Continuous Global Optimization Research Articles

Improving the Performance of Whale Optimization Algorithm through OpenCL-Based FPGA Accelerator

Whale optimization algorithm (WOA), known as a novel nature-inspired swarm optimization algorithm, demonstrates superiority in handling global continuous optimization problems. However, its performance deteriorates when applied to large-scale complex problems due to rapidly increasing execution time required for huge computational tasks. Based on interactions within the population, WOA is naturally amenable to parallelism, prompting an effective approach to mitigate the drawbacks of sequential WOA. In this paper, field programmable gate array (FPGA) is used as an accelerator, of which the high-level synthesis utilizes open computing language (OpenCL) as a general programming paradigm for heterogeneous System-on-Chip. With above platform, a novel parallel framework of WOA named PWOA is presented. The proposed framework comprises two feasible parallel models called partial parallel and all-FPGA parallel, respectively. Experiments are conducted by performing WOA on CPU and PWOA on OpenCL-based FPGA heterogeneous platform, to solve ten well-known benchmark functions. Meanwhile, other two classic algorithms including particle swarm optimization (PSO) and competitive swarm optimizer (CSO) are adopted for comparison. Numerical results show that the proposed approach achieves a promising computational performance coupled with efficient optimization on relatively large-scale complex problems.

A diffusion algorithm based on P systems for continuous global optimization

This paper proposes a novel optimization algorithm, called Diffusion Algorithm Based on P Systems (DAPS), for continuous global optimization. This algorithm utilizes four different search strategies and a P system to explore the search space and find the global minima. These search strategies mimic the diffusion phenomena and a hybrid membrane structure inspired by chloroplasts and mitochondria is used as a distributed-parallel computing framework in the P system. The basic concepts and principles of the diffusion search strategies and the P system framework are explained in detail. For verifying the results of DAPS, comparisons with several well-known and recent metaheuristic optimization algorithms on 13 widely used benchmark functions are conducted. The experimental results demonstrate that DAPS is highly competitive and can provide better solution accuracy on the majority of the benchmark functions.

A deterministic method for continuous global optimization using a dense curve

In this paper, we develop a new approach for solving a large class of global optimization problems for objective functions which are only continuous on a rectangle of Rn. This method is based on the reducing transformation technique by running in the feasible domain a single parametrized Lissajous curve, which becomes increasingly denser and progressively fills the feasible domain. By means of the one-dimensional Evtushenko algorithm, we realize a mixed method which explores the feasible domain. To speed up the mixed exploration algorithm, we have incorporated a DIRECT local search type algorithm to explore promising regions. This method converges in a finite number of iterations to the global minimum within a prescribed accuracy ε>0. Simulations on some typical test problems with diverse properties and different dimensions indicate that the algorithm is promising and competitive.

Subset selection via continuous optimization with applications to network design.

Choosing a subset of representative items from a set of alternatives is an important problem in many scientific fields such as environmental science and statistics. For most practical problems, however, a computationally efficient solution method is not known to exist. While this problem has attracted a significant amount of attention, the majority of specifically designed algorithms do not scale well with respect to the problem size or do not provide a usable open-source package. In this study, we show that any global continuous optimization technique can be used for solving the representative subset selection problem. The latter is achieved by designing a simple transformation which embeds the problem's discrete space into a larger continuous space. The proposed methodology is applied to design problems in environmental and statistical domains. We evaluate the proposed method using several open-source global optimization packages, and show that this technique compares favorably with existing direct methods.

