EURO Journal on Computational Optimization最新文献

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.

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 $\phi \left(t\right)=\sqrt{t}$.

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.

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.

Solving large-scale Mixed Integer Linear Programs (MIP) can be difficult without advanced algorithms such as decomposition based techniques. Even if a decomposition technique might be appropriate, there are still many possible decompositions for any large MIP and it may not be obvious which will be the most effective. The quality of a decomposition depends on both the tightness of the dual bound, in our case generated via Lagrangian Relaxation, and the computational time required to produce that bound. Both of these factors are difficult to predict, motivating the use of a Machine Learning function to predict decomposition quality based a score that combines both bound quality and computational time. This paper presents a comprehensive analysis of the predictive capabilities of a ML function for predicting the quality of MIP decompositions created via constraint relaxation. In this analysis, the role of instance similarity and ML prediction quality is explored, as well as the benchmarking of a ML ranking function against existing heuristic functions. For this analysis, a new dataset consisting of over 40000 unique decompositions sampled from across 24 instances from the MIPLIB2017 library has been established. These decompostions have been created by both a greedy relaxation algorithm as well as a population based multi-objective algorithm, which has previously been shown to produce high quality decompositions. In this paper, we demonstrate that a ML ranking function is able to provide state-of-the-art predictions when benchmarked against existing heuristic ranking functions. Additionally, we demonstrate that by only considering a small set of features related to the relaxed constraints in each decomposition, a ML ranking function is still able to be competitive with heuristic techniques. Such a finding is promising for future constraint relaxation approaches, as these features can be used to guide decomposition creation. Finally, we highlight where a ML ranking function would be beneficial in a decomposition creation framework.

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.

We present and compare novel binary programs for linear ordering problems that involve the notion of asymmetric betweenness and expose relations to the quadratic linear ordering problem and its linearization. While two of the binary programs prove particularly superior from a computational point of view when many or all betweenness relations shall be modeled, the others arise as natural formulations that resemble important theoretical correspondences and provide a compact alternative for sparse problem instances. A reasoning for the strengths and weaknesses of the different formulations is derived by means of polyhedral considerations with respect to their continuous relaxations.