Firefly Algorithm for Optimization Problem

2013 ◽  
Vol 421 ◽  
pp. 512-517 ◽  
Author(s):  
Nur Farahlina Johari ◽  
Azlan Mohd Zain ◽  
Mustaffa H. Noorfa ◽  
Amirmudin Udin
Keyword(s):  
Computer Science ◽  
Firefly Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Metaheuristic Algorithms ◽  
Science And Engineering ◽  
Multi Objective

This paper reviews the applications of Firefly Algorithm (FA) in various domain of optimization problem. Optimization is a process of determining the best solution to make something as functional and effective as possible by minimizing or maximizing the parameters involved in the problems. Several categories of optimization problem such as discrete, chaotic, multi-objective and many more are addressed by inspiring the behavior of fireflies as mentioned in the literatures. Literatures found that FA was mostly applied by researchers to solve the optimization problems in Computer Science and Engineering domain. Some of them are enhanced or hybridized with other techniques to discover better performance. In addition, literatures found that most of the cases that used FA technique have outperformed compare to other metaheuristic algorithms.

Toward the Use of Pareto Performance Solutions and Pareto Robustness Solutions for Multi-Objective Robust Optimization Problems

2012 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis ◽  
Oscar Brito Augusto
Keyword(s):  
Robust Optimization ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Multi Objective Optimization ◽  
Robust Solutions ◽  
Multi Objective ◽  
Robust Optimization Problem ◽  
Design Solutions ◽  
Further Development

For Multi-Objective Robust Optimization Problem (MOROP), it is important to obtain design solutions that are both optimal and robust. To find these solutions, usually, the designer need to set a threshold of the variation of Performance Functions (PFs) before optimization, or add the effects of uncertainties on the original PFs to generate a new Pareto robust front. In this paper, we divide a MOROP into two Multi-Objective Optimization Problems (MOOPs). One is the original MOOP, another one is that we take the Robustness Functions (RFs), robust counterparts of the original PFs, as optimization objectives. After solving these two MOOPs separately, two sets of solutions come out, namely the Pareto Performance Solutions (PP) and the Pareto Robustness Solutions (PR). Make a further development on these two sets, we can get two types of solutions, namely the Pareto Robustness Solutions among the Pareto Performance Solutions (PR(PP)), and the Pareto Performance Solutions among the Pareto Robustness Solutions (PP(PR)). Further more, the intersection of PR(PP) and PP(PR) can represent the intersection of PR and PP well. Then the designer can choose good solutions by comparing the results of PR(PP) and PP(PR). Thanks to this method, we can find out the optimal and robust solutions without setting the threshold of the variation of PFs nor losing the initial Pareto front. Finally, an illustrative example highlights the contributions of the paper.

Multi-Objective Robust Optimization Under Interval Uncertainty Using Online Approximation and Constraint Cuts

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
W. Hu ◽  
M. Li ◽  
S. Azarm ◽  
A. Almansoori
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Computational Effort ◽  
Interval Uncertainty ◽  
Test Results ◽  
Robust Solution ◽  
Multi Objective ◽  
Function Calls ◽  
Level Problem ◽  
Upper Level

Many engineering optimization problems are multi-objective, constrained and have uncertainty in their inputs. For such problems it is desirable to obtain solutions that are multi-objectively optimum and robust. A robust solution is one that as a result of input uncertainty has variations in its objective and constraint functions which are within an acceptable range. This paper presents a new approximation-assisted MORO (AA-MORO) technique with interval uncertainty. The technique is a significant improvement, in terms of computational effort, over previously reported MORO techniques. AA-MORO includes an upper-level problem that solves a multi-objective optimization problem whose feasible domain is iteratively restricted by constraint cuts determined by a lower-level optimization problem. AA-MORO also includes an online approximation wherein optimal solutions from the upper- and lower-level optimization problems are used to iteratively improve an approximation to the objective and constraint functions. Several examples are used to test the proposed technique. The test results show that the proposed AA-MORO reasonably approximates solutions obtained from previous MORO approaches while its computational effort, in terms of the number of function calls, is significantly reduced compared to the previous approaches.

