Theoretical and Practical Convergence of a Self-Adaptive Penalty Algorithm for Constrained Global Optimization

Costa, M. Fernanda P.; Francisco, Rogério Brochado; Rocha, Ana Maria A. C.; Fernandes, Edite Manuela da G. P.

doi:10.1007/s10957-016-1042-7

Cited by 8 publications

(6 citation statements)

References 35 publications

(88 reference statements)

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“…We conclude this subsection by stating the following theorem, whose proof is omitted since it is similar to the one presented in [16].…”

Section: Solution Coding and Hybrid Constraint-handling Proceduresmentioning

confidence: 92%

“…The resulting mutated swarm is denoted by Pg . Successively, we apply the self-adaptive penalty approach by [16] to handle the turnover constraint and to guarantee the global optimality of solutions. More precisely, the objective function value at each projected individual in Pg , namely f (x p ), is normalized according to the formula…”

Section: Solution Coding and Hybrid Constraint-handling Proceduresmentioning

confidence: 99%

“…In (3.20), the reference point ž is a point belonging to Pg that satisfies the turnover constraint and has the lowest objective function value found so far. As in [16], if the population has no feasible points, f (ž) is initially and temporarily set to f max , so that f (x p ) ≤ f (ž) for all xp ∈ Pg and f (ž) = 1. The value of f (ž) is updated only when the first feasible point is encountered.…”

Section: Solution Coding and Hybrid Constraint-handling Proceduresmentioning

confidence: 99%

“…Therefore, to tackle the presented large-scale cardinality-constrained portfolio optimization problem, we combine the ALLSO with a novel hybrid constraint-handling technique, in which we integrate a projection operator into the self-adaptive penalty scheme developed by [16]. Moreover, to further improve the exploitation power of the algorithm and the quality of the solutions, we introduce a novel mutation procedure, applied to the best individuals in the first level, which generalises the one inspected in [25].…”

Section: Introductionmentioning

confidence: 99%

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A hybrid level-based learning swarm algorithm with mutation operator for solving large-scale cardinality-constrained portfolio optimization problems

Kaucic¹,

Piccotto²,

Sbaiz³

et al. 2022

Preprint

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In this work, we propose a hybrid variant of the level-based learning swarm optimizer (LLSO) for solving large-scale portfolio optimization problems. Our goal is to maximize a modified formulation of the Sharpe ratio subject to cardinality, box and budget constraints. The algorithm involves a projection operator to deal with these three constraints simultaneously and we implicitly control transaction costs thanks to a rebalancing constraint. We also introduce a suitable exact penalty function to manage the turnover constraint. In addition, we develop an ad hoc mutation operator to modify candidate exemplars in the highest level of the swarm. The experimental results, using three large-scale data sets, show that the inclusion of this procedure improves the accuracy of the solutions. Then, a comparison with other variants of the LLSO algorithm and two state-of-the-art swarm optimizers points out the outstanding performance of the proposed solver in terms of exploration capabilities and solution quality. Finally, we assess the profitability of the portfolio allocation strategy in the last five years using an investible pool of 1119 constituents from the MSCI World Index.

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“…We conclude this subsection by stating the following theorem, whose proof is omitted since it is similar to the one presented in [16].…”

Section: Solution Coding and Hybrid Constraint-handling Proceduresmentioning

confidence: 92%

Section: Solution Coding and Hybrid Constraint-handling Proceduresmentioning

confidence: 99%

Section: Solution Coding and Hybrid Constraint-handling Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A hybrid level-based learning swarm algorithm with mutation operator for solving large-scale cardinality-constrained portfolio optimization problems

Kaucic¹,

Piccotto²,

Sbaiz³

et al. 2022

Preprint

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show abstract

“…However, we found that for the instances we use this is not relevant due to the way the initial population is taken uniformly over the level set with a function value of 1. Actually, the algorithm can easily be extended to deal with constrained problems, [1].…”

Section: Firefly Algorithmmentioning

confidence: 99%

On Local Convergence of Stochastic Global Optimization Algorithms

Hendrix

Rocha

2021

Computational Science and Its Applications – ICCSA 2021

Self Cite

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In engineering optimization with continuous variables, the use of Stochastic Global Optimization (SGO) algorithms is popular due to the easy availability of codes. All algorithms have a global and local search character, where the global behaviour tries to avoid getting trapped in local optima and the local behaviour intends to reach the lowest objective function values. As the algorithm parameter set includes a final convergence criterion, the algorithm might be running for a while around a reached minimum point. Our question deals with the local search behaviour after the algorithm reached the final stage. How fast do practical SGO algorithms actually converge to the minimum point? To investigate this question, we run implementations of well known SGO algorithms in a final local phase stage.

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A hybrid level-based learning swarm algorithm with mutation operator for solving large-scale cardinality-constrained portfolio optimization problems

Kaucic

Piccotto

Sbaiz

et al. 2023

Information Sciences

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Theoretical and Practical Convergence of a Self-Adaptive Penalty Algorithm for Constrained Global Optimization

Abstract: This paper proposes a self-adaptive penalty function and presents a penalty-based algorithm for solving nonsmooth and nonconvex constrained Communicated by Dario Izzo

Cited by 8 publications

References 35 publications

A hybrid level-based learning swarm algorithm with mutation operator for solving large-scale cardinality-constrained portfolio optimization problems

A hybrid level-based learning swarm algorithm with mutation operator for solving large-scale cardinality-constrained portfolio optimization problems

On Local Convergence of Stochastic Global Optimization Algorithms

A hybrid level-based learning swarm algorithm with mutation operator for solving large-scale cardinality-constrained portfolio optimization problems

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