Penalty Function Methods for Constrained Optimization with Genetic Algorithms

Yeniay, Özgür

doi:10.3390/mca10010045

Cited by 399 publications

(242 citation statements)

References 26 publications

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“…Secondly the mean and median NFE required to solve the GNEP (Example 2) is almost twice that required to solve the NEP (Example 1). This should not come as a surprise because constrained problems are known [121] to be harder to solve than unconstrained ones. Finally, the constraint violation of all examples at termination is 0 as shown in the last row of Table 7.…”

Section: Discussionmentioning

confidence: 99%

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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%

“…In the past few years many techniques have been proposed. Among others these include penalty methods [121], adaptive techniques [104], techniques based on multiobjective optimisation [25,65] etc. The penalty method transforms the constrained problem into an unconstrained one.…”

Section: Overview Of Constraint Handling Techniques With Meta-heuristicsmentioning

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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“…Since some constraints are likely to be violated, they are penalized and infeasible solutions are fined using Eq. (16) [48].…”

Section: Solution Codingmentioning

confidence: 99%

Bi-objective vibration damping optimization for congested location–pricing problem

Hajipour

Farahani

2016

Computers & Operations Research

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This paper presents a bi-objective mathematical programming model for the restricted facility location problem, under a congestion and pricing policy. Motivated by various applications such as locating server on internet mirror sites and communication networks, this research investigates congested systems with immobile servers and stochastic demand as M/M/m/k queues. For this problem, we consider two simultaneous perspectives; (1) customers who desire to limit waiting time for service and (2) service providers who intend to increase profits. We formulate a bi-objective facility location problem with two objective functions: (i) maximizing total profit of the whole system and (ii) minimizing the sum of waiting time in queues; the model type is mixed-integer nonlinear. Then, a multi-objective optimization algorithm based on vibration theory (so-called multi-objective vibration damping optimization (MOVDO)), is developed to solve the model. Moreover, the Taguchi method is also implemented, using a response metric to tune the parameters.The results are analyzed and compared with a non-dominated sorting genetic algorithm (NSGA-II) as a well-developed multi-objective evolutionary optimization algorithm. Computational results demonstrate the efficiency of the proposed MOVDO to solve large-scale problems.

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“…GA is initially designed to handle unconstrained optimisation problems, there is a need to use additional tools to keep the solutions within the feasible domain [16]. The penalty function method is the most commonly used method to handle the constraints and it is also used in this paper.…”

Section: Genetic Algorithm With a Non-stationary Penalty Functionmentioning

confidence: 99%

A multiple objective optimisation model for building energy efficiency investment decision

Malatji

Zhang

Xia

2013

Energy and Buildings

122

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A multiple objective optimisation model is formulated to help decision makers to make an optimal decision when investing in energy-efficient building retrofitting.The objectives are to maximise the energy savings and minimise the payback period for a given fixed initial investment. The model is formulated as a multiobjective optimisation problem with the net present value (NPV), initial investment, energy target and payback period as constraints and it is solved using genetic algorithms (GAs). The optimal decision is reached by choosing the most optimal actions during energy retrofit in buildings. The model is applied to a case study of a building with 25 facilities that can be retrofitted that illustrates the potential of high energy savings and short payback periods. The sensitivity analysis is also performed by analysing the influence of the auditing error of the facilities, wrongly specified energy savings, the initial investment, changes in interest rate and the changes of electricity prices on the payback period, the maximum energy saved and NPV of the investment. The outcome of this analysis proves that the model is robust.

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Penalty Function Methods for Constrained Optimization with Genetic Algorithms

Cited by 399 publications

References 26 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

Bi-objective vibration damping optimization for congested location–pricing problem

A multiple objective optimisation model for building energy efficiency investment decision

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