This paper presents a nature-inspired metaheuristic called Marine Predators Algorithm (MPA) and its application in engineering. The main inspiration of MPA is the widespread foraging strategy namely Levy and Brownian movements in ocean predators along with optimal encounter rate policy in biological interaction between predator and prey. MPA follows the rules that naturally govern in optimal foraging strategy and encounters rate policy between predator and prey in marine ecosystems. This paper evaluates the MPA's performance on twenty-nine test functions, test suite of CEC-BC-2017, randomly generated landscape, three engineering benchmarks, and two real-world engineering design problems in the areas of ventilation and building energy performance. MPA is compared with three classes of existing optimization methods, including (1) GA and PSO as the most well-studied metaheuristics, (2) GSA, CS and SSA as almost recently developed algorithms and (3) CMA-ES, SHADE and LSHADE-cnEpSin as high performance optimizers and winners of IEEE CEC competition. Among all methods, MPA gained the second rank and demonstrated very competitive results compared to LSHADE-cnEpSin as the best performing method and one of the winners of CEC 2017 competition. The statistical post hoc analysis revealed that MPA can be nominated as a high-performance optimizer and is a significantly superior algorithm than GA, PSO, GSA, CS, SSA and CMA-ES while its performance is statistically similar to SHADE and LSHADE-cnEpSin. The source code is publicly available at: https://github.com/afshinfaramarzi/Marine-Predators-Algorithm, http://built-envi.com/portfolio/marine-predators-algorithm/, https://www.mathworks.com/matlabcentral/fileexchange/74578-marine-predators-algorithm-mpa, and http://www.alimirjalili.com/MPA.html.

Marine Predators Algorithm: A nature-inspired metaheuristic

We introduce COCO, an open source platform for Comparing Continuous Optimizers in a black-box setting. COCO aims at automatizing the tedious and repetitive task of benchmarking numerical optimization algorithms to the greatest possible extent. The platform and the underlying methodology allow to benchmark in the same framework deterministic and stochastic solvers for both single and multiobjective optimization. We present the rationales behind the (decade-long) development of the platform as a general proposition for guidelines towards better benchmarking. We detail underlying fundamental concepts of COCO such as the definition of a problem as a function instance, the underlying idea of instances, the use of target values, and runtime defined by the number of function calls as the central performance measure. Finally, we give a quick overview of the basic code structure and the currently available test suites.

COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting

Particle Swarm Optimization (PSO) is a metaheuristic global optimization paradigm that has gained prominence in the last two decades due to its ease of application in unsupervised, complex multidimensional problems which cannot be solved using traditional deterministic algorithms. The canonical particle swarm optimizer is based on the flocking behavior and social co-operation of birds and fish schools and draws heavily from the evolutionary behavior of these organisms. This paper serves to provide a thorough survey of the PSO algorithm with special emphasis on the development, deployment and improvements of its most basic as well as some of the state-of-the-art implementations. Concepts and directions on choosing the inertia weight, constriction factor, cognition and social weights and perspectives on convergence, parallelization, elitism, niching and discrete optimization as well as neighborhood topologies are outlined. Hybridization attempts with other evolutionary and swarm paradigms in selected applications are covered and an up-to-date review is put forward for the interested reader.

Particle Swarm Optimization: A survey of historical and recent developments with hybridization perspectives

The popularity of Bayesian optimization methods for efficient exploration of parameter spaces has lead to a series of papers applying Gaussian processes as surrogates in the optimization of functions. However, most proposed approaches only allow the exploration of the parameter space to occur sequentially. Often, it is desirable to simultaneously propose batches of parameter values to explore. This is particularly the case when large parallel processing facilities are available. These facilities could be computational or physical facets of the process being optimized. E.g. in biological experiments many experimental set ups allow several samples to be simultaneously processed. Batch methods, however, require modeling of the interaction between the evaluations in the batch, which can be expensive in complex scenarios. We investigate a simple heuristic based on an estimate of the Lipschitz constant that captures the most important aspect of this interaction (i.e. local repulsion) at negligible computational overhead. The resulting algorithm compares well, in running time, with much more elaborate alternatives. The approach assumes that the function of interest, $f$, is a Lipschitz continuous function. A wrap-loop around the acquisition function is used to collect batches of points of certain size minimizing the non-parallelizable computational effort. The speed-up of our method with respect to previous approaches is significant in a set of computationally expensive experiments.

Batch Bayesian Optimization via Local Penalization

A procedure for generating non-differentiable, continuously differentiable, and twice continuously differentiable classes of test functions for multiextremal multidimensional box-constrained global optimization is presented. Each test class consists of 100 functions. Test functions are generated by defining a convex quadratic function systematically distorted by polynomials in order to introduce local minima. To determine a class, the user defines the following parameters: (i) problem dimension, (ii) number of local minima, (iii) value of the global minimum, (iv) radius of the attraction region of the global minimizer, (v) distance from the global minimizer to the vertex of the quadratic function. Then, all other necessary parameters are generated randomly for all 100 functions of the class. Full information about each test function including locations and values of all local minima is supplied to the user. Partial derivatives are also generated where possible.

Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization

Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This work also contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremal and partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals, operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and the environmental sciences will find this title useful .

Introduction to Global Optimization Exploiting Space-Filling Curves

A procedure for generating non-differentiable, continuously differentiable, and twice continuously differentiable classes of test functions for multiextremal multidimensional box-constrained global optimization and a corresponding package of C subroutines are presented. Each test class consists of 100 functions. Test functions are generated by defining a convex quadratic function systematically distorted by polynomials in order to introduce local minima. To determine a class, the user defines the following parameters: (i) problem dimension, (ii) number of local minima, (iii) value of the global minimum, (iv) radius of the attraction region of the global minimizer, (v) distance from the global minimizer to the vertex of the quadratic function. Then, all other necessary parameters are generated randomly for all 100 functions of the class. Full information about each test function including locations and values of all local minima is supplied to the user. Partial derivatives are also generated where possible.

Software for Generation of Classes of Test Functions with Known Local and Global Minima for Global Optimization

This paper deals with two kinds of the one-dimensional global optimization problems over a closed finite interval: (i) the objective function $f(x)$ satisfies the Lipschitz condition with a constant $L$; (ii) the first derivative of $f(x)$ satisfies the Lipschitz condition with a constant $M$. In the paper, six algorithms are presented for the case (i) and six algorithms for the case (ii). In both cases, auxiliary functions are constructed and adaptively improved during the search. In the case (i), piece-wise linear functions are constructed and in the case (ii) smooth piece-wise quadratic functions are used. The constants $L$ and $M$ either are taken as values known a priori or are dynamically estimated during the search. A recent technique that adaptively estimates the local Lipschitz constants over different zones of the search region is used to accelerate the search. A new technique called the \emph{local improvement} is introduced in order to accelerate the search in both cases (i) and (ii). The algorithms are described in a unique framework, their properties are studied from a general viewpoint, and convergence conditions of the proposed algorithms are given. Numerical experiments executed on 120 test problems taken from the literature show quite a promising performance of the new accelerating techniques.

Daniela Lera

Papers

Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization

Introduction to Global Optimization Exploiting Space-Filling Curves

Software for Generation of Classes of Test Functions with Known Local and Global Minima for Global Optimization

Acceleration of univariate global optimization algorithms working with Lipschitz functions and Lipschitz first derivatives

Software for Generation of Classes of Test Functions with Known Local and Global Minima for Global Optimization