A Novel Mathematical Model for Radio Mean Square Labeling Problem

A radio mean square labeling of a connected graph is motivated by the channel assignment problem for radio transmitters to avoid interference of signals sent by transmitters. It is an injective map h from the set of vertices of the graph G to the set of positive integers N , such that for any two distinct vertices x , y , the inequality d x , y + h x 2 + h y 2 / 2 ≥ dim G + 1 holds. For a particular radio mean square labeling h , the maximum number of h v taken over all vertices of G is called its spam, denoted by rmsn h , and the minimum value of rmsn h taking over all radio mean square labeling h of G is called the radio mean square number of G , denoted by rmsn G . In this study, we investigate the radio mean square numbers rmsn P n and rmsn C n for path and cycle, respectively. Then, we present an approximate algorithm to determine rmsn G for graph G . Finally, a new mathematical model to find the upper bound of rmsn G for graph G is introduced. A comparison between the proposed approximate algorithm and the proposed mathematical model is given. We also show that the computational results and their analysis prove that the proposed approximate algorithm overcomes the integer linear programming model (ILPM) according to the radio mean square number. On the other hand, the proposed ILPM outperforms the proposed approximate algorithm according to the running time.

Optimization of Humanitarian Aid Distribution in Case of an Earthquake and Tsunami in the City of Iquique, Chile

In this paper, we introduce, model, and solve a clustered resource allocation and routing problem for humanitarian aid distribution in the event of an earthquake and subsequent tsunami. First, for the preparedness stage, we build a set of clusters to identify, classify, sort, focus, and prioritize the aid distribution. The clusters are built with k-means method and a modified version of the capacitated p-median model. Each cluster has a set of beneficiaries and candidate delivery aid points. Second, vehicle routes are strategically determined to visit the clusters for the response stage. A mixed integer linear programming model is presented to determine efficient vehicle routes, minimizing the aid distribution times. A vulnerability index is added to our model to prioritize aid distribution. A case study is solved for the city of Iquique, Chile.

Practice Summary: Solving the External Candidates Exam Schedule in Norway

We developed a mixed-integer linear programming model to plan exam sessions for external candidates in the Vestfold region, Norway. With our model, the administration planned the last session of 2018, the two sessions of 2019, and the first session of 2020. The plans produced are of high quality and saved three weeks of person effort per session.

Hybrid Multiagent Collaboration for Time-Critical Tasks: A Mathematical Model and Heuristic Approach

Principal–assistant agent teams are often employed to solve tasks in multiagent collaboration systems. Assistant agents attached to the principal agents are more flexible for task execution and can assist them to complete tasks with complex constraints. However, how to employ principal–assistant agent teams to execute time-critical tasks considering the dependency between agents and the constraints among tasks is still a challenge so far. In this paper, we investigate the principal–assistant collaboration problem with deadlines, which is to allocate tasks to suitable principal–assistant teams and construct routes satisfying the temporal constraints. Two cases are considered in this paper, including single principal–assistant teams and multiple principal–assistant teams. The former is formally formulated in an arc-based integer linear programming model. We develop a hybrid combination algorithm for adapting larger scales, the idea of which is to find an optimal combination of partial routes generated by heuristic methods. The latter is defined in a path-based integer linear programming model, and a branch-and-price-based (BP-based) algorithm is proposed that introduces the number of assistant-accessible tasks surrounding a task to guide the route construction. Experimental results validate that the hybrid combination algorithm and the BP-based algorithm are superior to the benchmarks in terms of the number of served tasks and the running time.

New Bounds on Roller Coaster Permutations

A roller coaster is a permutation \pi that maximizes the sum $\t(\pi) = \sum_{\tau\in X(\pi)}\id(\tau)$, where \(X(\pi)\) denotes the set of subsequences of \(\pi\) with cardinality at least \(3\); and \(\id(\tau)\) denotes the number of maximal increasing or decreasing subsequences of contiguous numbers of \(\tau\). We denote by \(\t_{\max}(n)\) the value \(\t(\pi)\), where \(\pi\) is a roller coaster of \(\{1,\ldots,n\}\), for \(n\geq 3\). Precise values of \(\t_{\max}(n)\) for \(n\leq 13\) were presented in \cite{AhmedTanbir}. In this paper, we explore the problem of computing lower bounds for \(\t_{\max}(n)\). More specifically, we present a cubic algorithm to compute $\t(\pi)$ for any given permutation $\pi$; and an Integer Linear Programming model to obtain roller coasters. As a result, we improve known lower bounds found in the literature for $n \leq 40$.

A Greedy Heuristic for Maximizing the Lifetime of Wireless Sensor Networks Based on Disjoint Weighted Dominating Sets

Dominating sets are among the most well-studied concepts in graph theory, with many real-world applications especially in the area of wireless sensor networks. One way to increase network lifetime in wireless sensor networks consists of assigning sensors to disjoint dominating node sets, which are then sequentially used by a sleep–wake cycling mechanism. This paper presents a greedy heuristic for solving a weighted version of the maximum disjoint dominating sets problem for energy conservation purposes in wireless sensor networks. Moreover, an integer linear programming model is presented. Experimental results based on a large set of 640 problem instances show, first, that the integer linear programming model is only useful for small problem instances. Moreover, they show that our algorithm outperforms recent local search algorithms from the literature with respect to both solution quality and computation time.