Asia-Pacific Journal of Operational Research

The least-squares is a common and important method in linear regression. However, it often leads to overfitting phenomenon as dealing with high-dimensional problems, and various regularization schemes regarding prior information for specific problems are studied to make up such a deficiency. In the sense of Kendall’s $\tau$ from the community of nonparametric analysis, we establish a new model wherein the ordinary least-squares is equipped with perfect positive correlation constraint, sought to maintain the concordance of the rankings of the observations and the systematic components. By sorting the observations into an ascending order, we reduce the perfect positive correlation constraint into a linear inequality system. The resulting linearly constrained least-squares problem together with its dual problem is shown to be solvable. In particular, we introduce a mild assumption on the observations and the measurement matrix which rules out the zero vector from the optimal solution set. This indicates that our proposed model is statistically meaningful. To handle large-scale instances, we propose an efficient alternating direction method of multipliers (ADMM) to solve the proposed model from the dual perspective. The effectiveness of our model compared to ordinary least-squares is evaluated in terms of rank correlation coefficient between outputs and the systematic components, and the efficiency of our dual algorithm is demonstrated with the comparison to three efficient solvers via CVX in terms of computation time, solution accuracy and rank correlation coefficient.

In this paper, we propose a simulated annealing-based Barzilai–Borwein (SABB) gradient method for unconstrained optimization problems. The SABB method accepts the Barzilai–Borwein (BB) step by a simulated annealing rule. If the BB step cannot be accepted, the Armijo line search is used. The global convergence of the SABB method is established under some mild conditions. Numerical experiments indicate that, compared to some existing BB methods using nonmonotone line search technique, the SABB method performs well with high efficiency.

This paper addresses a network optimization interdiction problem, called the maximum capacity path interdiction problem. The problem is a hierarchical game containing two players: one evader and one interdictor. In a capacitated network, the evader wants to find a simple path from his current position to a target point with maximum capacity to send his forces along it while the interdictor decreases arc capacities under a budget constraint to interdict the advance of the evader’s forces as much as possible. This paper studies the case that each arc has a fixed cost for decreasing its capacity. An algorithm is proposed to solve the problem in strongly polynomial time. Computational experiments on two real-world datasets guarantee the efficiency and accuracy of the algorithm.

Consider a queueing network with a large number $N$ nodes, in which each queue has a dedicated input stream, and, in addition, there is an extra input stream, balancing the network load by directing its arrivals to the shortest queue(s). A mean field interaction model is set up to study the performance of this network in terms of limiting results. One of our results shows that the stationary behavior of any of the queues is approximated by that of the $M/M/1$ queue with a modified arrival rate when the queue length is around zero.

The turnaround is a critical airport process where a set of interrelated operations need to be performed to get an aircraft ready for its next flight. These activities are carried out by different vehicles, which need to be coordinated to guarantee an efficient utilization of resources. Due to the relations between operations, the order in which these resources are scheduled has a critical influence on the planning and performance of the turnaround. In this work, we present a novel methodology for solving the proposed bi-objective ground handling scheduling problem from a global perspective. This means solving a set of interconnected routing problems with restrictive time windows for each operation. We first explore the solution space using a fast heuristic, focusing then on the most promising solutions to intensify the search in the vicinity of the Pareto frontier. This two-step schema permits significantly reducing the required computational time, which, in turn, allows a more thorough exploration of solutions. Different experiments over real data from two Spanish airports have been conducted to assess the proposed methodology. Our results show that the new method not only outperforms previous approaches in terms of computational requirements, but can also improve the quality of scheduling solutions.

Optimality conditions are established in terms of Lagrange–Fritz–John multipliers as well as Lagrange–Kuhn–Tucker multipliers for set optimization problems (without any convexity assumption) by using new scalarization techniques. Additionally, we indicate how these results may be applied to some particular weak vector equilibrium problems.

We study a robust parameterized submodular function maximization inspired by [Mitrović, S, I Bogunovic, A Norouzi-Fard and Jakub Tarnawski (2017). Streaming robust submodular maximization: A partitioned thresholding approach. In Proc. NIPS, pp. 4560–4569] and [Bogunovic, I, J Zhao and V Cevher (2018). Robust maximization of nonsubmodular objectives. In Proc. AISTATS, pp. 890–899]. In our setting, given a parameterized set function, there are two additional twists. One is that elements arrive in a streaming style, and the other is that there are at most $\tau$ items deleted from the algorithm’s memory when the stream is finished. The goal is to choose a robust set from the stream such that the robust ratio is maximized. We propose a two-phase algorithm for maximizing a normalized monotone robust parameterized submodular function with a cardinality constraint and show the robust ratio is close to a constant as $k\to \infty$. In the end, we empirically demonstrate the performance of our algorithm on deletion robust support selection problem.