A rotationally invariant semi-autonomous particle swarm optimizer with directional diversity

Abstract The semi-autonomous particle swarm optimizer (SAPSO) [ 1 ] is a relatively recent algorithm for global continuous optimization based on gradient direction and diversity controlling approach, providing autonomy for the particles and the swarm for exploiting regions in the search space, and preserving exploration during the whole search process. In the first study, although SAPSO algorithm holds the property rotational invariance in which it normally brings a lack of directional diversity in PSO context, the algorithm has shown very good performance in comparison to other PSO-like algorithms. In this paper, an improved version of SAPSO, named rotationally invariant SAPSO (RI-SAPSO), is proposed, which still holds the same property, but now it incorporates a rotation matrix generated by an exponential map to maintain directional diversity. A mathematical proof to prove that the RI-SAPSO algorithm is rotationally invariant is given. RI-SAPSO was evaluated on test functions extracted from CEC 2017 benchmark problems with six other PSO-like algorithms, along with its previous version. The comparative study was strengthened with a non-parametric Friedman's hypothesis test for 1 × k comparisons and p-values were adjusted in the post-hoc procedure. Simulation results showed that the proposed RI-SAPSO, in most problems, was able to find much better solutions and statistical significances were also observed.

An augmented filled function for global nonlinear integer optimization

The problem of finding global minima of nonlinear discrete functions arises in many fields of practical matters. In recent years, methods based on discrete filled functions have become popular as ways of solving these sort of problems. However, they rely on the steepest descent method for local searches. Here, we present an approach that does not depend on a particular local optimization method, and a new discrete filled function with the useful property that a good continuous global optimization algorithm applied to it leads to an approximation of the solution of the nonlinear discrete problem (Theorem 4). Numerical results are given showing the efficiency of the new approach.

Color Filter Polishing Optimization Using ANFIS With Sliding-Level Particle Swarm Optimizer

An adaptive network-based fuzzy inference system (ANFIS) with a sliding-level particle swarm optimization (SL-PSO) is proposed for optimizing parameters of a chemical-mechanical process for polishing a color filter (CMP-CF). The SL-PSO is used not only to find the best membership function types, but also to optimize the premise and consequent parameters for ANFIS. The important process parameters for CMP-CF included the initial time, polishing time, polishing pad weight (down force), slurry chemicals, and rotation speed. The output targets were red pixels, green pixels, blue pixels, and the surface roughness. First, the performance of the SL-PSO was tested with 18 continuous global numerical optimization problems, including six unimodal functions, seven multimodal functions, and five complex rotated and shifted functions. Nonparametric Wilcoxon tests were also used in multiple-problem analysis for simultaneous comparison of various algorithms over a problem set. The computational experiments showed that the proposed SL-PSO approach outperforms PSO-based methods reported in the literature. Finally, the proposed SL-PSO method was used to optimize CMP-CF parameters. The experimental results showed that the ANFIS with SL-PSO outperforms the conventional ANFIS method and conventional back propagation neural network in terms of prediction accuracy. A practical industrial application in a CF manufacturer showed that the ANFIS with SL-PSO obtained superior results compared to the previous method and immediately enhanced production efficiency. Together, these experimental results indicate that the proposed ANFIS with SL-PSO is a reliable method for optimizing CMP-CF processes.

An improved firefly algorithm for global continuous optimization problems

Global continuous optimization is populated by its implementation in many real-world applications. Such optimization problems are often solved by nature-inspired and meta-heuristic algorithms, including the firefly algorithm (FA), which offers fast exploration and exploitation. To further strengthen FA’s search for global optimum, a Levy-flight FA (LF-FA) has been developed through sampling from a Levy distribution instead of the traditional uniform one. However, due to its poor exploitation in local areas, the LF-FA does not guarantee fast convergence. To address this problem, this paper provides an adaptive logarithmic spiral-Levy FA (AD-IFA) that strengthens the LF-FA’s local exploitation and accelerates its convergence. Our AD-IFA is integrated with logarithmic-spiral guidance to its fireflies’ paths, and adaptive switching between exploration and exploitation modes during the search process. Experimental results show that the AD-IFA presented in this paper consistently outperforms the standard FA and LF-FA for 29 test functions and 6 real cases of global optimization problems in terms of both computation speed and derived optimum.

