An Evolutionary Algorithm Using Parameter Space Searching for Interval Linear Fractional Bilevel Programming Problems

2016 ◽  
Vol 30 (04) ◽  
pp. 1659011
Author(s):  
Hecheng Li ◽  
Zhicang Wang
Keyword(s):  
Evolutionary Algorithm ◽  
Parameter Space ◽  
Optimization Problems ◽  
Search Space ◽  
Interval Numbers ◽  
Bilevel Program ◽  
Fractional Programs ◽  
Interval Linear ◽  
Bilevel Programming Problems ◽  
The Right

Interval programming is one of main approaches treating imprecise and uncertain elements involved in optimization problems. In this paper, an interval linear fractional bilevel program is considered, which is characterized in that both objective coefficients and the right-hand side vector are interval numbers, and an evolutionary algorithm (EA) is proposed to solve the problem. First, the interval parameter space of the follower’s problem is taken as the search space of the proposed EA. For each individual, one can evaluate it by dealing with a simplified interval bilevel program in which only the leader’s objective involves interval parameters. In addition, the optimality conditions of linear fractional programs are applied to convert and solve the simplified problem. Finally, some computational examples were solved and the results show that the proposed algorithm is efficient and robust.

scholarly journals An Evolutionary Algorithm Using Duality-Base-Enumerating Scheme for Interval Linear Bilevel Programming Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hecheng Li ◽  
Lei Fang
Keyword(s):  
Evolutionary Algorithm ◽  
Bilevel Programming ◽  
Search Space ◽  
Linear Programs ◽  
Single Level ◽  
Linear Bilevel Programming ◽  
Interval Linear ◽  
Bilevel Programming Problems ◽  
The Right ◽  
Nonlinear Equality

Interval bilevel programming problem is hard to solve due to its hierarchical structure as well as the uncertainty of coefficients. This paper is focused on a class of interval linear bilevel programming problems, and an evolutionary algorithm based on duality bases is proposed. Firstly, the objective coefficients of the lower level and the right-hand-side vector are uniformly encoded as individuals, and the relative intervals are taken as the search space. Secondly, for each encoded individual, based on the duality theorem, the original problem is transformed into a single level program simply involving one nonlinear equality constraint. Further, by enumerating duality bases, this nonlinear equality is deleted, and the single level program is converted into several linear programs. Finally, each individual can be evaluated by solving these linear programs. The computational results of 7 examples show that the algorithm is feasible and robust.

Multimodal Optimization Using a Bi-Objective Evolutionary Algorithm

2012 ◽  
Vol 20 (1) ◽  
pp. 27-62 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Amit Saha
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Search Space ◽  
Test Problems ◽  
Multimodal Optimization ◽  
Optimal Solutions ◽  
Optimization Task ◽  
Pareto Optimal Set ◽  
Single Objective

In a multimodal optimization task, the main purpose is to find multiple optimal solutions (global and local), so that the user can have better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable optimum solution. To this end, evolutionary optimization algorithms (EA) stand as viable methodologies mainly due to their ability to find and capture multiple solutions within a population in a single simulation run. With the preselection method suggested in 1970, there has been a steady suggestion of new algorithms. Most of these methodologies employed a niching scheme in an existing single-objective evolutionary algorithm framework so that similar solutions in a population are deemphasized in order to focus and maintain multiple distant yet near-optimal solutions. In this paper, we use a completely different strategy in which the single-objective multimodal optimization problem is converted into a suitable bi-objective optimization problem so that all optimal solutions become members of the resulting weak Pareto-optimal set. With the modified definitions of domination and different formulations of an artificially created additional objective function, we present successful results on problems with as large as 500 optima. Most past multimodal EA studies considered problems having only a few variables. In this paper, we have solved up to 16-variable test problems having as many as 48 optimal solutions and for the first time suggested multimodal constrained test problems which are scalable in terms of number of optima, constraints, and variables. The concept of using bi-objective optimization for solving single-objective multimodal optimization problems seems novel and interesting, and more importantly opens up further avenues for research and application.

Localization for Solving Noisy Multi-Objective Optimization Problems

2009 ◽  
Vol 17 (3) ◽  
pp. 379-409 ◽  
Author(s):  
Lam T. Bui ◽  
Hussein A. Abbass ◽  
Daryl Essam
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Search Space ◽  
Local Models ◽  
Multi Objective Optimization ◽  
Global Models ◽  
Average Performance ◽  
Multi Objective ◽  
Wide Range ◽  
Filter Noise

This paper investigates the use of a framework of local models in the context of noisy evolutionary multi-objective optimization. Within this framework, the search space is explicitly divided into several nonoverlapping hyperspheres. A direction of improvement, which is related to the average performance of the spheres, is used for moving solutions within each sphere. This helps the local models to filter noise and increase the robustness of the evolutionary algorithm in the presence of noise. A wide range of noisy problems we used for testing and the experimental results demonstrate the ability of local models to better filter noise in comparison with that of global models.

