Optimal Portfolio Management for Engineering Problems Using Nonconvex Cardinality Constraint: A Computing Perspective

The problem of portfolio management relates to the selection of optimal stocks, which results in a maximum return to the investor while minimizing the loss. Traditional approaches usually model the portfolio selection as a convex optimization problem and require the calculation of gradient. Note that gradient-based methods can stuck at local optimum for complex problems and the simplification of portfolio optimization to convex, and further solved using gradient-based methods, is at a high cost of solution accuracy. In this paper, we formulate a nonconvex model for the portfolio selection problem, which considers the transaction cost and cardinality constraint, thus better reflecting the decisive factor affecting the selection of portfolio in the real-world. Additionally, constraints are put into the objective function as penalty terms to enforce the restriction. Note that this reformulated problem cannot be readily solved by traditional methods based on gradient search due to its nonconvexity. Then, we apply the Beetle Antennae Search (BAS), a nature-inspired metaheuristic optimization algorithm capable of efficient global optimization, to solve the problem. We used a large real-world dataset containing historical stock prices to demonstrate the efficiency of the proposed algorithm in practical scenarios. Extensive experimental results are presented to further demonstrate the efficacy and scalability of the BAS algorithm. The comparative results are also performed using Particle Swarm Optimizer (PSO), Genetic Algorithm (GA), Pattern Search (PS), and gradient-based fmincon (interior-point search) as benchmarks. The comparison results show that the BAS algorithm is six times faster in the worst case (25 times in the best case) as compared to the rival algorithms while achieving the same level of performance

Non-linear Activated Beetle Antennae Search: A novel technique for non-convex tax-aware portfolio optimization problem

The non-convex tax-aware portfolio optimization problem is traditionally approximated as a convex problem, which compromises the quality of the solution and converges to a local-minima instead of global minima. In this paper, we proposed a non-deterministic meta-heuristic algorithm called Non-linear Activated Beetle Antennae Search (NABAS). NABAS explores the search space at the given gradient estimate measure until it is smaller than a threshold known as “Activation Threshold”, which increases its convergence rate and avoids local minima. To test the validity of NABAS, we formulated an optimization-based tax-aware portfolio problem. The objective is to maximize the profit and minimize the risk and tax liabilities and fulfill other constraints. We collected stock data of 20 companies from the NASDAQ stock market and performed a simulation using MATLAB. A comprehensive comparison is made with BAS, PSO, and GA algorithms. The results also showed that a better-optimized portfolio is achieved with a non-convex problem than a convex problem. © 2022 Elsevier Lt

Optimal Portfolio Management for Engineering Problems Using Nonconvex Cardinality Constraint: A Computing Perspective

The problem of portfolio management relates to the selection of optimal stocks, which results in a maximum return to the investor while minimizing the loss. Traditional approaches usually model the portfolio selection as a convex optimization problem and require the calculation of gradient. Note that gradient-based methods can stuck at local optimum for complex problems and the simplification of portfolio optimization to convex, and further solved using gradient-based methods, is at a high cost of solution accuracy. In this paper, we formulate a nonconvex model for the portfolio selection problem, which considers the transaction cost and cardinality constraint, thus better reflecting the decisive factor affecting the selection of portfolio in the real-world. Additionally, constraints are put into the objective function as penalty terms to enforce the restriction. Note that this reformulated problem cannot be readily solved by traditional methods based on gradient search due to its nonconvexity. Then, we apply the Beetle Antennae Search (BAS), a nature-inspired metaheuristic optimization algorithm capable of efficient global optimization, to solve the problem. We used a large real-world dataset containing historical stock prices to demonstrate the efficiency of the proposed algorithm in practical scenarios. Extensive experimental results are presented to further demonstrate the efficacy and scalability of the BAS algorithm. The comparative results are also performed using Particle Swarm Optimizer (PSO), Genetic Algorithm (GA), Pattern Search (PS), and gradient-based fmincon (interior-point search) as benchmarks. The comparison results show that the BAS algorithm is six times faster in the worst case (25 times in the best case) as compared to the rival algorithms while achieving the same level of performance. © 2013 IEEE

A hybrid of Simple Constrained artificial bee colony algorithm and flux balance analysis for enhancing Lactate and Succinate in Escherichia Coli

In the past decades, metabolic engineering has received great attention from different sectors of science due to its important role in enhancing the over expression of the target phenotype by manipulating the metabolic pathway. The advent of metabolic engineering has further laid the foundation for computational biology, leading to the development of computational approaches for suggesting genetic manipulation. Previously, conventional methods have been used to enhance the production of lactate and succinate in E. coli. However, these products are always far below their theoretical maxima. In this research, a hybrid algorithm is developed to seek optimal solutions in order to increase the overproduction of lactate and succinate by gene knockout in E. coli. The hybrid algorithm employed the Simple Constrained Artificial Bee Colony (SCABC) algorithm, using swarm intelligence as an optimization algorithm to optimize the objective function, where lactate and succinate productions are maximized by simulating gene knockout in E. coli. In addition, Flux Balance Analysis (FBA) is used as a fitness function in the SCABC algorithm to assess the growth rate of E. coli and the productivity of lactate and succinate. As a result of the research, the gene knockout list which induced the highest production of lactate and succinate is obtained

A novel recurrent neural network based online portfolio analysis for high frequency trading

Abstract The Markowitz model, a Nobel Prize winning model for portfolio analysis, paves the theoretical foundation in finance for modern investment. However, it remains a challenging problem in the high frequency trading (HFT) era to find a more time efficient solution for portfolio analysis, especially when considering circumstances with the dynamic fluctuation of stock prices and the desire to pursue contradictory objectives for less risk but more return. In this paper, we establish a recurrent neural network model to address this challenging problem in runtime. Rigorous theoretical analysis on the convergence and the optimality of portfolio optimization are presented. Numerical experiments are conducted based on real data from Dow Jones Industrial Average (DJIA) components and the results reveal that the proposed solution is superior to DJIA index in terms of higher investment returns and lower risks