### Citation:

Mourtas, S. D., & Katsikis, V. N. (2021). V-Shaped BAS: Applications on Large Portfolios Selection Problem. Computational Economics. presented at the 2021. Copy at http://www.tinyurl.com/yzmszbcl

Mourtas, S. D., & Katsikis, V. N. (2021). V-Shaped BAS: Applications on Large Portfolios Selection Problem. Computational Economics. presented at the 2021. Copy at http://www.tinyurl.com/yzmszbcl

**National and Kapodistrian University of Athens**

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Katsikis, V. N., Mourtas, S. D., Stanimirović, P. S., Li, S., & Cao, X. (2022). Time-varying mean–variance portfolio selection problem solving via LVI-PDNN. Computers and Operations Research, 138, 105582. presented at the 2022. Publisher's VersionAbstract

It is widely acclaimed that the Markowitz mean–variance portfolio selection is a very important investment strategy. One approach to solving the static mean–variance portfolio selection (MVPS) problem is based on the usage of quadratic programming (QP) methods. In this article, we define and study the time-varying mean–variance portfolio selection (TV-MVPS) problem both in the cases of a fixed target portfolio’s expected return and for all possible portfolio’s expected returns as a time-varying quadratic programming (TVQP) problem. The TV-MVPS also comprises the properties of a moving average. These properties make the TV-MVPS an even greater analysis tool suitable to evaluate investments and identify trading opportunities across a continuous-time period. Using an originally developed linear-variational-inequality primal–dual neural network (LVI-PDNN), we also provide an online solution to the static QP problem. To the best of our knowledge, this is an innovative approach that incorporates robust neural network techniques to provide an online, thus more realistic, solution to the TV-MVPS problem. In this way, we present an online solution to a time-varying financial problem while eliminating static method limitations. It has been shown that when applied simultaneously to TVQP problems subject to equality, inequality and boundary constraints, the LVI-PDNN approaches the theoretical solution. Our approach is also verified by numerical experiments and computer simulations as an excellent alternative to conventional MATLAB methods.

Khan, A. T., Cao, X., Li, S., Katsikis, V. N., Brajevic, I., & Stanimirovic, P. S. (2021). Fraud detection in publicly traded U.S firms using Beetle Antennae Search: A machine learning approach. Expert Systems with Applications. presented at the 2021. Publisher's VersionAbstract

In this paper, we present a fraud detection framework for publicly traded firms using an optimization approach integrated with a meta-heuristic algorithm known as Beetle Antennae Search (BAS). Existing techniques include human resources, like financial experts and audit teams, to determine the ambiguities or financial frauds in the companies based on financial and non-financial ratios. It is a laborious task, time-consuming, and prone to errors. We designed an optimization problem to minimize the loss function based on a non-linear decision function combined with the maximization of recall (Sensitivity and Specificity). We solved the optimization problem iteratively using the BAS. It is a nature-inspired algorithm and mimics the beetle’s food-searching nature. It includes a single searching particle to find an optimal solution to the optimization problem in n-dimensional space. We used a benchmark dataset collected from SEC’s Accounting and Auditing Enforcement Releases (AAERs) for the simulation. It includes 28 raw financial variables and the data collected between 1991-2008. For the comparison, we evaluated the performance of BAS with the recently proposed approach using RUSBoost. We also compared it with some additional algorithms, i.e., Logit and SVM-FK. The results showed that BAS is comparable with these algorithms and outperformed them in time consumption.

Katsikis, V. N., Stanimirovic, P. S., Mourtas, S. D., Xiao, L., Karabasevic, D., & Stanujkic, D. (2021). Zeroing Neural Network with Fuzzy Parameter for Computing Pseudoinverse of Arbitrary Matrix. IEEE Transactions on Fuzzy Systems. Publisher's Version

Simos, T. E., Katsikis, V. N., & Mourtas, S. D. (2021). Multi-input bio-inspired weights and structure determination neuronet with applications in European Central Bank publications. Mathematics and Computers in Simulation. presented at the 2021. Publisher's VersionAbstract

