VNS Metaheuristics to Solve a Financial Portfolio Design Problem

2020 ◽  
pp. 148-164
Keyword(s):  
Mathematical Model ◽  
Simulated Annealing ◽  
Local Search ◽  
Design Problem ◽  
Quadratic Model ◽  
Financial Problem ◽  
Financial Portfolio ◽  
The Mathematical Model ◽  
Portfolio Design

This chapter introduces a VNS-based local search for solving efficiently a financial portfolio design problem described in Chapter 1 and modeled in Chapter 3. The mathematical model tackled is a 0-1 quadratic model. It is well known that exact solving approaches on large instances of this kind of model are costly. The authors have proposed local search approaches to solve the problem, and the efficiency of this type of method has been proved. This chapter shows that the matricial 0-1 model of the problem enables specialized VNS algorithms by taking into account the particular structure of the financial problem considered. First experiments show that VNS with simulated annealing is effective on non-trivial instances of the problem.

A Local Search Approach to Solve a Financial Portfolio Design Problem

2015 ◽  
Vol 6 (2) ◽  
pp. 1-17 ◽  
Author(s):  
Fatima Zohra Lebbah ◽  
Yahia Lebbah
Keyword(s):  
Local Search ◽  
Design Problem ◽  
Optimization Technique ◽  
Quadratic Program ◽  
Evaluation Functions ◽  
Search Optimization ◽  
Quadratic Integer ◽  
Financial Portfolio ◽  
Search Approach ◽  
Portfolio Design

This paper introduces a local search optimization technique for solving efficiently a financial portfolio design problem which consists to affect assets to portfolios, allowing a compromise between maximizing gains and minimizing losses. This practical problem appears usually in financial engineering, such as in the design of CDO-squared portfolios. This problem has been modeled by Flener et al. who proposed an exact method to solve it. It can be formulated as a quadratic program on the 0-1 domain. It is well known that exact solving approaches on difficult and large instances of quadratic integer programs are known to be inefficient. That is why this work has adopted a local search method. It proposes neighborhood and evaluation functions specialized on this problem. To boost the local search process, it also proposes a greedy algorithm to start the search with an optimized initial configuration. Experimental results on non-trivial instances of the problem show the effectiveness of this work's approach.

scholarly journals Speeding-up the Fitting of the Model Defining the Ribs-bounded Contour

2017 ◽  
Vol 21 (1) ◽  
pp. 66-70
Author(s):  
Mykolas J. Bilinskas ◽  
Gintautas Dzemyda ◽  
Martynas Sabaliauskas
Keyword(s):  
Mathematical Model ◽  
Local Search ◽  
Computer Tomography ◽  
Vertical Axis ◽  
Newton Methods ◽  
Optimal Parameters ◽  
Analytical Derivatives ◽  
The Mathematical Model ◽  
Quasi Newton ◽  
Derivatives Of

Abstract The method for analysing transversal plane images from computer tomography scans is considered in the paper. This method allows not only approximating ribs-bounded contour but also evaluating patient rotation around the vertical axis during a scan. In this method, a mathematical model describing the ribs-bounded contour was created and the problem of approximation has been solved by finding the optimal parameters of the mathematical model using least-squares-type objective function. The local search has been per-formed using local descent by quasi-Newton methods. The benefits of analytical derivatives of the function are disclosed in the paper.

Global Results Synthesis

2020 ◽  
pp. 165-175
Keyword(s):  
Linear Programming ◽  
Simulated Annealing ◽  
Tabu Search ◽  
Local Search ◽  
Constraint Programming ◽  
Cpu Time ◽  
Exact Approach ◽  
First Results ◽  
Programming Techniques ◽  
Portfolio Design

This chapter provides a global synthesis of the realized results by applying exact and approximate approaches on the portfolio design (PD) problem. The authors introduce an experimental analysis of best approaches based on linear programming and constraint programming techniques, according to the CPU time. Next, a global experiment synthesis of the best approximate approaches based on Simulated Annealing, IDWalk, Tabu Search, GWW, and VNS is realized according to the number of success and the CPU time. First results show that constraint programming with breaking all the detected symmetries is the best as an exact approach, VNS combined with simulated annealing is effective on non-trivial instances of the problem, and simulated annealing is the most effective as a simple local search.

Simple and Population Local Search Approaches for Portfolio Design Problem

2020 ◽  
pp. 119-147
Keyword(s):  
Local Search ◽  
Design Problem ◽  
Practical Problem ◽  
Optimization Technique ◽  
Quadratic Program ◽  
Integer Programs ◽  
Evaluation Functions ◽  
Search Optimization ◽  
Quadratic Integer ◽  
Portfolio Design

This chapter introduces a local search optimization technique for solving efficiently a ðnancial portfolio design problem that consists of assigning assets to portfolios, allowing a compromise between maximizing gains, and minimizing losses. This practical problem appears usually in ðnancial engineering, such as in the design of CDO-squared portfolios. This problem has been modeled by Flener et al., who proposed an exact method to solve it. It can be formulated as a quadratic program on the (0,1) domain. It is well known that exact solving approaches on difficult and large instances of quadratic integer programs are known inefficient. That is why the authors have adopted local search methods, namely simple local search and population local search. They propose neighborhood and evaluation functions specialized on this problem. To boost the local search process, they propose also a greedy algorithm to start the search with an optimized initial configuration. Experimental results on non-trivial instances of the problem show the effectiveness of the incomplete approach.

