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Penalty functions and two-step selection procedure based direct-type algorithm for constrained global optimization

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2019年第6期59卷 2155-2175页

作者： Stripinis, Linas Paulavicius, Remigijus Zilinskas, Julius Vilnius Univ Inst Data Sci & Digital Technol Akad Str 4 LT-08663 Vilnius Lithuania

Applied optimization problems often include constraints. Although the well-known derivative-free global-search direct algorithm performs well solving box-constrained global optimization problems, it does not naturally address constraints. In this article, we develop a new algorithm direct-GLce for general constrained global optimization problems incorporating two-step selection procedure and penalty function approach in our recent direct-GL algorithm. The proposed algorithm effectively explores hyper-rectangles with infeasible centers which are close to boundaries of feasibility and may cover feasible regions. An extensive experimental investigation revealed the potential of the proposed approach compared with other existing direct-type algorithms for constrained global optimization problems, including important engineering problems.

关键词： direct-type algorithm direct-type constraint-handling Nonconvex optimization Derivative-free optimization

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A new partition method for direct-type algorithm based on minimax design

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JOURNAL OF GLOBAL OPTIMIZATION 2024年第1期88卷 171-197页

作者： Jia, Kai Duan, Xiaojun Wang, Zhengming Yi, Taihe Yan, Liang Chen, Xuan Natl Univ Def Technol Coll Sci Changsha 410005 Hunan Peoples R China Natl Univ Def Technol Coll Syst Engn Changsha 410005 Hunan Peoples R China

This article presents a new direct-type SCABALL (scattering balls) algorithm with a new partition method for derivation-free optimization problems. It does not focus on dividing the region of interest into specific geometric shapes, but rather scatters several balls to cover it. In SCABALL, several potential optimal regions are selected at each iteration, and they are covered by smaller balls sequentially. In this way, the SCABALL ensures the everywhere dense convergence. The center points and radii of the scattered balls significantly influence the efficiency of SCABALL;therefore, the minimax designs are used in the initial and sequential stages to obtain better coverage. The SCABALL parameters, including the number of balls and their radii, were analyzed by numerical investigation. We provided the empirical choices for those parameters and found that the balls' radii can be contracted to balance efficiency and global convergence. Numerical experiments show that the SCABALL algorithm is locally biased and robust.

关键词： Derivative-free optimization direct-type algorithm Minimax design Covering radius

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Lipschitz-inspired HALRECT algorithm for derivative-free global optimization

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JOURNAL OF GLOBAL OPTIMIZATION 2024年第1期88卷 139-169页

作者： Stripinis, Linas Paulavicius, Remigijus Vilnius Univ Inst Data Sci & Digital Technol Akad 4 LT-08663 Vilnius Lithuania

This article considers a box-constrained global optimization problem for Lipschitz-continuous functions with an unknown Lipschitz constant. Motivated by the famous direct (DIviding RECTangles), a new HALRECT (HALving RECTangles) algorithm is introduced. A new deterministic approach combines halving (bisection) with a new multi-point sampling scheme in contrast to trisection and midpoint sampling used in most existing direct-type algorithms. A new partitioning and sampling scheme uses more comprehensive information on the objective function. Four different strategies for selecting potentially optimal hyper-rectangles are introduced to exploit the objective function's information effectively. The original algorithm HALRECT and other introduced HALRECT variations (twelve in total) are tested and compared with the other twelve recently introduced direct-type algorithms on 96 box-constrained benchmark functions from directGOLib v1.1, and 96 perturbed their versions. Extensive experimental results are advantageous compared to state-of-the-art direct-type global optimization. New HALRECT approaches offer high robustness across problems of different degrees of complexity, varying from simple-uni-modal and low dimensional to complex-multi-modal and higher dimensionality.

关键词： direct-type algorithm Global optimization Derivative-free optimization Lipschitz optimization Sampling-based algorithm

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Derivative-free global ship design optimization using global/local hybridization of the direct algorithm

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OPTIMIZATION AND ENGINEERING 2016年第1期17卷 127-156页

作者： Campana, Emilio F. Diez, Matteo Iemma, Umberto Liuzzi, Giampaolo Lucidi, Stefano Rinaldi, Francesco Serani, Andrea Natl Res Council Marine Technol Res Inst CNR INSE Via Vallerano 139 I-00128 Rome Italy Univ Rome Tre Dept Engn Via Vito Volterra 62 I-00146 Rome Italy Univ Roma La Sapienza Dept Comp Control & Management Engn A Ruberti Via Ariosto 25 I-00185 Rome Italy Natl Res Council Inst Syst Anal & Comp Sci CNR IA Via Taurini 19 I-00185 Rome Italy Univ Padua Dept Math Via Trieste 63 I-35121 Padua Italy

