A GRASP based solution approach to solve cardinality constrained portfolio optimization problems

Baykasoğlu, Adil; Yunusoglu, Mualla Gonca; Özsoydan, Fehmi Burçin

doi:10.1016/j.cie.2015.10.009

Cited by 37 publications

(28 citation statements)

References 11 publications

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“…However, they did not address the problem of solving the optimization problem. Baykasoğlu et al [21] proposed a greedy randomized adaptive search procedure (GRASP) to solve the portfolio selection problem with cardinality constraints. The GRASP based approach decouples the original problems into two sub-problems: stock selection and proportion determination.…”

Section: A Background and Related Workmentioning

confidence: 99%

See 1 more Smart Citation

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

Khan¹,

Cao²,

Katsikis³

et al. 2020

IEEE Access

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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. INDEX TERMS Portfolio management, constrained optimization, nature-inspired algorithms, beetle search optimization.

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Section: A Background and Related Workmentioning

confidence: 99%

“…Based on the definitions of penalty function (17), and replacing the value of individual penalty-term from (18), (21), (19), and 20, the final form of the penalty function can be written as…”

Section: A Unconstrained Optimization Problemmentioning

confidence: 99%

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

Khan¹,

Cao²,

Katsikis³

et al. 2020

IEEE Access

View full text Add to dashboard Cite

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“…Woodside-Oriakhi et al [10] presented metaheuristics based upon GA, simulated annealing, and Tabu search for Markovitz's mean variance model considering the discrete constraints of buy-in thresholds and cardinality. A greedy randomized adaptive search procedure has been developed in [11] for CCPO. An arti cial bee colony algorithm is also proposed in [12] for CCPO.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Eqs. (10) and (11) are used in scenario generation with 2, 5, 10, 20, and 50 paths for 4 and 7 periods. Each path from T = 0 to T = represents a scenario.…”

Section: Scenario Generation Using Vectormentioning

confidence: 99%

An Effective League Championship Algorithm for the Stochastic Multi-Period Portfolio Optimization Problem

2018

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The Multi-Period Portfolio Optimization (MPPO) models have been introduced to overcome the weaknesses of the single-period models via considering a dynamic optimization system. However, considering the nonlinear nature of the problem and rapid growth of the size complexity with increase in the number of periods and scenarios, this study is devoted to developing a novel League Championship Algorithm (LCA) to maximize the mean variance function of the portfolio subject to di erent constraints. A Vector Auto-Regression (VAR) model was developed to estimate the return on risky assets in di erent time periods and to simulate di erent scenarios of the rate of return, accordingly. Besides, we proved a valid upper bound of the objective function based on the idea of using surrogate relaxation of constraints. Our computational results based on sample data collected from S&P 500 and 10-year T. bond indices indicated that the quality of portfolios, in terms of the mean variance measure, obtained by LCA was 10 to 20 percent better than that by the commercial software. It seems promising that our method can be a suitable tool for solving a variety of portfolio optimization problems.

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“…Cesarone et al 7 extended the method of dealing with the small‐scale problems to an efficient and accurate heuristic program, which can be used to find the optimal solution for large‐scale problems. In the study of Baykasoglu et al, 33 the assets were selected by a greedy randomized adaptive search procedure (GRASP) and the proportions of the selected assets were determined by QP. Similarly, Akbay et al 34 combine parallel variable neighborhood search algorithm with QP.…”

Section: Introductionmentioning

confidence: 99%

A hybrid approach based on double roulette wheel selection and quadratic programming for cardinality constrained portfolio optimization

Xiao

Nan

et al. 2021

Concurrency and Computation

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The portfolio optimization problem with cardinality constraint is usually solved by exact algorithms, heuristic algorithms, or combinations of them. We decompose the cardinality constraint mean-variance model, and determine the assets and proportions by double roulette wheel selection (DRWS) and quadratic programming (QP), respectively. Then the accuracy of the solution is improved by a local search after we obtain the preliminary solution by combining DRWS and QP. Experimental results show that the proposed algorithm achieves better accuracy and more efficiency than the algorithms in the literature. Therefore, we can see that the algorithm designed according to the characteristics of specific problems can improve the computational efficiency, but the algorithm needs to be adjusted for different problems.

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A GRASP based solution approach to solve cardinality constrained portfolio optimization problems

Cited by 37 publications

References 11 publications

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

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

An Effective League Championship Algorithm for the Stochastic Multi-Period Portfolio Optimization Problem

A hybrid approach based on double roulette wheel selection and quadratic programming for cardinality constrained portfolio optimization

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