Large-scale Global Optimization Problems Research Articles

Parallel Implementation of Synchronous Type Artificial Bee Colony Algorithm for Global Optimization

Evolutionary algorithms often need huge running times when solving large-scale optimization problems. One of the solutions for this issue is to introduce parallelization into the algorithm. To benefit from this approach for the artificial bee colony optimization algorithm, we present a new synchronous and parallel version of the algorithm. Performances of the proposed version and the original asynchronous algorithm are compared in terms of efficiency and speedup. Algorithms are competed to solve 20 large-scale global optimization problems. Comparative results show that the proposed parallel algorithm is still efficient as asynchronous version while it requires much less time to solve complex and large problems.

Global Optimization of Tersoff Clusters Using Differential Evolution with Inexact Line Search

Differential Evolution with Inexact Line Search (DEILS) is proposed to determination of the ground-state geometry of atom clusters. DEILS algorithm adopts probabilistic inexact line search method in acceptance rule of differential evolution to accelerate the convergence as the region of global minimum is approached. More realistic many-body potential energy functions, namely the Tersoff and Tersoff-like semi-empirical potentials for silicon, are considered. Numerical studies indicate that the new algorithm is considerably faster and more reliable than original differential evolution algorithm, especially for large-scale global optimization problem of MBP6/Si(C). Moreover, some ground-state solutions, which are superior to the known best solution given in literature, are reported.

A DIRECT-based approach exploiting local minimizations for the solution of large-scale global optimization problems

In this paper we propose a new algorithm for solving difficult large-scale global optimization problems. We draw our inspiration from the well-known DIRECT algorithm which, by exploiting the objective function behavior, produces a set of points that tries to cover the most interesting regions of the feasible set. Unfortunately, it is well-known that this strategy suffers when the dimension of the problem increases. As a first step we define a multi-start algorithm using DIRECT as a deterministic generator of starting points. Then, the new algorithm consists in repeatedly applying the previous multi-start algorithm on suitable modifications of the variable space that exploit the information gained during the optimization process. The efficiency of the new algorithm is pointed out by a consistent numerical experimentation involving both standard test problems and the optimization of Morse potential of molecular clusters.

Local optima smoothing for global optimization

It is widely believed that in order to solve large-scale global optimization problems, an appropriate mixture of local approximation and global exploration is necessary. Local approximation, if first-order information on the objective function is available, is efficiently performed by means of local optimization methods. Unfortunately, global exploration, in absence of some kind of global information on the problem, is a ‘blind’ procedure, aimed at placing observations as evenly as possible in the search domain. Often, this procedure reduces to uniform random sampling (like in Multistart algorithms or in techniques based on clustering). In this paper, we propose a new framework for global exploration which tries to guide random exploration towards the region of attraction of low-level local optima. The main idea originated by the use of smoothing techniques (based on Gaussian convolutions): the possibility of applying a smoothing transformation not to the objective function but to the result of local searches seems to have never been explored yet. Although an exact smoothing of the results of local searches is impossible to implement, in this paper we propose a computational approximation scheme which has proven to be very efficient and (maybe more important) extremely robust in solving large-scale global optimization problems with huge numbers of local optima and, in particular, for problems displaying a ‘funnel’ structure.

Global Optimization in Multiproduct and Multipurpose Batch Design under Uncertainty

This paper addresses the design of multiproduct and multipurpose batch plants with uncertainty in both product demands and processing parameters. The uncertain demands may be described by any continuous/discrete probability distribution. Uncertain processing parameters are handled in a scenario-based approach. Through the relaxation of the feasibility requirement, the design problem with a fixed number of pieces of equipment per stage is formulated as a single large-scale nonconvex optimization problem. This problem is solved using a branch and bound technique in which a convex relaxation of the original nonconvex problem is solved to provide a lower bound on the global solution. Several different expressions for the tight convex lower bounding functions are proposed. Using these expressions, a tight lower bound on the global optimum solution can be obtained at each iteration. The αBB algorithm is subsequently employed to refine the upper and lower bounds and converge to the global solution. The tight lower bounds and the efficiency of the proposed approach is demonstrated in several example problems. These case studies correspond to large-scale global optimization problems with nonconvex constraints ranging in number from 25 to 3750, variables ranging from 30 to 15 636 and nonconvex terms ranging from 50 to 15 000. It is shown that such large-scale multiproduct and multipurpose batch design problems can be solved to global optimality with reasonable computational effort.

A view of the limitations, opportunities, and challenges in parallel nonlinear optimization

The availability and power of parallel and distributed computers is having a significant impact on how expensive problems are solved in all areas of numerical computation, and is likely to have an even larger impact in the future. This paper presents a view of how the consideration of parallelism is affecting, and is likely to affect, one important field within numerical computation, the field of nonlinear optimization. It does not attempt to survey the research that has been done in parallel nonlinear optimization. Rather it presents a set of examples, drawn mainly from our own research, that illustrate many of the limitations, opportunities, and challenges inherent in incorporating parallelism into the field of nonlinear optimization. These examples include parallel methods for unconstrained optimization problems with a small to moderate number of variables, parallel methods for large block bordered systems of nonlinear equations, and parallel methods for small-scale and large-scale global optimization problems. Our overall conclusions are mixed. For most generic optimization problems with a small to moderate number of variables, the consideration of parallelism does not appear to be leading to major algorithmic innovations. For many classes of large-scale problems, however, the consideration of parallelism appears to be creating opportunities for the development of interesting new methods that may be advantageous on parallel and sometimes even on sequential computers. In addition, a number of large-scale parallel optimization algorithms exhibit irregular, coarse-grain structure, which leads to interesting computer science challenges in areas such as dynamic scheduling and load-balancing.