A Hybrid Optimization Algorithm for Single and Multi-Objective Optimization Problems

2017 ◽  
pp. 491-521 ◽  
Author(s):  
Rizk M. Rizk-Allah ◽  
Aboul Ella Hassanien
Keyword(s):  
Optimization Algorithm ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Hybrid Optimization ◽  
Multi Objective Optimization ◽  
Local Optima ◽  
Fruit Fly Optimization ◽  
Multi Objective ◽  
Hybrid Optimization Algorithm

This chapter presents a hybrid optimization algorithm namely FOA-FA for solving single and multi-objective optimization problems. The proposed algorithm integrates the benefits of the fruit fly optimization algorithm (FOA) and the firefly algorithm (FA) to avoid the entrapment in the local optima and the premature convergence of the population. FOA operates in the direction of seeking the optimum solution while the firefly algorithm (FA) has been used to accelerate the optimum seeking process and speed up the convergence performance to the global solution. Further, the multi-objective optimization problem is scalarized to a single objective problem by weighting method, where the proposed algorithm is implemented to derive the non-inferior solutions that are in contrast to the optimal solution. Finally, the proposed FOA-FA algorithm is tested on different benchmark problems whether single or multi-objective aspects and two engineering applications. The numerical comparisons reveal the robustness and effectiveness of the proposed algorithm.

An Interactive Neural Network for Constrained Multi-Objective Optimization with Application to the Design of Digital Filters

2012 ◽  
Vol 433-440 ◽  
pp. 2808-2816
Author(s):  
Jian Jin Zheng ◽  
You Shen Xia
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Computational Complexity ◽  
Digital Filters ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Objective

This paper presents a new interactive neural network for solving constrained multi-objective optimization problems. The constrained multi-objective optimization problem is reformulated into two constrained single objective optimization problems and two neural networks are designed to obtain the optimal weight and the optimal solution of the two optimization problems respectively. The proposed algorithm has a low computational complexity and is easy to be implemented. Moreover, the proposed algorithm is well applied to the design of digital filters. Computed results illustrate the good performance of the proposed algorithm.

The Relationship between Metaheuristics Stopping Criteria and Performances

2014 ◽  
Vol 5 (3) ◽  
pp. 44-70 ◽  
Author(s):  
Mohamed-Mahmoud Ould Sidi ◽  
Bénédicte Quilot-Turion ◽  
Abdeslam Kadrani ◽  
Michel Génard ◽  
Françoise Lescourret
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Statistical Tests ◽  
Particle Swarm ◽  
Computational Time ◽  
Plant Management ◽  
Stopping Criterion ◽  
Nsga Ii ◽  
Multi Objective ◽  
Crowding Distance

A major difficulty in the use of metaheuristics (i.e. evolutionary and particle swarm algorithms) to deal with multi-objective optimization problems is the choice of a convenient point at which to stop computation. Indeed, it is difficult to find the best compromise between the stopping criterion and the algorithm performance. This paper addresses this issue using the Non-dominated Sorting Genetic Algorithm (NSGA-II) and the Multi-Objective Particle Swarm Optimization with Crowding Distance (MOPSO-CD) for the model-based design of sustainable peach fruits. The optimization problem of interest contains three objectives: maximize fruit fresh mass, maximize fruit sugar content, and minimize the crack density on the fruit skin. This last objective targets a reduction in the use of fungicides and can thus enhance preservation of the environment and human health. Two versions of the NSGA-II and two of the MOPSO-CD were applied to tackle this difficult optimization problem: the original versions with a maximum number of generations used as stopping criterion and modified versions using the stopping criterion proposed by the authors of (Roudenko & Schoenauer, 2004). This second stopping criterion is based on the stabilization of the maximal crowding distance and aims to stop computation when many generations are performed without further improvement in the quality of the solutions. A benchmark consisting of four plant management scenarios has been used to compare the performances of the original versions (OV) and the modified versions (MV) of the NSGA-II and the MOPSO-CD. Twelve independent simulations were performed for each version and for each scenario, and a high number of generations were generated for the OV (e.g., 1500 for the NSGA-II and 200 for the MOPSO-CD). This paper compares the performances of the two versions of both algorithms using four standard metrics and statistical tests. For both algorithms, the MV obtained solutions similar in quality to those of the OV but after significantly fewer generations. The resulting reduction in computational time for the optimization step will provide opportunities for further studies on the sustainability of peach ideotypes.

