Unconstrained scalable test problems for single-objective bilevel optimization

2012 ◽  
Author(s):  
Ankur Sinha ◽  
Pekka Malo ◽  
Kalyanmoy Deb
Keyword(s):  
Bilevel Optimization ◽  
Test Problems ◽  
Single Objective

scholarly journals Test Problem Construction for Single-Objective Bilevel Optimization

2014 ◽  
Vol 22 (3) ◽  
pp. 439-477 ◽  
Author(s):  
Ankur Sinha ◽  
Pekka Malo ◽  
Kalyanmoy Deb
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Algorithm ◽  
Test Problem ◽  
Bilevel Optimization ◽  
Standard Test ◽  
Test Problems ◽  
Problem Construction ◽  
Constrained Problems ◽  
Construction Procedure ◽  
Single Objective

In this paper, we propose a procedure for designing controlled test problems for single-objective bilevel optimization. The construction procedure is flexible and allows its user to control the different complexities that are to be included in the test problems independently of each other. In addition to properties that control the difficulty in convergence, the procedure also allows the user to introduce difficulties caused by interaction of the two levels. As a companion to the test problem construction framework, the paper presents a standard test suite of 12 problems, which includes eight unconstrained and four constrained problems. Most of the problems are scalable in terms of variables and constraints. To provide baseline results, we have solved the proposed test problems using a nested bilevel evolutionary algorithm. The results can be used for comparison, while evaluating the performance of any other bilevel optimization algorithm. The code related to the paper may be accessed from the website http://bilevel.org .

A Surrogate Assisted Approach for Single-Objective Bilevel Optimization

2017 ◽  
Vol 21 (5) ◽  
pp. 681-696 ◽  
Author(s):  
Md Monjurul Islam ◽  
Hemant Kumar Singh ◽  
Tapabrata Ray
Keyword(s):  
Bilevel Optimization ◽  
Single Objective

scholarly journals Optimistic Variants of Single-Objective Bilevel Optimization for Evolutionary Algorithms

2020 ◽  
Vol 19 (03) ◽  
pp. 2050020
Author(s):  
Anuraganand Sharma
Keyword(s):  
Optimization Problems ◽  
Bilevel Optimization ◽  
Benchmark Problems ◽  
New Variant ◽  
Real World Applications ◽  
Bilevel Problems ◽  
Specialized Form ◽  
Comparative Statistical Analysis ◽  
Constraint Optimization Problems ◽  
Single Objective

Single-objective bilevel optimization is a specialized form of constraint optimization problems where one of the constraints is an optimization problem itself. These problems are typically non-convex and strongly NP-Hard. Recently, there has been an increased interest from the evolutionary computation community to model bilevel problems due to its applicability in real-world applications for decision-making problems. In this work, a partial nested evolutionary approach with a local heuristic search has been proposed to solve the benchmark problems and have outstanding results. This approach relies on the concept of intermarriage-crossover in search of feasible regions by exploiting information from the constraints. A new variant has also been proposed to the commonly used convergence approaches, i.e., optimistic and pessimistic. It is called an extreme optimistic approach. The experimental results demonstrate the algorithm converges differently to known optimum solutions with the optimistic variants. Optimistic approach also outperforms pessimistic approach. Comparative statistical analysis of our approach with other recently published partial to complete evolutionary approaches demonstrates very competitive results.

An Enhanced Memetic Algorithm for Single-Objective Bilevel Optimization Problems

2017 ◽  
Vol 25 (4) ◽  
pp. 607-642 ◽  
Author(s):  
Md Monjurul Islam ◽  
Hemant Kumar Singh ◽  
Tapabrata Ray ◽  
Ankur Sinha
Keyword(s):  
Local Search ◽  
Memetic Algorithm ◽  
Optimization Problems ◽  
Computational Cost ◽  
Real Life ◽  
Practical Interest ◽  
Bilevel Optimization ◽  
Standard Test ◽  
Computational Effort ◽  
Test Problems

