Differential Evolution for Multiobjective Portfolio Optimization

Financial portfolio optimization is a challenging problem. First, the problem is multiobjective (i.e.: minimize risk and maximize profit) and the objective functions are often multimodal and non smooth (e.g.: value at risk). Second, managers have often to face real-world constraints, which are typically non-linear. Hence, conventional optimization techniques, such as quadratic programming, cannot be used. Stochastic search heuristic can be an attractive alternative. In this paper, we propose a new multiobjective algorithm for portfolio optimization: DEMPO - Differential Evolution for Multiobjective Portfolio Optimization. The main advantage of this new algorithm is its generality, i.e., the ability to tackle a portfolio optimization task as it is, without simplifications. Our empirical results show the capability of our approach of obtaining highly accurate results in very reasonable runtime, in comparison with quadratic programming and another state-of-art search heuristic, the so-called NSGA II.Portfolio Optimization, Multiobjective, Real-world Constraints, Value at Risk, Expected Shortfall, Differential Evolution

A Feature-Based Analysis on the Impact of Set of Constraints for e-Constrained Differential Evolution

Different types of evolutionary algorithms have been developed for constrained continuous optimization. We carry out a feature-based analysis of evolved constrained continuous optimization instances to understand the characteristics of constraints that make problems hard for evolutionary algorithm. In our study, we examine how various sets of constraints can influence the behaviour of e-Constrained Differential Evolution. Investigating the evolved instances, we obtain knowledge of what type of constraints and their features make a problem difficult for the examined algorithm.Comment: 17 Page

Evolutionary Dynamic Optimization Laboratory: A MATLAB Optimization Platform for Education and Experimentation in Dynamic Environments

Many real-world optimization problems possess dynamic characteristics. Evolutionary dynamic optimization algorithms (EDOAs) aim to tackle the challenges associated with dynamic optimization problems. Looking at the existing works, the results reported for a given EDOA can sometimes be considerably different. This issue occurs because the source codes of many EDOAs, which are usually very complex algorithms, have not been made publicly available. Indeed, the complexity of components and mechanisms used in many EDOAs makes their re-implementation error-prone. In this paper, to assist researchers in performing experiments and comparing their algorithms against several EDOAs, we develop an open-source MATLAB platform for EDOAs, called Evolutionary Dynamic Optimization LABoratory (EDOLAB). This platform also contains an education module that can be used for educational purposes. In the education module, the user can observe a) a 2-dimensional problem space and how its morphology changes after each environmental change, b) the behaviors of individuals over time, and c) how the EDOA reacts to environmental changes and tries to track the moving optimum. In addition to being useful for research and education purposes, EDOLAB can also be used by practitioners to solve their real-world problems. The current version of EDOLAB includes 25 EDOAs and three fully-parametric benchmark generators. The MATLAB source code for EDOLAB is publicly available and can be accessed from [https://github.com/EDOLAB-platform/EDOLAB-MATLAB].Comment: This work was submitted to ACM Transactions on Mathematical Software on December 7, 202

Lightning search algorithm: a comprehensive survey

The lightning search algorithm (LSA) is a novel meta-heuristic optimization method, which is proposed in 2015 to solve constraint optimization problems. This paper presents a comprehensive survey of the applications, variants, and results of the so-called LSA. In LSA, the best-obtained solution is defined to improve the effectiveness of the fitness function through the optimization process by finding the minimum or maximum costs to solve a specific problem. Meta-heuristics have grown the focus of researches in the optimization domain, because of the foundation of decision-making and assessment in addressing various optimization problems. A review of LSA variants is displayed in this paper, such as the basic, binary, modification, hybridization, improved, and others. Moreover, the classes of the LSA’s applications include the benchmark functions, machine learning applications, network applications, engineering applications, and others. Finally, the results of the LSA is compared with other optimization algorithms published in the literature. Presenting a survey and reviewing the LSA applications is the chief aim of this survey paper

