Constrained two-line center problems

Heuristic Methods for Location-Allocation Problems

Almost all facility location models seek to minimize either the average distance traveled by all customers to the facility (the median problem), or the distance of the furthest customer from the facility (the center problem). In practice the two objectives are usually antagonistic and yet in many cases both criteria are important (called the cent-dian problem). For such cases the paper presents two possible approaches to model formulation. First is to minimize a function which is a (convex) combination of the furthest (center) and the average (median) objective functions. Second is to minimize one of the criteria, subject to an upper bound on the value of the other criterion. For facility location on a network, it is shown that the first approach is a special case of the second. Furthermore, the two different constrained problems, which exist under the second approach, are dual problems in a well defined sense. Finally the paper provides several features of the tradeoff between the two criteria.

In this paper, we consider a restricted covering problem, in which a convex polygon [Formula: see text] with [Formula: see text] vertices and an integer [Formula: see text] are given, the objective is to cover the entire region of [Formula: see text] using [Formula: see text] congruent disks of minimum radius [Formula: see text], centered on the boundary of [Formula: see text]. For [Formula: see text] and any [Formula: see text], we propose an [Formula: see text]-factor approximation algorithm for this problem, which runs in [Formula: see text] time. The best known approximation factor of the algorithm for the problem in the literature is 1.8841 [H. Du and Y. Xu: An approximation algorithm for [Formula: see text]-center problem on a convex polygon, J. Comb. Optim. 27(3) (2014) 504–518].

The longest common subsequence (LCS) problem is a central problem in stringology that finds the longest common subsequence of given two strings A and B. More recently, a set of four constrained LCS problems (called generalized constrained LCS problem) were proposed by Chen and Chao [J. Comb. Optim, 2011]. In this paper, we consider the substring-excluding constrained LCS (STR-EC-LCS) problem. A string Z is said to be an STR-EC-LCS of two given strings A and B excluding P if, Z is one of the longest common subsequences of A and B that does not contain P as a substring. Wang et al. proposed a dynamic programming solution which computes an STR-EC-LCS in O(mnr) time and space where \(m = |A|, n = |B|, r = |P|\) [Inf. Process. Lett., 2013]. In this paper, we show a new solution for the STR-EC-LCS problem. Our algorithm computes an STR-EC-LCS in \(O(n|\varSigma | + (L+1)(m-L+1)r)\) time where \(|\varSigma | \le \min \{m, n\}\) denotes the set of distinct characters occurring in both A and B, and L is the length of the STR-EC-LCS. This algorithm is faster than the O(mnr)-time algorithm for short/long STR-EC-LCS (namely, \(L \in O(1)\) or \(m-L \in O(1)\)), and is at least as efficient as the O(mnr)-time algorithm for all cases.

Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic sparse regression methods, has become a dominant tool for learning parsimonious models. We propose an exact formulation of the SINDy problem using mixed-integer optimization (MIO-SINDy) to solve the sparsity constrained regression problem to provable optimality in seconds. On a large number of canonical ordinary and partial differential equations, we illustrate the dramatic improvement in our approach in accurate model discovery while being more sample efficient, robust to noise, and flexible in accommodating physical constraints.

Routing problems have been considered as central problems in the fields of transportation, distribution and logistics. LS(Graph) is a generic framework allowing to model and solve constrained optimum paths problems on graphs by local search where paths are known to be elementary (i.e., edges, vertices cannot be repeated on paths). In many real-world situations, the paths to be determined are not known to be neither simple nor elementary. In this paper, we extend the LS(Graph) framework by designing and implementing abstractions that allow to model and solve constrained paths problem where edges, vertices can be repeated on paths (call non-simple paths). We also propose an instance of such problem class: the routing for network covering (RNC) problem which arises in the context of rescue after a natural disaster in which we have to route a fleet of identical vehicles with limited capacity on a transportation network in order to collect the informations of the disaster. Given an undirected weighted graph G = (V, E) representing a transportation network and a vertex v0 ∈ V representing the depot, the RNC problem consists of routing a fleet of unlimited number of identical vehicles with limited capacity that cannot perform a path of length > L such that each vehicle starts from and teminates at the depot and all the edges of a given set S (S ⊆ E) must be visited. The objective of the routing plan is to minimize the number of vehicles used. This paper discusses the challenge around this problem and applies the constructed framework to the resolution of this problem. The proposed model is generic; it allows to solve some variants of the problem where side constraints are required to be added.

Quadratic constrained maximization appears as the central problem in many filter design methods and signal processing applications, whenever the processing or filtering entails the maximization of a signal to noise ratio. Furthermore, self reference systems for MSE filters, beamformers and equalizers which manage either time or frequency diversity of the desired signal, give rise to the same mathematical problem. This work reports an adaptive algorithm based on two coupled LMS-like algorithms. It is shown how the Lagrange multiplier, involved in constrained minimization problems, plays the role of gain control in forming the error signal for the filter updates. This gain is power controlled by the output signals keeping the proper equilibrium between the outputs of the two LMS loops.

We address the following problem: Given two subsets Γ and Φ of the plane, find the minimum enclosing circle of Γ whose center is constrained to lie on Φ. We first study the case when Γ is a set of n points and Φ is either a set of points, a set of segments (lines) or a simple polygon. We propose several algorithms, the first solves the problem when Φ is a set of m segments (or m points) in expected Θ((n + m)logω) time, where ω = min {n, m}. Surprisingly, when Φ is a simple m-gon, we can improve the expected running time to Θ(m + nlogn). Moreover, if Γ is the set of vertices of a convex n-gon and Φ is a simple m-gon, we can solve the problem in expected Θ(n + m) time. We provide matching lower bounds in the algebraic computation tree model for all the algorithms presented in this paper. While proving these results, we obtained a Ω(n logm) lower bound for the following problem: Given two sets A and B in ℝ of sizes m and n, respectively, decide if A is a subset of B.

This archive is distributed in association with the INFORMS Journal on Computing under the MIT License. This repository contains supporting material for the paper Distributionally Robust Chance Constrained p-Hub Center Problem by Y. Zhao, Z. Chen and Z.Z. Zhang.

Combinatorial Interaction Testing is a black-box testing technique particularly used for highly configurable software systems, which involve a number of factors (and values) that can be combined, according to some constraints. In this context, constrained covering array (CCA) is a central combinatorial problem tasked with building a test suite of minimum size and maximum coverage of the factors' interactions.In this paper, we propose CATS (Covering Array by Tabu Search), a new penalty-based tabu search algorithm for the CCA problem. Our local search approach differs from the ones previously proposed primarily by its use of a search space that allows solutions that violate inter-factor constraints. Other prominent features of CATS are the definition of strategic moves used to restrict the neighborhood, and a technique to vary the tabu tenure throughout the search.We performed tests with CATS on 2-way constrained problems using 35 widely used benchmarks. Results suggest that CATS consistently outperforms previous approaches, both on the size of the test suites and the needed computation times.