Bilevel optimization, as the name reflects, deals with optimization at two interconnected hierarchical levels. The aim is to identify the optimum of an upper-level  leader problem, subject to the optimality of a lower-level follower problem. Several problems from the domain of engineering, logistics, economics, and transportation have an inherent nested structure which requires them to be modeled as bilevel optimization problems. Increasing size and complexity of such problems has prompted active theoretical and practical interest in the design of efficient algorithms for bilevel optimization. Given the nested nature of bilevel problems, the computational effort (number of function evaluations) required to solve them is often quite high. In this article, we explore the use of a Memetic Algorithm (MA) to solve bilevel optimization problems. While MAs have been quite successful in solving single-level optimization problems, there have been relatively few studies exploring their potential for solving bilevel optimization problems. MAs essentially attempt to combine advantages of global and local search strategies to identify optimum solutions with low computational cost (function evaluations). The approach introduced in this article is a nested Bilevel Memetic Algorithm (BLMA). At both upper and lower levels, either a global or a local search method is used during different phases of the search. The performance of BLMA is presented on twenty-five standard test problems and two real-life applications. The results are compared with other established algorithms to demonstrate the efficacy of the proposed approach.

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.

scholarly journals An integrated cuckoo search optimizer for single and multi-objective optimization problems

2021 ◽  
Vol 7 ◽  
pp. e370
Author(s):  
Xiangbo Qi ◽  
Zhonghu Yuan ◽  
Yan Song
Keyword(s):  
Optimization Problems ◽  
Cuckoo Search ◽  
Search Strategies ◽  
Comprehensive Analysis ◽  
Experimental Results ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Multiple Strategies ◽  
Single Objective

Integrating heterogeneous biological-inspired strategies and mechanisms into one algorithm can avoid the shortcomings of single algorithm. This article proposes an integrated cuckoo search optimizer (ICSO) for single objective optimization problems, which incorporates the multiple strategies into the cuckoo search (CS) algorithm. The paper also considers the proposal of multi-objective versions of ICSO called MOICSO. The two algorithms presented in this paper are benchmarked by a set of benchmark functions. The comprehensive analysis of the experimental results based on the considered test problems and comparisons with other recent methods illustrate the effectiveness of the proposed integrated mechanism of different search strategies and demonstrate the performance superiority of the proposed algorithm.

ROTATED PROBLEMS AND ROTATIONALLY INVARIANT CROSSOVER IN EVOLUTIONARY MULTI-OBJECTIVE OPTIMIZATION

2008 ◽  
Vol 07 (02) ◽  
pp. 149-186 ◽  
Author(s):  
ANTONY IORIO ◽  
XIAODONG LI
Keyword(s):  
Evolutionary Algorithms ◽  
Coordinate System ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Problem Domain ◽  
Nsga Ii ◽  
Multi Objective ◽  
Parameter Interactions ◽  
Rotationally Invariant ◽  
Single Objective

Problems that are not aligned with the coordinate system can present difficulties to many optimization algorithms, including evolutionary algorithms, by trapping the search on a ridge. The ridge problem in single-objective optimization is understood, but until now little work has been done on understanding this issue in the multi-objective domain. Multi-objective problems with parameter interactions present difficulties to an optimization algorithm, which are not present in the single-objective domain. In this work, we have explained the nature of these difficulties, and investigated the behavior of the NSGA-II, which has difficulties with problems not aligned with the principle coordinate system. This study has investigated Simplex Crossover (SPX), Unimodal Normally Distributed Crossover (UNDX), Parent-Centric Crossover (PCX), and Differential Evolution (DE), as possible alternatives to the Simulated Binary Crossover (SBX) operator within the NSGA-II, on problems exhibiting parameter interactions through a rotation of the coordinate system. An analysis of these operators on three rotated bi-objective test problems, and a four-and eight-objective problem is provided. New observations on the behavior of rotationally invariant crossover operators in the multi-objective problem domain have been reported.

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