On the use of two reference points in decomposition based multiobjective evolutionary algorithms

Decomposition based multiobjective evolutionary algorithms approximate the Pareto front of a multiobjective optimization problem by optimizing a set of subproblems in a collaborative manner. Often, each subproblem is associated with a direction vector and a reference point. The settings of these parameters have a very critical impact on convergence and diversity of the algorithm. Some work has been done to study how to set and adjust direction vectors to enhance algorithm performance for particular problems. In contrast, little effort has been made to study how to use reference points for controlling diversity in decomposition based algorithms. In this paper, we first study the impact of the reference point setting on selection in decomposition based algorithms. To balance the diversity and convergence, a new variant of the multiobjective evolutionary algorithm based on decomposition with both the ideal point and the nadir point is then proposed. This new variant also employs an improved global replacement strategy for performance enhancement. Comparison of our proposed algorithm with some other state-of-the-art algorithms is conducted on a set of multiobjective test problems. Experimental results show that our proposed algorithm is promising

A convergence and diversity guided leader selection strategy for many-objective particle swarm optimization

Recently, particle swarm optimizer (PSO) is extended to solve many-objective optimization problems (MaOPs) and becomes a hot research topic in the field of evolutionary computation. Particularly, the leader particle selection (LPS) and the search direction used in a velocity update strategy are two crucial factors in PSOs. However, the LPS strategies for most existing PSOs are not so efficient in high-dimensional objective space, mainly due to the lack of convergence pressure or loss of diversity. In order to address these two issues and improve the performance of PSO in high-dimensional objective space, this paper proposes a convergence and diversity guided leader selection strategy for PSO, denoted as CDLS, in which different leader particles are adaptively selected for each particle based on its corresponding situation of convergence and diversity. In this way, a good tradeoff between the convergence and diversity can be achieved by CDLS. To verify the effectiveness of CDLS, it is embedded into the PSO search process of three well-known PSOs. Furthermore, a new variant of PSO combining with the CDLS strategy, namely PSO/CDLS, is also presented. The experimental results validate the superiority of our proposed CDLS strategy and the effectiveness of PSO/CDLS, when solving numerous MaOPs with regular and irregular Pareto fronts (PFs)

Portfolio Optimization Using Evolutionary Algorithms

Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced AnalyticsPortfolio optimization is a widely studied field in modern finance. It involves finding the optimal balance between two contradictory objectives, the risk and the return. As the number of assets rises, the complexity in portfolios increases considerably, making it a computational challenge. This report explores the application of the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) and Genetic Algorithm (GA) in the field of portfolio optimization. MOEA/D and GA have proven to be effective at finding portfolios. However, it remains unclear how they perform when compared to traditional approaches used in finance. To achieve this, a framework for portfolio optimization is proposed, using MOEA/D, and GA separately as optimization algorithms and Capital Asset Pricing Model (CAPM) and Mean-Variance Model as methods to evaluate portfolios. The proposed framework is able to produce weighted portfolios successfully. These generated portfolios were evaluated using a simulation with subsequent (unseen) prices of the assets included in the portfolio. The simulation was compared with well known portfolios in the same market and other market benchmarks (Security Market Line and Market Portfolio). The results obtained in this investigation exceeded expectation by creating portfolios that perform better than the market. CAPM and Mean-Variance Model, although they fail to model all the variables that affect the stock market, provide a simple valuation for assets and portfolios. MOEA/D using Differential Evolution operators and the CAPM model produced the best portfolios in this research. Work can still be done to accommodate more variables that can affect markets and portfolios, such as taxes, investment horizon and costs for transactions

A competitive co-evolutionary approach for the multi-objective evolutionary algorithms

In multi-objective evolutionary algorithms (MOEAs), convergence and diversity are two basic issues and keeping a balance between them plays a vital role. There are several studies that have attempted to address this problem, but this is still an open challenge. It is thus the purpose of this research to develop a dual-population competitive co-evolutionary approach to improving the balance between convergence and diversity. We utilize two populations to solve separate tasks. The first population uses Pareto-based ranking scheme to achieve better convergence, and the second one tries to guarantee population diversity via the use of a decomposition-based method. Next, by operating a competitive mechanism to combine the two populations, we create a new one with a view to having both characteristics (i.e. convergence and diversity). The proposed method’s performance is measured by the renowned benchmarks of multi-objective optimization problems (MOPs) using the hypervolume (HV) and the inverted generational distance (IGD) metrics. Experimental results show that the proposed method outperforms cutting-edge coevolutionary algorithms with a robust performance