Static and Dynamic Multimodal Optimization by Improved Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations

The covariance matrix self-adaptation evolution strategy with repelling subpopulations (RS-CMSA-ES) is one of the most successful multimodal optimization (MMO) methods currently available. However, some of its components may become inefficient in certain situations. This study introduces the second variant of this method, called RS-CMSA-ESII. It improves the adaptation schemes for the normalized taboo distances of the archived solutions and the covariance matrix of the subpopulation, the termination criteria for the subpopulations, and the way in which the infeasible solutions are treated. It also improves the time complexity of RS-CMSA-ES by updating the initialization procedure of a subpopulation and developing a more accurate metric for determining critical taboo regions. The effects of these modifications are illustrated by designing controlled numerical simulations. RS-CMSA-ESII is then compared with the most successful and recent niching methods for MMO on a widely adopted test suite. The results obtained reveal the superiority of RS-CMSA-ESII over these methods, including the winners of the competition on niching methods for MMO in previous years. Besides, this study extends RS-CMSA-ESII to dynamic MMO and compares it with a few recently proposed methods on the modified moving peak benchmark functions

Integrating continuous differential evolution with discrete local search for meander line RFID antenna design

The automated design of meander line RFID antennas is a discrete self-avoiding walk(SAW) problem for which efficiency is to be maximized while resonant frequency is to beminimized. This work presents a novel exploration of how discrete local search may beincorporated into a continuous solver such as differential evolution (DE). A prior DE algorithmfor this problem that incorporates an adaptive solution encoding and a bias favoringantennas with low resonant frequency is extended by the addition of the backbite localsearch operator and a variety of schemes for reintroducing modified designs into the DEpopulation. The algorithm is extremely competitive with an existing ACO approach and thetechnique is transferable to other SAW problems and other continuous solvers. The findingsindicate that careful reintegration of discrete local search results into the continuous populationis necessary for effective performance

A multi-tier adaptive grid algorithm for the evolutionary multi-objective optimisation of complex problems

The multi-tier Covariance Matrix Adaptation Pareto Archived Evolution Strategy (m-CMA-PAES) is an evolutionary multi-objective optimisation (EMO) algorithm for real-valued optimisation problems. It combines a non-elitist adaptive grid based selection scheme with the efficient strategy parameter adaptation of the elitist Covariance Matrix Adaptation Evolution Strategy (CMA-ES). In the original CMA-PAES, a solution is selected as a parent for the next population using an elitist adaptive grid archiving (AGA) scheme derived from the Pareto Archived Evolution Strategy (PAES). In contrast, a multi-tiered AGA scheme to populate the archive using an adaptive grid for each level of non-dominated solutions in the considered candidate population is proposed. The new selection scheme improves the performance of the CMA-PAES as shown using benchmark functions from the ZDT, CEC09, and DTLZ test suite in a comparison against the (μ+λ) μ λ Multi-Objective Covariance Matrix Adaptation Evolution Strategy (MO-CMA-ES). In comparison with MO-CMA-ES, the experimental results show that the proposed algorithm offers up to a 69 % performance increase according to the Inverse Generational Distance (IGD) metric

Surrogate-based maximization of belief function for robust design optimization

This paper proposes an approach based on surrogate models to reduce the computational cost of evidence-based robust design optimization. Evidence Theory provides two quantitative measures, Belief and Plausibility, that defines the lower and upper probability that a given proposition is true under uncertainty. The maximization of the Belief is of great interest to the designers because it provides the design solution such that a given proposition on the system budgets is always true, given the current evidence on the set of uncertain design parameters. The paper introduces a novel min-max multi-objective optimization algorithm to maximize the Belief in multiple conicting propositions. Then an approach based on surrogate models is presented to substantially reduce the computational cost associated with the optimization of the design solutions that maximize the Belief in the given proposition. A simple test case of spacecraft system design is presented will illustrate how to apply the proposed approach