This paper introduces a 3-layer feed-forward neuronet model, trained by novel beetle antennae search weights-and-structure-determination (BASWASD) algorithm. On the one hand, the beetle antennae search (BAS) algorithm is a memetic meta-heuristic optimization algorithm capable of solving combinatorial optimization problems. On the other hand, neuronets trained by a weights-and-structure-determination (WASD) algorithm are known to resolve the shortcomings of traditional back-propagation neuronets, including slow speed of training and local minimum. Combining the BAS and WASD algorithms, a novel BASWASD algorithm is created for training neuronets, and a multi-input BASWASD neuronet (MI-BASWASDN) model is introduced. Using a power sigmoid activation function and while managing the model fitting and validation, the BASWASD algorithm finds the optimal weights and structure of the MI-BASWASDN. Four financial datasets, taken from the European Central Bank publications, validate and demonstrate the MI-BASWASDN model’s outstanding learning and predicting performance. Also included is a comparison of the MI-BASWASDN model to three other well-performing neural network models, as well as a MATLAB kit that is publicly available on GitHub to promote and support this research.

Simos, T. E., Katsikis, V. N., & Mourtas, S. D. (2021). A fuzzy WASD neuronet with application in breast cancer prediction. Neural Computing and Applications. presented at the 2021. Publisher's VersionAbstract

Cancer is one of the world’s leading causes of human mortality, and the most prevalent type is breast cancer. However, when diagnosed early, breast cancer may be treated. In this paper, a 5-layer feed-forward neuronet model, trained by a novel fuzzy WASD (weights-and-structure-determination) algorithm, called FUZWASD, is introduced and employed to predict whether the breast cancer is benign or malignant. In general, WASD-trained neuronets are known to overcome the limitations of traditional back-propagation neuronets, including slow training speed and local minimum; however, multi-input WASD-trained neuronets with no dimension explosion weakness are few. In this work, a novel FUZWASD algorithm for training neuronets is modeled by embedding a fuzzy logic controller (FLC) in a WASD algorithm, and a multi-input FUZWASD neuronet (MI-FUZWASDN) model for classification problems with no dimension explosion weakness is proposed. The FUZWASD algorithm uses a FLC to map the input data into a specific interval that enhances the accuracy of the weights-direct-determination (WDD) method. In this way, the FUZWASD algorithm detects the optimal weights and structure of the MI-FUZWASDN using a power softplus activation function and while handling the model fitting and validation. Applications on two diagnostic breast cancer datasets validate and demonstrate the MI-FUZWASDN model’s exceptional learning and predicting performance. In addition, for the intrigued user, we have created a MATLAB kit, which is freely accessible via GitHub, to promote and support the results of this work.

Mourtas, S. D., & Katsikis, V. N. (2021). V-Shaped BAS: Applications on Large Portfolios Selection Problem. Computational Economics. presented at the 2021. Publisher's VersionAbstract

The beetle antennae search (BAS) algorithm is a memetic meta-heuristic optimization algorithm capable of solving combinatorial optimization problems. In this paper, the binary version of BAS (BBAS) is modified by adding a V-shaped transfer function. In this way, we introduce the V-shaped transfer function-based binary BAS (VSBAS) algorithm, which is a more effective and efficient version of BBAS in the case of large input data. Applications using real-world data sets on a binary Markowitz-based portfolio selection (BMPS) problem validate the excellent performance of VSBAS on large input data and demonstrate that it is a marvelous alternative against other ordinary memetic meta-heuristic optimization algorithms. Note that, because the meta-heuristic algorithms compared in this paper are directly applicable only to unconstrained optimization, the penalty function method was used to keep their solutions in the feasible district. In order to support and promote the findings of this work, we have constructed a complete MATLAB package for the interested user, which is freely available through GitHub.

Simos, T. E., Mourtas, S. D., & Katsikis, V. N. (2021). Time-varying Black–Litterman portfolio optimization using a bio-inspired approach and neuronets. Applied Soft Computing, 112, 107767. WebsiteAbstract