AbsTaylor: upper bounding with inner regions in nonlinear continuous global optimization problems

In this paper we propose AbsTaylor, a simple and quick method for extracting inner polytopes, i.e., entirely feasible convex regions in which all points satisfy the constraints. The method performs an inner linearization of the nonlinear constraints by using a Taylor form. Unlike a previous proposal, the expansion point of the Taylor form is not limited to the bounds of the domains, thus producing, in general, a tighter approximation. For testing the approach, AbsTaylor was introduced as an upper bounding method in a state-of-the-art global branch & bound optimizer. Furthermore, we implemented a local search method which extracts feasible inner polytopes for iteratively finding better solutions inside them. In the studied instances, the new method finds in average four times more inner regions and significantly improves the optimizer performance.

Применение многомерной квантильной функции в задаче пептид-белок докинга

The paper presents an exploration of using evolutionary optimization algorithms in protein-peptide docking. The main assumptions that reduce docking to the continuous global optimization problem are described. Some special features of the given problem and the difficulties of using evolutionary algorithms are discussed. The paper provides a way of using evolutionary optimization algorithms based on using empirical quantile function. The multivariate quantile function structure is defined recursively using univariate quantile transform. The grid-based approach of using quantile function is presented. The disadvantages of this approach are indicated. The deterministic sampling algorithm is proposed. The used scheme of parallel sampling and the resulting speed-up are described. The GPU-accelerated approach for quantile function evaluation is presented. This paper provides multiple GPU-based ways which use a sample in explicit form. Their speed-up depending on sample size is shown. The paper presents the results of docking using an evolutionary algorithm and its quantile-function-based modification. The comparison with the relevant docking method within a particular force-field is made. The results of the experiments are analyzed.

Accelerating continuous GRASP with a GPU

This work proposes a GPU-based parallelization for the Continuous GRASP (C-GRASP), a local search metaheuristic for finding cost-efficient solutions to continuous global optimization problems subject to box constraints. C-GRASP has demonstrated competitive performance on several well-known multimodal test functions as well as on difficult real-world problems, hence a GPU parallelization might increase even further the applicability of this metaheuristic. Although GPU parallelizations have been proposed for many metaheuristics, little has been done for C-GRASP. We conduct an extensive set of experiments and compare our proposal with state-of-the-art GPU parallelizations of other metaheuristics, such as Scatter Search and Differential Evolution. We also compare our GPU approach with two other C-GRASP implementations: a sequential version and a multi-core version. Experimental results show our GPU C-GRASP outperforms other GPU-based metaheuristics and the multi-core C-GRASP. Besides, we observed speedups of up to $$154{\times }$$ over the sequential version.

Influence of a neighborhood shape on the efficiency of continuous variable neighborhood search

The efficiency of a Variable neighborhood search metaheuristic for continuous global optimization problems greatly depends on geometric shape of neighborhood structures used by the algorithm. Among the neighborhoods defined by balls in ?p, 1 ?p ? ? metric, we tested the ?1, ?2, and ?? ball shape neighborhoods, for which there exist efficient algorithms for obtaining uniformly distributed points. On many challenging high-dimensional problems, our exhaustive testings showed that, popular and the easiest for implementation, ?? ball shape of neighborhoods performed the worst, and much better efficiency was obtained with ?1 and ?2.

A conceptual comparison of several metaheuristic algorithms on continuous optimisation problems

The field of continuous optimisation has witnessed an explosion of the so-called new or novel metaheuristic algorithms. Though not all of these algorithms are efficient as proclaimed by their inventors, a few of them have proved to be very efficient and thus have become popular tools for solving complex optimisation problems. Therefore, there is a need for a systematic analysis approach to fairly evaluate and compare the results of some of these optimisation algorithms. In this paper, a set of well-known mathematical benchmark functions are compiled to provide an easily accessible collection of standard benchmark test problems for continuous global optimisation. This set of test problems are used to investigate the computational capabilities and the microscopic behaviour of twelve different metaheuristic algorithms. The required number of function evaluations for reaching the best solution and the run-time complexity of the algorithms are compared. Furthermore, statistical tests are conducted to validate the concluding remarks.

