Search results for "mathematics"
showing 10 items of 22031 documents
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…
Variable neighborhood descent for the incremental graph drawing
2017
Abstract Graphs are used to represent reality in several areas of knowledge. Drawings of graphs have many applications, from project scheduling to software diagrams. The main quality desired for drawings of graphs is readability, and crossing reduction is a fundamental aesthetic criterion for a good representation of a graph. In this paper we target the edge crossing reduction in the context of incremental graph drawing, in which we want to preserve the layout of a graph over successive drawings. We propose a hybrid method based on the GRASP (Greedy Randomized Adaptive Search Procedure) and VND (Variable Neighborhood Descent) methodologies and compare it with previous methods via simulation.
The ELECTRE I method to support the FMECA
2018
Abstract In traditional Failure Modes, Effects and Criticality Analysis (FMECA), risk priorities of failure modes are determined through the Risk Priority Number (RPN), which is a function of the three risk parameters Occurrence (O), Severity (S), and Detection (D). In the present paper, an alternative approach to RPN is proposed for the criticality assessment of system failure modes. Particularly, the Multi-Criteria Decision Making (MCDM) method ELECTRE I is proposed to select the most critical failure mode in the set of the failure modes charactering a complex system. The method has been applied to a case study previously proposed by Zammori and Gabrielli (2012).