scholarly journals Solving Portfolio Optimization Problems Using MOEA/D and Lévy Flight

2020 ◽  
Vol 12 (03n04) ◽  
pp. 2050005
Author(s):  
Yifan He ◽  
Claus Aranha
Keyword(s):  
Evolutionary Algorithms ◽  
Portfolio Optimization ◽  
Optimization Problems ◽  
Statistical Test ◽  
Financial Assets ◽  
Lévy Flight ◽  
Nsga Ii ◽  
Levy Flight ◽  
Trade Off ◽  
Multi Objective

Portfolio optimization is a financial task which requires the allocation of capital on a set of financial assets to achieve a better trade-off between return and risk. To solve this problem, recent studies applied multi-objective evolutionary algorithms (MOEAs) for its natural bi-objective structure. This paper presents a method injecting a distribution-based mutation method named Lévy Flight into a decomposition based MOEA named MOEA/D. The proposed algorithm is compared with three MOEA/D-like algorithms, NSGA-II, and other distribution-based mutation methods on five portfolio optimization benchmarks sized from 31 to 225 in OR library without constraints, assessing with six metrics. Numerical results and statistical test indicate that this method can outperform comparison methods in most cases. We analyze how Lévy Flight contributes to this improvement by promoting global search early in the optimization. We explain this improvement by considering the interaction between mutation method and the property of the problem. We additionally show that our method perform well with a round-lot constraint on Nikkei.

scholarly journals Mobile Robot Path Planning with a Non-Dominated Sorting Genetic Algorithm

2018 ◽  
Vol 8 (11) ◽  
pp. 2253 ◽  
Author(s):  
Yang Xue
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Path Planning ◽  
Optimization Problems ◽  
Planning Problem ◽  
Nsga Ii ◽  
Multi Objective ◽  
Mutation Operators ◽  
Comparison Results ◽  
Path Planning Problem

In many areas, such as mobile robots, video games and driverless vehicles, path planning has always attracted researchers’ attention. In the field of mobile robotics, the path planning problem is to plan one or more viable paths to the target location from the starting position within a given obstacle space. Evolutionary algorithms can effectively solve this problem. The non-dominated sorting genetic algorithm (NSGA-II) is currently recognized as one of the evolutionary algorithms with robust optimization capabilities and has solved various optimization problems. In this paper, NSGA-II is adopted to solve multi-objective path planning problems. Three objectives are introduced. Besides the usual selection, crossover and mutation operators, some practical operators are applied. Moreover, the parameters involved in the algorithm are studied. Additionally, another evolutionary algorithm and quality metrics are employed for examination. Comparison results demonstrate that non-dominated solutions obtained by the algorithm have good characteristics. Subsequently, the path corresponding to the knee point of non-dominated solutions is shown. The path is shorter, safer and smoother. This path can be adopted in the later decision-making process. Finally, the above research shows that the revised algorithm can effectively solve the multi-objective path planning problem in static environments.

Evolutionary Algorithms for Multi-Objective Scheduling in a Hybrid Manufacturing System

2018 ◽  
pp. 162-187 ◽  
Author(s):  
Ömer Faruk Yılmaz ◽  
Mehmet Bülent Durmuşoğlu
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Manufacturing System ◽  
Optimization Problems ◽  
Multiple Objectives ◽  
Hybrid Manufacturing ◽  
Nsga Ii ◽  
Multi Objective ◽  
Comprehensive Information ◽  
Manufacturing Environments

Problems encountered in real manufacturing environments are complex to solve optimally, and they are expected to fulfill multiple objectives. Such problems are called multi-objective optimization problems(MOPs) involving conflicting objectives. The use of multi-objective evolutionary algorithms (MOEAs) to find solutions for these problems has increased over the last decade. It has been shown that MOEAs are well-suited to search solutions for MOPs having multiple objectives. In this chapter, in addition to comprehensive information, two different MOEAs are implemented to solve a MOP for comparison purposes. One of these algorithms is the non-dominated sorting genetic algorithm (NSGA-II), the effectiveness of which has already been demonstrated in the literature for solving complex MOPs. The other algorithm is fast Pareto genetic algorithm (FastPGA), which has population regulation operator to adapt the population size. These two algorithms are used to solve a scheduling problem in a Hybrid Manufacturing System (HMS). Computational results indicate that FastPGA outperforms NSGA-II.

scholarly journals A New Hybrid Evolutionary Algorithm for the Treatment of Equality Constrained MOPs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 7 ◽  
Author(s):  
Oliver Cuate ◽  
Antonin Ponsich ◽  
Lourdes Uribe ◽  
Saúl Zapotecas-Martínez ◽  
Adriana Lara ◽  
...  
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Continuation Method ◽  
Finite Size ◽  
Equality Constraints ◽  
Evolutionary Strategies ◽  
Minor Role ◽  
Nsga Ii ◽  
Adequate Treatment ◽  
Multi Objective

