Search Biases in Constrained Evolutionary Optimization

Rúnarsson, Thomas Philip; Yao, Xin

doi:10.1109/tsmcc.2004.841906

Cited by 414 publications

(237 citation statements)

References 19 publications

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“…Algorithm 3 with a population size, π = 50 and allowed a maximum of 250 iterations. Following [99,100], the probability factor, η used in SR was set to 0.45. Table 7 reports the mean,median and standard deviations (SD) of the number of function evaluations (NFE) over the 30 independent runs of DEBLP-SR to meet the convergence criteria (i.e.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Koh

2013

Metaheuristics for Bi-Level Optimization

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Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. Several problems arising in engineering and economics can be cast within the bi-level programming framework. The bi-level programming model is also known as a Stackleberg or leader-follower game in which the leader chooses his variables so as to optimise his objective function, taking into account the response of the follower(s) who separately optimise their own objectives, treating the leader's decisions as exogenous. In this chapter, we present a unified framework fully consistent with the Stackleberg paradigm of bi-level programming that allows for the integration of meta-heuristic algorithms with traditional gradient based optimisation algorithms for the solution of bi-level programming problems. In particular we employ Differential Evolution as the main meta-heuristic in our proposal. We subsequently apply the proposed method (DEBLP) to a range of problems from many fields such as transportation systems management, parameter estimation and game theory. It is demonstrated that DEBLP is a robust and powerful search heuristic for this class of problems characterised by non smoothness and non convexity.

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Section: Discussionmentioning

confidence: 99%

“…Runarsson and Yao [99,100] proposed an alternative constraint handling method known as stochastic ranking (SR) 7 to aid in answering this question. To use SR, the first step is to obtain a measure of the constraint violation, v(x k ), of vector x k using Eqn.…”

Section: Stochastic Rankingmentioning

confidence: 99%

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Koh

2013

Metaheuristics for Bi-Level Optimization

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“…IVRA was used to reduce the search space and thereafter optimizers were used within this reduced space to find the optima. The optimization algorithms tested were Controlled Random Search (CRS) with local mutation (Kaelo and Ali 2006) and Improved Stochastic Ranking Evolution Strategy (ISRES) (Runarsson and Yao 2005).…”

Section: Methodsmentioning

confidence: 99%

Classification aided domain reduction for high dimensional optimization

Singh

Ferranti

Deschrijver

et al. 2014

Proceedings of the Winter Simulation Conference 2014

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Engineering design optimization often involves computationally expensive time consuming simulations. Although surrogate-based optimization has been used to alleviate the problem to some extent, surrogate models (like Kriging) struggle as the dimensionality of the problem increases to medium-scale. The enormity of the design space in higher dimensions (above ten) makes the search for optima challenging and time consuming. This paper proposes the use of probabilistic support vector machine classifiers to reduce the search space for optimization. The proposed technique transforms the optimization problem into a binary classification problem to differentiate between feasible (likely containing the optima) and infeasible (not likely containing the optima) regions. A model-driven sampling scheme selects batches of probably-feasible samples while reducing the search space. The result is a reduced subspace within which existing optimization algorithms can be used to find the optima. The technique is validated on analytical benchmark problems.

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“…In this paper, the upper level constraints in Eq 2 are handled using stochastic ranking [20]. Hence this version of DEBLP is termed DEBLP-SR.…”

Section: Differential Evolution For Bi-level Programmingmentioning

confidence: 99%

“…(See [20] for more details). In the first iteration (line 9) the best member of the population is the member that is assigned a rank of 1 (one) by the SR algorithm.…”

Section: Differential Evolution For Bi-level Programmingmentioning

confidence: 99%

Differential Evolution Based Bi-Level Programming Algorithm for Computing Normalized Nash Equilibrium

Koh

2011

Advances in Intelligent and Soft Computing

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The Generalised Nash Equilibrium Problem (GNEP) is a Nash game with the distinct feature that the feasible strategy set of a player depends on the strategies chosen by all her opponents in the game. This characteristic distinguishes the GNEP from a conventional Nash Game. These shared constraints on each player's decision space, being dependent on decisions of others in the game, increases its computational difficulty. A special solution of the GNEP is the Nash Normalized Equilibrium which can be obtained by transforming the GNEP into a bi-level program with an optimal value of zero in the upper level. In this paper, we propose a Differential Evolution based Bi-Level Programming algorithm embodying Stochastic Ranking to handle constraints (DEBLP-SR) to solve the resulting bi-level programming formulation. Numerical examples of GNEPs drawn from the literature are used to illustrate the performance of the proposed algorithm.

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Search Biases in Constrained Evolutionary Optimization

Cited by 414 publications

References 19 publications

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Classification aided domain reduction for high dimensional optimization

Differential Evolution Based Bi-Level Programming Algorithm for Computing Normalized Nash Equilibrium

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