Dynamic cuckoo search algorithm based on Taguchi opposition-based search

The cuckoo search (CS) algorithm is a relatively new, nature-inspired intelligent algorithm that uses a whole updating and evaluation strategy to find solutions for continuous global optimisation problems. Despite its efficiency and wide use, CS suffers from premature convergence and poor balance between exploitation and exploration. These issues result from interference phenomena among dimensions that arise when solving multi-dimension function optimisation problems. To overcome these issues, we proposed an enhanced CS algorithm called dynamic CS with Taguchi opposition-based search (TOB-DCS) that employed two new strategies: Taguchi opposition-based search and dynamic evaluation. The Taguchi search strategy provided random generalised learning based on opposing relationships to enhance the exploration ability of the algorithm. The dynamic evaluation strategy reduced the number of function evaluations, and accelerated the convergence property. For this research, we conducted experiments on 22 classic benchmark functions, including unimodal, multi-modal and shifted test functions. Statistical comparisons of our experimental results showed that the proposed TOB-DCS algorithm made an appropriate trade-off between exploration and exploitation.

Large scale continuous global optimization based on micro differential evolution with local directional search

Over the years, many optimization algorithms have been developed to solve large-scale optimization problems accurately and efficiently. In this regard, Memetic Algorithms offer robust and efficient framework that hybridizes the Evolutionary Algorithms with a local heuristic search. In this work, we propose micro Differential Evolution with a Directional Local Search (µDSDE) algorithm using a small population size to solve large scale continuous optimization problems. In this technique, the best individual retains its position, the second best individual undergoes mutation and crossover processes of DE, and the rest are reinitialized on the search space. Exploration of the search is carried out with the dispersal of the worst individuals whereas exploitation is performed through DE operators and Directional Local Search (DLS). We conducted extensive empirical studies using two test suites on Large Scale Global Optimization benchmark with up to 5000 dimensions. The results show that µDSDE considerably outperforms existing solutions in terms of the convergence rate and solution quality.

A PSO based approach: Scout particle swarm algorithm for continuous global optimization problems

AbstractIn the literature, most studies focus on designing new methods inspired by biological processes, however hybridization of methods and hybridization way should be examined carefully to generate more suitable optimization methods. In this study, we handle Particle Swarm Optimization (PSO) and an efficient operator of Artificial Bee Colony Optimization (ABC) to design an efficient technique for continuous function optimization. In PSO, velocity and position concepts guide particles to achieve convergence. At this point, variable and stable parameters are ineffective for regenerating awkward particles that cannot improve their personal best position (Pbest). Thus, the need for external intervention is inevitable once a useful particle becomes an awkward one. In ABC, the scout bee phase acts as external intervention by sustaining the resurgence of incapable individuals. With the addition of a scout bee phase to standard PSO, Scout Particle Swarm Optimization (ScPSO) is formed which eliminates the most important handicap of PSO. Consequently, a robust optimization algorithm is obtained.ScPSO is tested on constrained optimization problems and optimum parameter values are obtained for the general use of ScPSO. To evaluate the performance, ScPSO is compared with Genetic Algorithm (GA), with variants of the PSO and ABC methods, and with hybrid approaches based on PSO and ABC algorithms on numerical function optimization. As seen in the results, ScPSO results in better optimal solutions than other approaches. In addition, its convergence is superior to a basic optimization method, to the variants of PSO and ABC algorithms, and to the hybrid approaches on different numerical benchmark functions. According to the results, the Total Statistical Success (TSS) value of ScPSO ranks first (5) in comparison with PSO variants; the second best TSS (2) belongs to CLPSO and SP-PSO techniques. In a comparison with ABC variants, the best TSS value (6) is obtained by ScPSO, while TSS of BitABC is 2. In comparison with hybrid techniques, ScPSO obtains the best Total Average Rank (TAR) as 1.375, and TSS of ScPSO ranks first (6) again. The fitness values obtained by ScPSO are generally more satisfactory than the values obtained by other methods. Consequently, ScPSO achieve promising gains over other optimization methods; in parallel with this result, its usage can be extended to different working disciplines.Highlights PSO parameters are ineffective to regenerate the awkward particle that cannot improve its pbest. An external intervention is inevitable once a particle becomes an awkward one. ScPSO is obtained with the addition of scout bee phase into the PSO. So an evolutionary method eliminating the most important handicap of PSO is gained. ScPSO is compared with the variants and with hybrid versions of PSO and ABC methods. According to the experiments, ScPSO results in better optimal solutions. The fitness values of ScPSO are generally more satisfactory than the others. Consequently, ScPSO achieve promising gains over other optimization methods. In parallel with this, its usage can be extended to different working disciplines.

