Continuous GRASP Research Articles

A FPGA-based accelerated architecture for the Continuous GRASP

This work proposes a FPGA-based architecture for accelerating the Continuous GRASP (C-GRASP), a prominent metaheuristic for solving continuous optimization problems. Although FPGA implementations have been proposed for other metaheuristics, nothing has been done for C-GRASP. We conduct a comprehensive set of experiments on well-known hard test problems, and compare our FPGA architecture with C-GRASP implementations running on four other architectures: a single-core ARM Cortex A9-based, a single-core Intel i7-based, a multi-core Intel i7-based, and a GPU-based. Experimental results demonstrate that the proposed architecture outperforms the others in terms of performance-to-power-efficiency. For instance, it is on average 3x faster and 15x less power consuming than the single-core Intel i7-based implementation. Moreover, we introduce a model-based method that helps designers with little experience in FPGA development to use our high-performance architecture to optimize their problem. Our solution is a very interesting option for the emerging technology of FPGA-based data centers (e.g, Microsoft’s Catapult project), and also for resource-constrained embedded systems (e.g., drones).

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.

DC-GRASP: directing the search on continuous-GRASP

Several papers in the scientific literature use metaheuristics to solve continuous global optimization. To perform this task, some metaheuristics originally proposed for solving combinatorial optimization problems, such as Greedy Randomized Adaptive Search Procedure (GRASP), Tabu Search and Simulated Annealing, among others, have been adapted to solve continuous global optimization problems. Proposed by Hirsch et al., the Continuous-GRASP (C-GRASP) is one example of this group of metaheuristics. The C-GRASP is an adaptation of GRASP proposed to solve continuous global optimization problems under box constraints. It is simple to implement, derivative-free and widely applicable method. However, according to Hedar, due to its random construction, C-GRASP may fail to detect promising search directions especially in the vicinity of minima, which may result in a slow convergence. To minimize this problem, in this paper we propose a set of methods to direct the search on C-GRASP, called Directed Continuous-GRASP (DC-GRASP). The proposal is to combine the ability of C-GRASP to diversify the search over the space with some efficient local search strategies to accelerate its convergence. We compare the DC-GRASP with the C-GRASP and other metaheuristics from literature on a set of standard test problems whose global minima are known. Computational results show the effectiveness and efficiency of the proposed methods, as well as their ability to accelerate the convergence of the C-GRASP.

A Python/C library for bound-constrained global optimization with continuous GRASP

This paper describes \({\texttt{libcgrpp}}\) , a GNU-style dynamic shared Python/C library of the continuous greedy randomized adaptive search procedure (C-GRASP) for bound constrained global optimization. C-GRASP is an extension of the GRASP metaheuristic (Feo and Resende, 1989) and has been used to solve unstable and nondifferentiable problems, as well as hard global optimization problems, such as chemical equilibrium systems and robot kinematics applications (Hirsch et al. in Optim lett 1:201–212, 2007). After a brief introduction to C-GRASP, we show how to download, install, configure, and use the library through an illustrative example.

Correspondence of projected 3-D points and lines using a continuous GRASP

The field of computer vision has experienced rapid growth over the past 50 years. Many computer vision problems have been solved using theory and ideas from algebraic projective geometry. In this paper, we look at a previously unsolved problem from object recognition, namely object recognition when the correspondences between the object and image data are not known a priori. We formulate this problem as a mixed-integer non-linear optimization problem in terms of the unknown projection relating the object and image, as well as the unknown assignments of object points and lines to those in the image. The global optimum of this problem recovers the relationship between the object points and lines with those in the image. When certain assumptions are enforced on the allowable projections mapping the object into the image, a proof is provided which permits one to solve the optimization problem via a simple decomposition. We illustrate this decomposition approach on some example scenarios.

Double Azeotropy: calculations with Newton-like methods and continuous GRASP (C-GRASP)

Azeotropy is a thermodynamic phenomenon where a boiling liquid produces a vapour with identical composition. This situation is a challenge for separation engineering, since distillation processes explore the differences among relative volatilities and, thus, an azeotrope can be a barrier for the separation. In binary mixtures, the azeotropy calculation problem is characterised by a 2 × 2 non-linear system with pressure or temperature and a molar fraction as unknowns. An interesting and rare case is the so-called double azeotropy, when this non-linear system has two solutions, corresponding to two distinct azeotropes. In this paper, we present some numerical aspects of double azeotropy using classical approaches (Newton’s methods with globalisation techniques) and a new non-linear optimisation algorithm (the C-GRASP method).

Continuous GRASP with a local active-set method for bound-constrained global optimization

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic--based on the CGRASP and GENCAN methods--for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP---GENCAN on a set of benchmark multimodal test functions.

Solving systems of nonlinear equations with continuous GRASP

A method for finding all roots of a system of nonlinear equations is described. Our method makes use of C-GRASP, a recently proposed continuous global optimization heuristic. Given a nonlinear system, we solve a corresponding adaptively modified global optimization problem multiple times, each time using C-GRASP, with areas of repulsion around roots that have already been found. The heuristic makes no use of derivative information. We illustrate the approach using systems found in the literature.