Resolution Methods

2020 ◽  
pp. 29-60
Keyword(s):  
Linear Programming ◽  
Simulated Annealing ◽  
Tabu Search ◽  
Symmetry Breaking ◽  
Constraint Programming ◽  
Design Problem ◽  
Variable Neighborhood Search ◽  
Neighborhood Search ◽  
Performance Profiles ◽  
Portfolio Design

The aim of this chapter is to introduce the different notions of the techniques used to solve the portfolio design problem. These techniques can be divided into two exact (or complete) methods and approached (or incomplete) methods. In the first part, the authors provide the exact approaches, namely linear programming and constraint programming, as well as the techniques of symmetry breaking, the modeling notions, and the different solving algorithms. The second part concerns approached methods, namely Simulated Annealing, IDWalk, Tabu Search, GWW, and Variable Neighborhood Search, including the techniques of studying the performance profiles of a method.

scholarly journals The Optimization Algorithm of the Forced Current Cathodic Protection Base on Simulated Annealing

Algorithms ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 83 ◽  
Author(s):  
Song ◽  
Wang ◽  
Qin ◽  
Wang ◽  
Liu
Keyword(s):  
Mathematical Model ◽  
Simulated Annealing ◽  
Cathodic Protection ◽  
Optimization Algorithm ◽  
Simulated Annealing Algorithm ◽  
Element Model ◽  
Parameter Design ◽  
Variable Metric ◽  
Grounding Grid ◽  
The Mathematical Model

The grounding grid of a substation is important for the safety of substation equipment. Especially to address the difficulty of parameter design in the auxiliary anode system of a grounding grid, an algorithm is proposed that is an optimization algorithm for the auxiliary anode system of a grounding grid based on improved simulated annealing. The mathematical model of the auxiliary anode system is inferred from the mathematical model of cathodic protection. On that basis, the parameters of the finite element model are optimized with the improved simulated annealing algorithm, thereby the auxiliary anode system of a grounding grid with optimized parameters is structured. Then the algorithm is proven as valid through experiments. The precision of the optimized parameters is improved by about 1.55% with respect to the Variable Metric Method and the Genetic Algorithm, so it can provide a basis for parameter design in the auxiliary anode system of a grounding grid.

Linear Integer Programming Techniques for Portfolio Design Problem

2020 ◽  
pp. 80-102
Keyword(s):  
Linear Programming ◽  
Integer Programming ◽  
Design Problem ◽  
Linear Models ◽  
Linear Constraint ◽  
Quadratic Model ◽  
Linear Integer Programming ◽  
Constraint Systems ◽  
Programming Techniques ◽  
Portfolio Design

This chapter introduces Integer Linear Programming (ILP) approaches for solving efficiently a ðnancial portfolio design problem. The authors proposed a matricial model in Chapter 3, which is a mathematical quadratic model. A linearization step is considered necessary to apply linear programming techniques. The corresponding matricial model shows clearly that the problem is strongly symmetrical. The row and column symmetries are easily handled by adding a negligible number of new constraints. The authors propose two linear models, which are given in detail and proven. These models represent the problem as linear constraint systems with 0-1 variables, which will be implemented in ILP solver. Experimental results in non-trivial instances of portfolio design problem are given.

Research on the Vehicle Scheduling Problem in Wartime Spare Parts Distribution

2013 ◽  
Vol 421 ◽  
pp. 883-888
Author(s):  
Xue Jun Chen ◽  
Fang Geng Zhao ◽  
Xiao Yan Shi
Keyword(s):  
Mathematical Model ◽  
Local Search ◽  
Spare Parts ◽  
Vehicle Scheduling ◽  
Transition Rule ◽  
Scheduling Problem ◽  
Ant Colony Optimization Algorithm ◽  
Search Heuristics ◽  
Benchmark Instances ◽  
The Mathematical Model

The distribution-based logistics support is an important way to improve the efficiency of spare parts supply, and the scientific scheduling of vehicle is crucial to achieve this target. The mathematical model of the vehicle scheduling problem in wartime spare parts distribution was formulated, and an improved ant colony optimization algorithm was utilized to solve it. In our algorithm, the transition rule was improved, and the local search heuristics were integrated into the algorithm. The VRPTW benchmark instances were revised and solved under different parameter settings, and the experimental results showed that our improved transition rule can significantly enhance the algorithm's performance.

Portfolio Design Models

2020 ◽  
pp. 61-79
Keyword(s):  
General Model ◽  
Financial Engineering ◽  
Design Problem ◽  
Practical Problem ◽  
Diversification Rate ◽  
Design Models ◽  
Financial Portfolio ◽  
Financial Portfolios ◽  
Risk Rate ◽  
Portfolio Design

This chapter applies different models to the financial portfolio design problem that affect assignment of assets to portfolios subject to a compromise between maximizing gains and minimizing losses. This practical problem appears in financial engineering, such as in the design of a CDO Squared portfolio. The aim of the authors is to propose and to solve a general model corresponding to the problem, within well classified assets. The authors express the diversification problem through a panoply of models such as the set model, matricial model, and MiniZinc model. These models represent an optimized problem of building efficient financial portfolios by maximizing the diversification rate. As long as the diversification rate is increased, the profit is increased, and the risk rate is decreased.

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