Multi-objective evolutionary algorithms are widely used by researchers and practitioners to solve multi-objective optimization problems (MOPs), since they require minimal assumptions and are capable of computing a finite size approximation of the entire solution set in one run of the algorithm. So far, however, the adequate treatment of equality constraints has played a minor role. Equality constraints are particular since they typically reduce the dimension of the search space, which causes problems for stochastic search algorithms such as evolutionary strategies. In this paper, we show that multi-objective evolutionary algorithms hybridized with continuation-like techniques lead to fast and reliable numerical solvers. For this, we first propose three new problems with different characteristics that are indeed hard to solve by evolutionary algorithms. Next, we develop a variant of NSGA-II with a continuation method. We present numerical results on several equality-constrained MOPs to show that the resulting method is highly competitive to state-of-the-art evolutionary algorithms.

scholarly journals Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters

2021 ◽  
Vol 26 (2) ◽  
pp. 36
Author(s):  
Alejandro Estrada-Padilla ◽  
Daniela Lopez-Garcia ◽  
Claudia Gómez-Santillán ◽  
Héctor Joaquín Fraire-Huacuja ◽  
Laura Cruz-Reyes ◽  
...  
Keyword(s):  
Steady State ◽  
Portfolio Optimization ◽  
Optimization Problem ◽  
Solution Process ◽  
Density Estimator ◽  
Nsga Ii ◽  
Spatial Spread ◽  
Multi Objective ◽  
Significant Difference ◽  
Portfolio Optimization Problem

A common issue in the Multi-Objective Portfolio Optimization Problem (MOPOP) is the presence of uncertainty that affects individual decisions, e.g., variations on resources or benefits of projects. Fuzzy numbers are successful in dealing with imprecise numerical quantities, and they found numerous applications in optimization. However, so far, they have not been used to tackle uncertainty in MOPOP. Hence, this work proposes to tackle MOPOP’s uncertainty with a new optimization model based on fuzzy trapezoidal parameters. Additionally, it proposes three novel steady-state algorithms as the model’s solution process. One approach integrates the Fuzzy Adaptive Multi-objective Evolutionary (FAME) methodology; the other two apply the Non-Dominated Genetic Algorithm (NSGA-II) methodology. One steady-state algorithm uses the Spatial Spread Deviation as a density estimator to improve the Pareto fronts’ distribution. This research work’s final contribution is developing a new defuzzification mapping that allows measuring algorithms’ performance using widely known metrics. The results show a significant difference in performance favoring the proposed steady-state algorithm based on the FAME methodology.

scholarly journals Elite Exploitation: A Combination of Mathematical Concept and EMO Approach for Multi-Objective Decision Making

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 136
Author(s):  
Wenxiao Li ◽  
Yushui Geng ◽  
Jing Zhao ◽  
Kang Zhang ◽  
Jianxin Liu
Keyword(s):  
Decision Making ◽  
Optimization Problems ◽  
Hybrid Genetic Algorithm ◽  
Decision Makers ◽  
Superior Performance ◽  
Test Problems ◽  
Mathematical Function ◽  
Hyperbolic Tangent ◽  
Nsga Ii ◽  
Multi Objective

This paper explores the combination of a classic mathematical function named “hyperbolic tangent” with a metaheuristic algorithm, and proposes a novel hybrid genetic algorithm called NSGA-II-BnF for multi-objective decision making. Recently, many metaheuristic evolutionary algorithms have been proposed for tackling multi-objective optimization problems (MOPs). These algorithms demonstrate excellent capabilities and offer available solutions to decision makers. However, their convergence performance may be challenged by some MOPs with elaborate Pareto fronts such as CFs, WFGs, and UFs, primarily due to the neglect of diversity. We solve this problem by proposing an algorithm with elite exploitation strategy, which contains two parts: first, we design a biased elite allocation strategy, which allocates computation resources appropriately to elites of the population by crowding distance-based roulette. Second, we propose a self-guided fast individual exploitation approach, which guides elites to generate neighbors by a symmetry exploitation operator, which is based on mathematical hyperbolic tangent function. Furthermore, we designed a mechanism to emphasize the algorithm’s applicability, which allows decision makers to adjust the exploitation intensity with their preferences. We compare our proposed NSGA-II-BnF with four other improved versions of NSGA-II (NSGA-IIconflict, rNSGA-II, RPDNSGA-II, and NSGA-II-SDR) and four competitive and widely-used algorithms (MOEA/D-DE, dMOPSO, SPEA-II, and SMPSO) on 36 test problems (DTLZ1–DTLZ7, WGF1–WFG9, UF1–UF10, and CF1–CF10), and measured using two widely used indicators—inverted generational distance (IGD) and hypervolume (HV). Experiment results demonstrate that NSGA-II-BnF exhibits superior performance to most of the algorithms on all test problems.

Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

2014 ◽  
Vol 984-985 ◽  
pp. 419-424
Author(s):  
P. Sabarinath ◽  
M.R. Thansekhar ◽  
R. Saravanan
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Nsga Ii ◽  
Multi Objective ◽  
Total Displacement ◽  
Design Variables ◽  
Conflicting Objectives

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

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