Benchmarking and Evaluating MATLAB Derivative-Free Optimisers for Single-Objective Applications

Li, Lin; Chen, Yi; Liu, Qunfeng; Lazić, Jasmina; Luo, Wuqiao; Li, Yun

doi:10.1007/978-3-319-63312-1_7

Cited by 4 publications

(4 citation statements)

References 6 publications

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“…The book by Conn, Scheinberg and Vicente [35] deals only with derivative-free unconstrained minimization, except for its last chapter (of 10 pages out of the 275) entitled "Review of constrained and other extensions to derivative-free optimization." Li et al [58] do not even mention constraints. In [41] the numerical work deals with: "The dimension of the problems [i.e., the size of the vector x] varies between 2 and 16, while the number of constraints are between 1 and 38, exceeding 10 in only 5 cases."…”

Section: Derivative-free Superiorizationmentioning

confidence: 99%

Superiorization: The asymmetric roles of feasibility-seeking and objective function reduction

2023

Appl. Set-Valued Anal. Optim.

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The superiorization methodology can be thought of as lying conceptually between feasibilityseeking and constrained minimization. It is not trying to solve the full-fledged constrained minimization problem composed from the modeling constraints and the chosen objective function. Rather, the task is to find a feasible point which is "superior" (in a well-defined manner) with respect to the objective function, to one returned by a feasibility-seeking only algorithm. We telegraphically review the superiorization methodology and where it stands today and propose a rigorous formulation of its, yet only partially resolved, guarantee problem. The real-world situation in an application field is commonly represented by constraints defined by the modeling process and the data, obtained from measurements or otherwise dictated by the model-user. The feasibility-seeking problem requires to find a point in the intersection of all constraints without using any objective function to aim at any specific feasible point. At the heart of the superiorization methodology lies the modeler desire to use an objective function, that is exogenous to the constraints, in order to seek a feasible solution that will have lower (not necessarily minimal) objective function value. This aim is less demanding than full-fledged constrained minimization but more demanding than plain feasibility-seeking. Putting emphasis on the need to satisfy the constraints, because they represent the real-world situation, one recognizes the "asymmetric roles of feasibility-seeking and objective function reduction", namely, that fulfilling the constraints is the main task while reduction of the exogenous objective function plays only a secondary role. There are two research directions in the superiorization methodology that nourish from this same general principle: Weak superiorization and strong superiorization. Since its inception in 2007, the superiorization methodology has evolved and gained ground, as can be seen from the, compiled and continuously updated, bibliography at: http://math.haifa.ac.il/yair/bib-superiorization-censor.html.

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Section: Derivative-free Superiorizationmentioning

confidence: 99%

Superiorization: The asymmetric roles of feasibility-seeking and objective function reduction

2023

Appl. Set-Valued Anal. Optim.

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“…The book by Conn, Scheinberg and Vicente [10] deals only with derivative-free unconstrained minimization, except for its last chapter (of 10 pages out of the 275) entitled "Review of constrained and other extensions to derivative-free optimization." Li et al [23] do not even mention constraints. In [12] the numerical work deals with: "The dimension of the problems [i.e., the size of the vector x] varies between 2 and 16, while the number of constraints are between 1 and 38, exceeding 10 in only 5 cases."…”

Section: Derivative-free Superiorization Versus Derivative-free Optim...mentioning

confidence: 99%

Derivative-free superiorization: principle and algorithm

et al. 2020

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The superiorization methodology is intended to work with input data of constrained minimization problems, that is, a target function and a set of constraints. However, it is based on an antipodal way of thinking to what leads to constrained minimization methods. Instead of adapting unconstrained minimization algorithms to handling constraints, it adapts feasibility-seeking algorithms to reduce (not necessarily minimize) target function values. This is done by inserting target-function-reducing perturbations into a feasibility-seeking algorithm while retaining its feasibility-seeking ability and without paying a high computational price. A superiorized algorithm that employs component-wise target function reduction steps is presented. This enables derivative-free superiorization (DFS), meaning that superiorization can be applied to target functions that have no calculable partial derivatives or subgradients. The numerical behavior of our derivative-free superiorization algorithm is illustrated on a data set generated by simulating a problem of image reconstruction from projections. The plots of proximity-target curves of our experiments demonstrate the advantage of the proposed derivative-free superiorization algorithm.

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“…Further, a scoring system for benchmarking DFOs and a decision tree are to be developed to facilitate their selection and use without the need for deep knowledge of the DFOs on the user's part. We shall carry out complete benchmark tests against four Congress on Evolution Computation (CEC) benchmarking problems [7]- [11], and then verify the conclusion against a practical application -the particle filtering (PF) problem [12].…”

Section: Introductionmentioning

confidence: 99%

“…Included in the benchmarking tests are five MATLAB built-in DFO functions [2]- [4], i.e. simulated annealing (SA), particle swarm optimization (PSO), the genetic algorithm (with elitism, GAe), simplex search (SS), and pattern search (PS), plus one third-party implementation of the widely used Powell's conjugate (PC) method (as an open-source m-file available from MATLAB's official user repository [13]) recommended by MathWorks R [7]. Among these six DFO algorithms, the SS, PS and PC are direct search algorithms and the other three are heuristics, where the GAe uses encoding.…”

Section: Introductionmentioning

confidence: 99%

Benchmarks for Evaluating Optimization Algorithms and Benchmarking MATLAB Derivative-Free Optimizers for Practitioners’ Rapid Access

et al. 2019

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MATLAB R has built in five derivative-free optimizers (DFOs), including two direct search algorithms (simplex search, pattern search) and three heuristic algorithms (simulated annealing, particle swarm optimization, and genetic algorithm), plus a few in the official user repository, such as Powell's conjugate (PC) direct search recommended by MathWorks R. To help a practicing engineer or scientist to choose a MATLAB DFO most suitable for their application at hand, this paper presents a set of five benchmarking criteria for optimization algorithms and then uses four widely adopted benchmark problems to evaluate the DFOs systematically. Comprehensive tests recommend that the PC be most suitable for a unimodal or relatively simple problem, whilst the genetic algorithm (with elitism in MATLAB, GAe) for a relatively complex, multimodal or unknown problem. This paper also provides an amalgamated scoring system and a decision tree for specific objectives, in addition to recommending the GAe for optimizing structures and categories as well as for offline global search together with PC for local parameter tuning or online adaptation. To verify these recommendations, all the six DFOs are further tested in a case study optimizing a popular nonlinear filter. The results corroborate the benchmarking results. It is expected that the benchmarking system would help select optimizers for practical applications.

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Benchmarking and Evaluating MATLAB Derivative-Free Optimisers for Single-Objective Applications

Cited by 4 publications

References 6 publications

Superiorization: The asymmetric roles of feasibility-seeking and objective function reduction

Superiorization: The asymmetric roles of feasibility-seeking and objective function reduction

Derivative-free superiorization: principle and algorithm

Benchmarks for Evaluating Optimization Algorithms and Benchmarking MATLAB Derivative-Free Optimizers for Practitioners’ Rapid Access

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