The application of global/local hybrid direct algorithms to the simulation-based hull form optimization of a military vessel is presented, aimed at the reduction of the resistance in calm water. The specific features of the black-box-type objective function make the problem suitable for the application of direct-type algorithms. The objective function is given by numerical iterative procedures, which could lead to inaccurate derivative calculations. In addition, the presence of local minima cannot be excluded a priori. The algorithms proposed (namely DIRMIN and DIRMIN-2) are hybridizations of the classic direct algorithm, with deterministic derivative-free local searches. The algorithms' performances are first assessed on a set of test problems, and then applied to the ship optimization application. The numerical results show that the local hybridization of the direct algorithm has beneficial effects on the overall computational cost and on the efficiency of the simulation-based optimization procedure.

关键词： Ship design Simulation-based design optimization direct-type algorithm Global optimization Local search

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A multi-objective direct algorithm for ship hull optimization

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2018年第1期71卷 53-72页

作者： Campana, E. F. Diez, M. Liuzzi, G. Lucidi, S. Pellegrini, R. Piccialli, V. Rinaldi, F. Serani, A. CNR Ist Nazl Studi & Esperienze Architettura Navale Via Vallerano 139 I-00128 Rome Italy CNR Ist Anal Sistemi & Informat Via Taurini 19 I-00185 Rome Italy Sapienza Univ Roma Dipartimento Ingn Informat Automat & Gest Via Ariosto 25 I-00185 Rome Italy Univ Roma Tor Vergata Dipartimento Ingn Civile & Ingn Informat Via Politecn 1 I-00133 Rome Italy Univ Padua Dipartimento Matemat Via Trieste 63 I-35121 Padua Italy

The paper is concerned with black-box nonlinear constrained multi-objective optimization problems. Our interest is the definition of a multi-objective deterministic partition-based algorithm. The main target of the proposed algorithm is the solution of a real ship hull optimization problem. To this purpose and in pursuit of an efficient method, we develop an hybrid algorithm by coupling a multi-objective direct-type algorithm with an efficient derivative-free local algorithm. The results obtained on a set of "hard" nonlinear constrained multi-objective test problems show viability of the proposed approach. Results on a hull-form optimization of a high-speed catamaran (sailing in head waves in the North Pacific Ocean) are also presented. In order to consider a real ocean environment, stochastic sea state and speed are taken into account. The problem is formulated as a multi-objective optimization aimed at (i) the reduction of the expected value of the mean total resistance in irregular head waves, at variable speed and (ii) the increase of the ship operability, with respect to a set of motion-related constraints. We show that the hybrid method performs well also on this industrial problem.

关键词： Multi-objective nonlinear programming Derivative-free optimization direct-type algorithm

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An empirical study of various candidate selection and partitioning techniques in the direct framework

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JOURNAL OF GLOBAL OPTIMIZATION 2024年第3期88卷 723-753页

作者： Stripinis, Linas Paulavicius, Remigijus Vilnius Univ Inst Data Sci & Digital Technol Akad 4 LT-08663 Vilnius Lithuania

Over the last three decades, many attempts have been made to improve the direct (DIviding RECTangles) algorithm's efficiency. Various novel ideas and extensions have been suggested. The main two steps of direct-type algorithms are selecting and partitioning potentially optimal rectangles. However, the most efficient combination of these two steps is an area that has not been investigated so far. This paper presents a study covering an extensive examination of various candidate selection and partitioning techniques within the same direct algorithmic framework. Twelve direct-type algorithmic variations are compared on 800 randomly generated GKLS-type test problems and 96 box-constrained global optimization problems from directGOLib v1.1 with varying complexity. Based on these studies, we have identified the most efficient selection and partitioning combinations leading to new, more efficient, direct-type algorithms. All these algorithms are included in the latest version of directGO v1.1.0 and are publicly available.