The Black–Litterman model is a very important analytical tool for active portfolio management because it allows investment analysts to incorporate investor’s views into market equilibrium returns. In this paper, we define and study the time-varying Black–Litterman portfolio optimization under nonlinear constraints (TV-BLPONC) problem as a nonlinear programming (NLP) problem. More precisely, the nonlinear constraints refer to transaction costs and cardinality constraints. Furthermore, a speedy weights-and-structure-determination (WASD) algorithm for the power-activation feed-forward neuronet (PFN) is presented to solve time-series modeling and forecasting problems. Inhere, the investor’s views in the TV-BLPONC problem are considered as a forecasting problem and, thus, they are produced by the WASD-based PFN. In addition, using the beetle antennae search (BAS) algorithm a computational method is introduced to solve the TV-BLPONC problem. For all we know, this is an innovative approach that integrates modern neural network and meta-heuristic optimization methods to provide a solution to the TV-BLPONC problem in large portfolios. Our approach is tested on portfolios of up to 90 stocks with real-world data, and the results show that it is more than 30 times faster than other methods. Our technique’s speed and precision are verified in this way, showing that it is an outstanding alternative to ordinary methods. In order to support and promote the findings of this work, we have constructed two complete MATLAB packages for the interested user, which are freely available through GitHub.

Mosić, D., Stanimirović, P. S., & Katsikis, V. N. (2021). Weighted composite outer inverses. Applied Mathematics and Computation, 411, 126493. WebsiteAbstract

In order to extend and unify the definitions of W-weighted DMP, W-weighted MPD, W-weighted CMP and composite outer inverses, we present the weighted composite outer inverses. Precisely, the notions of MNOMP, MPMNO and MPMNOMP inverses are introduced as appropriate expressions involving the (M,N)-weighted (B,C)-inverse and Moore–Penrose inverse. Basic properties and a number of characterizations for the MNOMP, MPMNO or MPMNOMP inverse are discovered. Various representations and characterizations of weighted composite outer inverses are studied. General solutions for certain systems of linear equations are given in terms of weighted composite outer inverses. Numerical examples are presented on randomly generated matrices of various orders.

Stanujkić, D., Karabašević, D., Popović, G., Stanimirović, P. S., Saračević, M., Smarandache, F., Katsikis, V. N., et al. (2021). A New Grey Approach for Using SWARA and PIPRECIA Methods in a Group Decision-Making Environment. Mathematics, 9. Publisher's VersionAbstract

The environment in which the decision-making process takes place is often characterized by uncertainty and vagueness and, because of that, sometimes it is very hard to express the criteria weights with crisp numbers. Therefore, the application of the Grey System Theory, i.e., grey numbers, in this case, is very convenient when it comes to determination of the criteria weights with partially known information. Besides, the criteria weights have a significant role in the multiple criteria decision-making process. Many ordinary multiple criteria decision-making methods are adapted for using grey numbers, and this is the case in this article as well. A new grey extension of the certain multiple criteria decision-making methods for the determination of the criteria weights is proposed. Therefore, the article aims to propose a new extension of the Step-wise Weight Assessment Ratio Analysis (SWARA) and PIvot Pairwise Relative Criteria Importance Assessment (PIPRECIA) methods adapted for group decision-making. In the proposed approach, attitudes of decision-makers are transformed into grey group attitudes, which allows taking advantage of the benefit that grey numbers provide over crisp numbers. The main advantage of the proposed approach in relation to the use of crisp numbers is the ability to conduct different analyses, i.e., considering different scenarios, such as pessimistic, optimistic, and so on. By varying the value of the whitening coefficient, different weights of the criteria can be obtained, and it should be emphasized that this approach gives the same weights as in the case of crisp numbers when the whitening coefficient has a value of 0.5. In addition, in this approach, the grey number was formed based on the median value of collected responses because it better maintains the deviation from the normal distribution of the collected responses. The application of the proposed approach was considered through two numerical illustrations, based on which appropriate conclusions were drawn.

Katsikis, V. N., Mourtas, S. D., Stanimirović, P. S., & Zhang, Y. (2021). Continuous-Time Varying Complex QR Decomposition via Zeroing Neural Dynamics. Neural Processing Letters. presented at the 2021. Publisher's VersionAbstract

QR decomposition (QRD) is of fundamental importance for matrix factorization in both real and complex cases. In this paper, by using zeroing neural dynamics method, a continuous-time model is proposed for solving the time-varying problem of QRD in real-time. The proposed dynamics use time derivative information from a known real or complex matrix. Furthermore, its theoretical analysis is provided to substantiate the convergence and effectiveness of solving the time-varying QRD problem. In addition, numerical experiments in four different-dimensional time-varying matrices show that the proposed model is effective for solving the time-varying QRD problem both in the case of a real or a complex matrix as input.

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