Enhancing particle swarm optimization with binary quantum wave modulation and joint guiding forces

The searching mechanism of particle swarm optimization (PSO) derives from two principal forces of the moving direction to guide the particles toward their personal best (pbest) and the global best (gbest) positions. Modifying the behavior of the particles provides a solution to relieve the problem of local optimum trapping and increase the convergence speed. Inspired from quantum mechanics, we propose a continuous global optimization algorithm called binary quantum wave modulated particle swarm optimization (BQWPSO). The quantum particles are modulated with the binary form of wave functions, where the real positions of the particles have uncertainty that extend the searching areas. Unlike the unilateral force exerted on the particles in standard PSO and some other PSO variants, in BQWPSO both the attractive and repellent forces are jointly exerted on a particle so as to be led to a better direction to search the optimal solution. The artificial Laplacian operator is formulated to convey such information, which characterizes the momentum of a given particle. Experiments conducted on several test functions demonstrate the effectiveness of BQWPSO in solving optimization problems.

Eigen-MM: EigenAnt Modified Mtsls1 for local search

Abstract The EigenAnt, an algorithm for Ant Colony Optimization with convergence guarantees, has been shown to be suitable for continuous global optimization. Conventionally, the Multi-Trajectory Local Search (Mtsls1) algorithm was used for efficient local search, and it searches along function dimensions sequentially. On the other hand, EigenAnt provides an approach to select dimensions where higher gain in terms of function value is obtained. The Modified Mtsls1 (MMtsls1) approach improved the performance of the original Mtsls1 algorithm by implementing a strategy which requires fewer number of function evaluations during the local search procedure. This paper presents an approach called the EigenAnt Modified Mtsls1 (Eigen-MM), which combines the advantages of the Modified Mtsls1 with EigenAnt to better optimize benchmark functions by using fewer number of function evaluations. Our results demonstrate that the Eigen-MM approach is particularly effective for high-dimensional functions. On a number of selected benchmarks, we obtain upto 88.2% reduction in the number of function evaluations.

Convergence analysis of the plant propagation algorithm for continuous global optimization

The Plant Propagation Algorithm (PPA) is a Nature-Inspired stochastic algorithm, which emulates the way plants, in particular the strawberry plant, propagate using runners. It has been experimentally tested both on unconstrained and constrained continuous global optimization problems and was found to be competitive against well established algorithms. This paper is concerned with its convergence analysis. It first puts forward a general convergence theorem for a large class of random algorithms, before the PPA convergence theorem is derived and proved. It then illustrates the results on simple problems.

Parallel Evolutionary Optimization Algorithms for Peptide-Protein Docking

In this study we examine the possibility of using evolutionary optimization algorithms in protein-peptide docking. We present the main assumptions that reduce the docking problem to a continuous global optimization problem and provide a way of using evolutionary optimization algorithms. The Rosetta all-atom force field was used for structural representation and energy scoring. We describe the parallelization scheme and MPI/OpenMP realization of the considered algorithms. We demonstrate the efficiency and the performance for some algorithms which were applied to a set of benchmark tests.