关键词： direct-type algorithm Global optimization Derivative-free optimization

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A new direct-GLh algorithm for global optimization with hidden constraints

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OPTIMIZATION LETTERS 2021年第6期15卷 1865-1884页

作者： Stripinis, Linas Paulavicius, Remigijus Vilnius Univ Inst Data Sci & Digital Technol Akad 4 LT-08663 Vilnius Lithuania

In this paper, we consider the solution of global optimization problems involving hidden constraints. We present a novel deterministic derivative-free global optimization algorithm based on our recently introduced direct-GL (Stripinis et al. in Optim Lett. 12(7):1699-1712, 2018). The new algorithm (direct-GLh) incorporates two additional techniques for faster feasibility detection and solution improvement, especially when the solution lies on the border of the a priori unknown feasible region. The algorithm's potential is demonstrated on 67 problems from the current release of directLib and 100 Emmental-type test problems. The numerical comparison reveals the proposed algorithm's superiority to the considered direct-type approaches for such problems.

关键词： direct-type algorithm Derivative-free optimization Hidden constraints

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A partition-based global optimization algorithm

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JOURNAL OF GLOBAL OPTIMIZATION 2010年第1期48卷 113-128页

作者： Liuzzi, Giampaolo Lucidi, Stefano Piccialli, Veronica Sapienza Univ Roma Dipartimento Informat & Sistemist A Ruberti I-00185 Rome Italy Ist Analisi Sistemi & Informat A Ruberti I-00185 Rome Italy Univ Roma Tor Vergata Dipartimento Ingn Impresa I-00100 Rome Italy

This paper is devoted to the study of partition-based deterministic algorithms for global optimization of Lipschitz-continuous functions without requiring knowledge of the Lipschitz constant. First we introduce a general scheme of a partition-based algorithm. Then, we focus on the selection strategy in such a way to exploit the information on the objective function. We propose two strategies. The first one is based on the knowledge of the global optimum value of the objective function. In this case the selection strategy is able to guarantee convergence of every infinite sequence of trial points to global minimum points. The second one does not require any a priori knowledge on the objective function and tries to exploit information on the objective function gathered during progress of the algorithm. In this case, from a theoretical point of view, we can guarantee the so-called every-where dense convergence of the algorithm.

关键词： Global optimization Partition-based algorithm direct-type algorithm

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A direct-type approach for derivative-free constrained global optimization

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2016年第2期65卷 361-397页

作者： Di Pillo, G. Liuzzi, G. Lucidi, S. Piccialli, V. Rinaldi, F. CNR Ist Anal Sistemi & Informat A Ruberti Via Taurini 19 I-00185 Rome Italy Univ Roma La Sapienza Dept Comp Control & Management Engn Via Ariosto 25 I-00185 Rome Italy Univ Roma Tor Vergata Dipartimento Ingn Civile & Ingn Informat Viale Politecn 1 I-00133 Rome Italy Univ Padua Dipartimento Matemat Via Trieste 63 I-35121 Padua Italy

In the field of global optimization, many efforts have been devoted to globally solving bound constrained optimization problems without using derivatives. In this paper we consider global optimization problems where both bound and general nonlinear constraints are present. To solve this problem we propose the combined use of a direct-type algorithm with a derivative-free local minimization of a nonsmooth exact penalty function. In particular, we define a new direct-type strategy to explore the search space by explicitly taking into account the two-fold nature of the optimization problems, i.e. the global optimization of both the objective function and of a feasibility measure. We report an extensive experimentation on hard test problems to show viability of the approach.

关键词： Global optimization Derivative-free optimization Nonlinear optimization direct-type algorithm

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On MATLAB experience in accelerating direct-GLce algorithm for constrained global optimization through dynamic data structures and parallelization

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APPLIED MATHEMATICS AND COMPUTATION 2021年 390卷 125596-125596页

作者： Stripinis, Linas Zilinskas, Julius Casado, Leocadio G. Paulavicius, Remigijus Vilnius Univ Inst Data Sci & Digital Technol Akad 4 LT-08663 Vilnius Lithuania Univ Almeria CeiA3 Informat Dept Almeria Spain

In this paper, two different acceleration techniques for a deterministic direct (DIviding RECTangles)-type global optimization algorithm, direct-GLce, are considered. We adopt dynamic data structures for better memory usage in MATLAB implementation. We also study shared and distributed parallel implementations of the original direct-GLce algorithm, and a distributed parallel version for the aggressive counterpart. The efficiency of direct-type parallel versions is evaluated solving box- and generally constrained global optimizations problems with varying complexity, including a practical NASA speed reducer design problem. Numerical results show a good efficiency, especially for the distributed parallel version of the original direct-GLce on a multi-core PC. (C) 2020 Elsevier Inc. All rights reserved.

关键词： direct-type algorithm Derivative-free optimization Dynamic data structures Parallel optimization Parallel MATLAB Parallel computing toolbox

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