WHO: A New Evolutionary Algorithm Bio-Inspired by Wildebeests with a Case Study on Bank Customer Segmentation

2019 ◽  
Vol 33 (05) ◽  
pp. 1959017 ◽  
Author(s):  
Mohammad Mahdi Motevali ◽  
Ali Mohammadi Shanghooshabad ◽  
Reza Zohouri Aram ◽  
Hamidreza Keshavarz
Keyword(s):  
Data Mining ◽  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Banking Sector ◽  
Optimization Problems ◽  
High Mobility ◽  
Search Space ◽  
Customer Segmentation ◽  
Advantages And Disadvantages ◽  
And Migration

Numerous evolutionary algorithms have been proposed which are inspired by the amazing lives of creatures, such as animals, insects, and birds. Each inspired algorithm has its own advantages and disadvantages, and has its own way to accomplish exploration and exploitation. In this paper, a new evolutionary algorithm with novel concepts, called Wildebeests Herd Optimization (WHO), is proposed. This algorithm is inspired by the splendid life of wildebeests in Africa. Moving and migration are inseparable from wildebeests’ lives. When a wildebeest wants to choose its path during migration, it considers the best path known to itself, the location of the more mature wildebeests in the crowd, and the direction of wildebeests with high mobility. The WHO algorithm imitates these traits, and can concurrently explore and exploit the search space. For validating WHO, it is applied to optimization problems and data mining tasks. It is demonstrated that WHO outperforms other evolutionary algorithms, such as genetic algorithm (GA) and particle swarm optimization, in the assessed problems. Then, WHO is applied to the customer segmentation problem. Customer segmentation is one of the most important tasks of data mining, especially in the banking sector. In this paper, the customers of a bank with current accounts are segmented using WHO based on four aspects: profitability, cost, loyalty and credit; some of these aspects are calculated in a novel way. The results were welcome by the bank authorities.

Automatic Mining of Quantitative Association Rules with Gravitational Search Algorithm

2017 ◽  
Vol 27 (03) ◽  
pp. 343-372 ◽  
Author(s):  
Umit Can ◽  
Bilal Alatas
Keyword(s):  
Association Rules ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Fitness Function ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Search Space ◽  
Search Method ◽  
Quantitative Association Rules ◽  
Gravitational Search

The classical optimization algorithms are not efficient in solving complex search and optimization problems. Thus, some heuristic optimization algorithms have been proposed. In this paper, exploration of association rules within numerical databases with Gravitational Search Algorithm (GSA) has been firstly performed. GSA has been designed as search method for quantitative association rules from the databases which can be regarded as search space. Furthermore, determining the minimum values of confidence and support for every database which is a hard job has been eliminated by GSA. Apart from this, the fitness function used for GSA is very flexible. According to the interested problem, some parameters can be removed from or added to the fitness function. The range values of the attributes have been automatically adjusted during the time of mining of the rules. That is why there is not any requirements for the pre-processing of the data. Attributes interaction problem has also been eliminated with the designed GSA. GSA has been tested with four real databases and promising results have been obtained. GSA seems an effective search method for complex numerical sequential patterns mining, numerical classification rules mining, and clustering rules mining tasks of data mining.

scholarly journals Solving knapsack problems using a binary gaining sharing knowledge-based optimization algorithm

2021 ◽  
Author(s):  
Prachi Agrawal ◽  
Talari Ganesh ◽  
Ali Wagdy Mohamed
Keyword(s):  
Life Span ◽  
Population Size ◽  
Linear Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Search Space ◽  
Knapsack Problems ◽  
Local Optima ◽  
Knowledge Based ◽  
Two Stages

AbstractThis article proposes a novel binary version of recently developed Gaining Sharing knowledge-based optimization algorithm (GSK) to solve binary optimization problems. GSK algorithm is based on the concept of how humans acquire and share knowledge during their life span. A binary version of GSK named novel binary Gaining Sharing knowledge-based optimization algorithm (NBGSK) depends on mainly two binary stages: binary junior gaining sharing stage and binary senior gaining sharing stage with knowledge factor 1. These two stages enable NBGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. Moreover, to enhance the performance of NBGSK and prevent the solutions from trapping into local optima, NBGSK with population size reduction (PR-NBGSK) is introduced. It decreases the population size gradually with a linear function. The proposed NBGSK and PR-NBGSK applied to set of knapsack instances with small and large dimensions, which shows that NBGSK and PR-NBGSK are more efficient and effective in terms of convergence, robustness, and accuracy.

scholarly journals Binary Spring Search Algorithm for Solving Various Optimization Problems

2021 ◽  
Vol 11 (3) ◽  
pp. 1286 ◽  
Author(s):  
Mohammad Dehghani ◽  
Zeinab Montazeri ◽  
Ali Dehghani ◽  
Om P. Malik ◽  
Ruben Morales-Menendez ◽  
...  
Keyword(s):  
Optimization Algorithm ◽  
High Performance ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Bat Algorithm ◽  
Search Space ◽  
Binary Particle Swarm Optimization ◽  
Dragonfly Algorithm ◽  
Grasshopper Optimization Algorithm

One of the most powerful tools for solving optimization problems is optimization algorithms (inspired by nature) based on populations. These algorithms provide a solution to a problem by randomly searching in the search space. The design’s central idea is derived from various natural phenomena, the behavior and living conditions of living organisms, laws of physics, etc. A new population-based optimization algorithm called the Binary Spring Search Algorithm (BSSA) is introduced to solve optimization problems. BSSA is an algorithm based on a simulation of the famous Hooke’s law (physics) for the traditional weights and springs system. In this proposal, the population comprises weights that are connected by unique springs. The mathematical modeling of the proposed algorithm is presented to be used to achieve solutions to optimization problems. The results were thoroughly validated in different unimodal and multimodal functions; additionally, the BSSA was compared with high-performance algorithms: binary grasshopper optimization algorithm, binary dragonfly algorithm, binary bat algorithm, binary gravitational search algorithm, binary particle swarm optimization, and binary genetic algorithm. The results show the superiority of the BSSA. The results of the Friedman test corroborate that the BSSA is more competitive.

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