Search results for "Mathematic"
showing 10 items of 24974 documents
Aesthetic considerations for the min-max K-Windy Rural Postman Problem
2017
[EN] The aesthetic quality of routes is a feature of route planning that is of practical importance, but receives relatively little attention in the literature. Several practitioners have pointed out that the visual appeal of a proposed set of routes can have a strong influence on the willingness of a client to accept or reject a specific routing plan. While some work has analyzed algorithmic performance relative to traditional min-sum or min-max objective functions and aesthetic objective functions, we are not aware of any work that has considered a multi-objective approach. This work considers a multi-objective variant of the Min-Max K-Vehicles Windy Rural Postman Problem, discusses sever…
A Novel Border Identification Algorithm Based on an “Anti-Bayesian” Paradigm
2013
Published version of a chapter in the book: Computer Analysis of Images and Patterns. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-40261-6_23 Border Identification (BI) algorithms, a subset of Prototype Reduction Schemes (PRS) aim to reduce the number of training vectors so that the reduced set (the border set) contains only those patterns which lie near the border of the classes, and have sufficient information to perform a meaningful classification. However, one can see that the true border patterns (“near” border) are not able to perform the task independently as they are not able to always distinguish the testing samples. Thus, researchers have worked on thi…
Grading investment diversification options in presence of non-historical financial information
2021
Modern portfolio theory deals with the problem of selecting a portfolio of financial assets such that the expected return is maximized for a given level of risk. The forecast of the expected individual assets’ returns and risk is usually based on their historical returns. In this work, we consider a situation in which the investor has non-historical additional information that is used for the forecast of the expected returns. This implies that there is no obvious statistical risk measure any more, and it poses the problem of selecting an adequate set of diversification constraints to mitigate the risk of the selected portfolio without losing the value of the non-statistical information owne…
The minimum mean cycle-canceling algorithm for linear programs
2022
Abstract This paper presents the properties of the minimum mean cycle-canceling algorithm for solving linear programming models. Originally designed for solving network flow problems for which it runs in strongly polynomial time, most of its properties are preserved. This is at the price of adapting the fundamental decomposition theorem of a network flow solution together with various definitions: that of a cycle and the way to calculate its cost, the residual problem, and the improvement factor at the end of a phase. We also use the primal and dual necessary and sufficient optimality conditions stated on the residual problem for establishing the pricing step giving its name to the algorith…
Gray code for derangements
2004
AbstractWe give a Gray code and constant average time generating algorithm for derangements, i.e., permutations with no fixed points. In our Gray code, each derangement is transformed into its successor either via one or two transpositions or a rotation of three elements. We generalize these results to permutations with number of fixed points bounded between two constants.
Project portfolio selection and planning with fuzzy constraints
2018
Abstract Selecting a project portfolio is a complex process involving many factors and considerations from the time it is proposed to the time the project portfolio is finally selected. Given that making a good selection is of crucial importance, it is essential to develop well-founded mathematical models to lead the organization to its final goal. To achieve this, such models have to reflect as closely as possible both the real situation of the organization as well as its targets and preferences. However, since the process of selecting and implementing project portfolios occurs in real environments and not in laboratories, uncertainty and a lack of knowledge regarding some data is always a…
Comparing interactive evolutionary multiobjective optimization methods with an artificial decision maker
2021
AbstractSolving multiobjective optimization problems with interactive methods enables a decision maker with domain expertise to direct the search for the most preferred trade-offs with preference information and learn about the problem. There are different interactive methods, and it is important to compare them and find the best-suited one for solving the problem in question. Comparisons with real decision makers are expensive, and artificial decision makers (ADMs) have been proposed to simulate humans in basic testing before involving real decision makers. Existing ADMs only consider one type of preference information. In this paper, we propose ADM-II, which is tailored to assess several …
Best proximity point theorems for proximal cyclic contractions
2017
The purpose of this article is to compute a global minimizer of the function $$x\longrightarrow d(x, Tx)$$ , where T is a proximal cyclic contraction in the framework of a best proximally complete space, thereby ensuring the existence of an optimal approximate solution, called a best proximity point, to the equation $$Tx=x$$ when T is not necessarily a self-mapping.
Combined column-and-row-generation for the optimal communication spanning tree problem
2018
Abstract This paper considers the exact solution of the optimal communication spanning tree problem (OCSTP), which can be described as follows: Given an undirected graph with transportation costs on every edge and communication requirements for all pairs of vertices, the OCSTP seeks for a spanning tree that minimizes the sum of the communication costs between all pairs of vertices, where the communication cost of a pair of vertices is defined as their communication requirement multiplied by the transportation cost of the unique tree path that connects the two vertices. Two types of compact formulations for OCSTP were presented in the literature. The first one is a four-index model based on …
Heuristics for the min–max arc crossing problem in graphs
2018
Abstract In this paper, we study the visualization of complex structures in the context of automatic graph drawing. Constructing geometric representations of combinatorial structures, such as networks or graphs, is a difficult task that requires an expert system. The automatic generation of drawings of graphs finds many applications from software engineering to social media. The objective of graph drawing expert systems is to generate layouts that are easy to read and understand. This main objective is achieved by solving several optimization problems. In this paper we focus on the most important one: reducing the number of arc crossings in the graph. This hard optimization problem has been…