72,042 research outputs found
Constraint Handling in Efficient Global Optimization
This is the author accepted manuscript. The final version is available from ACM via the DOI in this record.Real-world optimization problems are often subject to several constraints which are expensive to evaluate in terms of cost or time. Although a lot of effort is devoted to make use of surrogate models for expensive optimization tasks, not many strong surrogate-assisted algorithms can address the challenging constrained problems. Efficient Global Optimization (EGO) is a Kriging-based surrogate-assisted algorithm. It was originally proposed to address unconstrained problems and later was modified to solve constrained problems. However, these type of algorithms still suffer from several issues, mainly: (1) early stagnation, (2) problems with multiple active constraints and (3) frequent crashes. In this work, we introduce a new EGO-based algorithm which tries to overcome these common issues with Kriging optimization algorithms. We apply the proposed algorithm on problems with dimension d ≤ 4 from the G-function suite [16] and on an airfoil shape example.This research was partly funded by Tekes, the Finnish Funding Agency for Innovation (the DeCoMo project), and by the Engineering and Physical Sciences Research Council [grant numbers EP/N017195/1, EP/N017846/1]
On Optimization over the Efficient Set in Linear Multicriteria Programming
The efficient set of a linear multicriteria programming problem can be representedby a reverse convex constraint of the form g(z) ≤ 0, where g is a concavefunction. Consequently, the problem of optimizing some real function over the efficientset belongs to an important problem class of global optimization called reverseconvex programming. Since the concave function used in the literature is only definedon some set containing the feasible set of the underlying multicriteria programmingproblem, most global optimization techniques for handling this kind of reverse convexconstraint cannot be applied. The main purpose of our article is to present amethod for overcoming this disadvantage. We construct a concave function which isfinitely defined on the whole space and can be considered as an extension of the existingfunction. Different forms of the linear multicriteria programming problem arediscussed, including the minimum maximal flow problem as an example
Interval propagation and search on directed acyclic graphs for numerical constraint solving
The fundamentals of interval analysis on directed acyclic graphs (DAGs) for global optimization and constraint propagation have recently been proposed in Schichl and Neumaier (J. Global Optim. 33, 541-562, 2005). For representing numerical problems, the authors use DAGs whose nodes are subexpressions and whose directed edges are computational flows. Compared to tree-based representations [Benhamou etal. Proceedings of the International Conference on Logic Programming (ICLP'99), pp. 230-244. Las Cruces, USA (1999)], DAGs offer the essential advantage of more accurately handling the influence of subexpressions shared by several constraints on the overall system during propagation. In this paper we show how interval constraint propagation and search on DAGs can be made practical and efficient by: (1) flexibly choosing the nodes on which propagations must be performed, and (2) working with partial subgraphs of the initial DAG rather than with the entire graph. We propose a new interval constraint propagation technique which exploits the influence of subexpressions on all the constraints together rather than on individual constraints. We then show how the new propagation technique can be integrated into branch-and-prune search to solve numerical constraint satisfaction problems. This algorithm is able to outperform its obvious contenders, as shown by the experiment
Penalty-free feasibility boundary convergent multi-objective evolutionary algorithm for the optimization of water distribution systems
This paper presents a new penalty-free multi-objective evolutionary approach (PFMOEA) for the optimization of water distribution systems (WDSs). The proposed approach utilizes pressure dependent analysis (PDA) to develop a multi-objective evolutionary search. PDA is able to simulate both normal and pressure deficient networks and provides the means to accurately and rapidly identify the feasible region of the solution space, effectively locating global or near global optimal solutions along its active constraint boundary. The significant advantage of this method over previous methods is that it eliminates the need for ad-hoc penalty functions, additional “boundary search” parameters, or special constraint handling procedures. Conceptually, the approach is downright straightforward and probably the simplest hitherto. The PFMOEA has been applied to several WDS benchmarks and its performance examined. It is demonstrated that the approach is highly robust and efficient in locating optimal solutions. Superior results in terms of the initial network construction cost and number of hydraulic simulations required were obtained. The improvements are demonstrated through comparisons with previously published solutions from the literature
Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control
Constrained optimization of high-dimensional numerical problems plays an
important role in many scientific and industrial applications. Function
evaluations in many industrial applications are severely limited and no
analytical information about objective function and constraint functions is
available. For such expensive black-box optimization tasks, the constraint
optimization algorithm COBRA was proposed, making use of RBF surrogate modeling
for both the objective and the constraint functions. COBRA has shown remarkable
success in solving reliably complex benchmark problems in less than 500
function evaluations. Unfortunately, COBRA requires careful adjustment of
parameters in order to do so.
In this work we present a new self-adjusting algorithm SACOBRA, which is
based on COBRA and capable to achieve high-quality results with very few
function evaluations and no parameter tuning. It is shown with the help of
performance profiles on a set of benchmark problems (G-problems, MOPTA08) that
SACOBRA consistently outperforms any COBRA algorithm with fixed parameter
setting. We analyze the importance of the several new elements in SACOBRA and
find that each element of SACOBRA plays a role to boost up the overall
optimization performance. We discuss the reasons behind and get in this way a
better understanding of high-quality RBF surrogate modeling
State-of-the-art in aerodynamic shape optimisation methods
Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners
Constraint handling strategies in Genetic Algorithms application to optimal batch plant design
Optimal batch plant design is a recurrent issue in Process Engineering, which can be formulated as a Mixed Integer Non-Linear Programming(MINLP) optimisation problem involving specific constraints, which can be, typically, the respect of a time horizon for the synthesis of various
products. Genetic Algorithms constitute a common option for the solution of these problems, but their basic operating mode is not always wellsuited to any kind of constraint treatment: if those cannot be integrated in variable encoding or accounted for through adapted genetic operators,
their handling turns to be a thorny issue. The point of this study is thus to test a few constraint handling techniques on a mid-size example in order to determine which one is the best fitted, in the framework of one particular problem formulation. The investigated methods are the elimination of infeasible individuals, the use of a penalty term added in the minimized criterion, the relaxation of the discrete variables upper bounds, dominancebased tournaments and, finally, a multiobjective strategy. The numerical computations, analysed in terms of result quality and of computational time, show the superiority of elimination technique for the former criterion only when the latter one does not become a bottleneck. Besides, when the problem complexity makes the random location of feasible space too difficult, a single tournament technique proves to be the most efficient
one
- …