A New Algorithm for Multilevel Optimization Problems Using Evolutionary Strategy, Inspired by Natural Adaptation

Tilahun, Surafel Luleseged; Kassa, Semu Mitiku; Ong, Hong Choon

doi:10.1007/978-3-642-32695-0_51

Cited by 12 publications

(6 citation statements)

References 19 publications

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“…In [21,23] evolutionary type approaches have been proposed to solve general non-linear MLOPs. The methods take the variables from other levels as fixed values and solve the problem at each levels starting from the upper level optimization problem down to the most inner level optimization problem.…”

Section: The Set Of Solutionsmentioning

confidence: 42%

A branch-and-bound multi-parametric programming approach for non-convex multilevel optimization with polyhedral constraints

Kassa

2015

J Glob Optim

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In this paper we develop a general but smooth global optimization strategy for nonlinear multilevel programming problems with polyhedral constraints. At each decision level successive convex relaxations are applied over the non-convex terms in combination with a multi-parametric programming approach. The proposed algorithm reaches the approximate global optimum in a finite number of steps through the successive subdivision of the optimization variables that contribute to the non-convexity of the problem and partitioning of the parameter space. The method is implemented and tested for a variety of bilevel, trilevel and fifth level problems which have non-convexity formulation at their inner levels.

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Section: The Set Of Solutionsmentioning

confidence: 42%

A branch-and-bound multi-parametric programming approach for non-convex multilevel optimization with polyhedral constraints

Kassa

2015

J Glob Optim

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“…They are very common in engineering, management and in many other disciplines. Different researchers used the concept of optimization in different applications, including engineering applications, transportation planning, management applications, economics, computational intelligence, decision science, agriculture, tourism, sport science and even political science [7][8][9][10][11][12][13][14][15][16][17][18].…”

Section: Optimization Problemsmentioning

confidence: 99%

A Review and Comparative Study of Firefly Algorithm and its Modified Versions

Khan¹,

Hamadneh²,

Tilahun³

et al. 2016

Optimization Algorithms - Methods and Applications

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Firefly algorithm is one of the well-known swarm-based algorithms which gained popularity within a short time and has different applications. It is easy to understand and implement. The existing studies show that it is prone to premature convergence and suggest the relaxation of having constant parameters. To boost the performance of the algorithm, different modifications are done by several researchers. In this chapter, we will review these modifications done on the standard firefly algorithm based on parameter modification, modified search strategy and change the solution space to make the search easy using different probability distributions. The modifications are done for continuous as well as non-continuous problems. Different studies including hybridization of firefly algorithm with other algorithms, extended firefly algorithm for multiobjective as well as multilevel optimization problems, for dynamic problems, constraint handling and convergence study will also be briefly reviewed. A simulationbased comparison will also be provided to analyse the performance of the standard as well as the modified versions of the algorithm. . IntroductionAn optimization problem refers to the maximization or minimization of an objective function by setting suitable values for the variables from a set of feasible values. These problems appear not only in complex scientific studies but also in our day-to-day activities. For instance, when a person wants to go from one place to another and has multiple possible routes, a decision needs to be made on which route to take. The decision can be with the objective to minimize travel time, fuel consumption and so on. However, these kinds of problems with fewer number of alternatives can easily be solved by looking at the outcome of each of the alternatives. However, in real problems, it is not always the case to have a finite and small number of alternatives. Hence, different solution methods are proposed based on the behaviour of the problem. Firefly algorithm is among those metaheuristic algorithms which have different applications. Its uncomplicated and easy steps with its effectiveness attract researchers from different disciplines it. Different studies have been performed to modify the standard firefly algorithm to boost its performance and to make it suitable for a problem at hand. In this chapter, a comprehensive study will be presented on firefly algorithm and its modified versions. A brief discussion on extended firefly algorithm with other relevant studies will also be provided. In the next section, a discussion on optimization problems with their solution methods will be given followed by a review on studies on firefly algorithm, which includes a discussion on the standard firefly algorithm with its modified versions and other relevant studies on firefly algorithm, in Section . In Section , a comparative study based on simulation results will be presented followed by summary of the chapter in Section . . Optimization problemsDecision-making problems can be found ...

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“…x n has been proposed in [21] for general n-level optimization problems. The effect of updating x i on the decision variables x i+1 , .…”

Section: Introductionmentioning

confidence: 99%

A Gradient Method for Multilevel Optimization

Sato¹,

Tanaka²

2021

Preprint

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Although application examples of multilevel optimization have already been discussed since the '90s, the development of solution methods was almost limited to bilevel cases due to the difficulty of the problem. In recent years, in machine learning, Franceschi et al. have proposed a method for solving bilevel optimization problems by replacing their lower-level problems with the T steepest descent update equations with some prechosen iteration number T . In this paper, we have developed a gradient-based algorithm for multilevel optimization with n levels based on their idea and proved that our reformulation with nT variables asymptotically converges to the original multilevel problem. As far as we know, this is one of the first algorithms with some theoretical guarantee for multilevel optimization. Numerical experiments show that a trilevel hyperparameter learning model considering data poisoning produces more stable prediction results than an existing bilevel hyperparameter learning model in noisy data settings.Preprint. Under review.

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A New Algorithm for Multilevel Optimization Problems Using Evolutionary Strategy, Inspired by Natural Adaptation

Cited by 12 publications

References 19 publications

A branch-and-bound multi-parametric programming approach for non-convex multilevel optimization with polyhedral constraints

A branch-and-bound multi-parametric programming approach for non-convex multilevel optimization with polyhedral constraints

A Review and Comparative Study of Firefly Algorithm and its Modified Versions

A Gradient Method for Multilevel Optimization

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