An Enhanced Memetic Algorithm for Single-Objective Bilevel Optimization Problems

Abstract

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.

Modified Evolutionary Algorithm and Chaotic Search for Bilevel Programming Problems

“…As indicated in Table 3, our proposed algorithm reaches optimal solutions for two problems SMD1, SMD3 and reaches near to optimal solutions for the remaining problems. To evaluate the CGA-BS algorithm for SMD problems, we compare CGA-BS results with the other four algorithms listed in [57] and three algorithms listed in [58]. Table 4 illustrates a comparison between CGA-BS and other algorithms.…”

“…CGA-BS functions evaluations and other algorithms function evaluations for SMD test set are compared to show proposed algorithm speed convergence to reach to the optimal solution. The upper-level function evaluations of proposed algorithm and BLMA, NBLE, BLEAQ, BIDE algorithms in [57] set are presented in Table 8. The lower-level function evaluations of proposed algorithm and BLMA, NBLE, BLEAQ, BIDE algorithms in [57] are presented in Table 9.…”

“…The upper-level function evaluations of proposed algorithm and BLMA, NBLE, BLEAQ, BIDE algorithms in [57] set are presented in Table 8. The lower-level function evaluations of proposed algorithm and BLMA, NBLE, BLEAQ, BIDE algorithms in [57] are presented in Table 9. The total function evaluations for both upper-level and lower-level of proposed algorithm and other compared algorithms are presented in Table 10.…”

Optimization of a Steam Reforming Plant Modeled with Artificial Neural Networks

“…MAs can be considered to be an extension of the GA, since they use the same algorithmic schema with the introduction of an additional powerful strategy used for intensification purposes in this context, the local search. MAs have also been demonstrated to be a very successful optimization technique for hard optimization problems, as can be seen in [26][27][28].…”

Solving Pessimistic Bilevel Optimisation Problems With Evolutionary Algorithms

“…Metaheuristic and evolutionary algorithms, in general, do not need to make any assumptions about the objective functions of the problem and can be applied to general bilevel problems [3]. Examples of this kind of Bilevel Evolutionary Algorithms (BLEAs) are BlDE with Differential Evolution (DE) in both levels [4], NBLEA with Genetic Algorithm in both levels [5], a memetic approach in [6], BLEAQ with genetic algorithm and quadratic approximations [7], BL-CMA-ES with CMA-ES in both levels [8], etc. However, all these evolutionary algorithms are adopting the optimistic approach for solving the BOP, as it is easier to track.…”