long-term time frame, the electric utility has enough capacity available to reliably satisfy the demand for electricity from its customers. However, the ability to operate the newly built power plants also has to be considered. Operation of these plants could be curtailed by fuel availability, environmental constraints, or intermittency of renewable generation. This suggests that when generation capacity expansion problems are solved, along with the yearly timescale necessary to capture the long-term effect of the decisions, it is necessary to include a timescale granular enough to represent operations of generators with a credible fidelity. Additionally, given that the time horizon for a capacity expansion model is long, stochastic modeling of key parameters may generate more insightful, realistic, and judicious results. In the current model, we allow the demand for electricity and natural gas to behave stochastically. Together with the dual timescales, the randomness results in a large problem that is challenging to solve. In this paper, we experiment with synergistically combining elements of several methods that are, for the most part, based on Benders decomposition and construct an algorithm which allows us to find near-optimal solutions to the problem with reasonable run times.