A Two-Phase Complete Algorithm for Multi-Objective Distributed Constraint Optimization

2014 ◽  
Vol 18 (4) ◽  
pp. 573-580
Author(s):  
Alexandre Medi ◽  
◽  
Tenda Okimoto ◽  
Katsumi Inoue ◽  
◽  
...  
Keyword(s):  
Branch And Bound ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Branch And Bound Algorithm ◽  
Constraint Optimization ◽  
Distributed Constraint Optimization ◽  
Multi Objective ◽  
Multi Agent ◽  
Distributed Constraint Optimization Problem

A Distributed Constraint Optimization Problem (DCOP) is a fundamental problem that can formalize various applications related to multi-agent cooperation. Many application problems in multi-agent systems can be formalized as DCOPs. However, many real world optimization problems involve multiple criteria that should be considered separately and optimized simultaneously. A Multi-Objective Distributed Constraint Optimization Problem (MO-DCOP) is an extension of a mono-objective DCOP. Compared to DCOPs, there exists few works on MO-DCOPs. In this paper, we develop a novel complete algorithm for solving an MO-DCOP. This algorithm utilizes a widely used method called Pareto Local Search (PLS) to generate an approximation of the Pareto front. Then, the obtained information is used to guide the search thresholds in a Branch and Bound algorithm. In the evaluations, we evaluate the runtime of our algorithm and show empirically that using a Pareto front approximation obtained by a PLS algorithm allows to significantly speed-up the search in a Branch and Bound algorithm.

An Improved Constrained Optimization Multi-Objective Genetic Algorithm and its Application in Engineering

2014 ◽  
Vol 962-965 ◽  
pp. 2903-2908
Author(s):  
Yun Lian Liu ◽  
Wen Li ◽  
Tie Bin Wu ◽  
Yun Cheng ◽  
Tao Yun Zhou ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Constrained Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Crossover Operator ◽  
Multi Objective Optimization ◽  
Constrained Optimization Problem ◽  
Great Ability ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm

An improved multi-objective genetic algorithm is proposed to solve constrained optimization problems. The constrained optimization problem is converted into a multi-objective optimization problem. In the evolution process, our algorithm is based on multi-objective technique, where the population is divided into dominated and non-dominated subpopulation. Arithmetic crossover operator is utilized for the randomly selected individuals from dominated and non-dominated subpopulation, respectively. The crossover operator can lead gradually the individuals to the extreme point and improve the local searching ability. Diversity mutation operator is introduced for non-dominated subpopulation. Through testing the performance of the proposed algorithm on 3 benchmark functions and 1 engineering optimization problems, and comparing with other meta-heuristics, the result of simulation shows that the proposed algorithm has great ability of global search. Keywords: multi-objective optimization;genetic algorithm;constrained optimization problem;engineering application

scholarly journals Comparative Analysis of Selection Hyper-Heuristics for Real-World Multi-Objective Optimization Problems

2021 ◽  
Vol 11 (19) ◽  
pp. 9153
Author(s):  
Vinicius Renan de Carvalho ◽  
Ender Özcan ◽  
Jaime Simão Sichman
Keyword(s):  
Real World ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Exact Algorithms ◽  
Mathematical Function ◽  
Multi Objective Optimization ◽  
Algorithm Selection ◽  
Multi Objective ◽  
Cross Domain ◽  
Domain Performance

As exact algorithms are unfeasible to solve real optimization problems, due to their computational complexity, meta-heuristics are usually used to solve them. However, choosing a meta-heuristic to solve a particular optimization problem is a non-trivial task, and often requires a time-consuming trial and error process. Hyper-heuristics, which are heuristics to choose heuristics, have been proposed as a means to both simplify and improve algorithm selection or configuration for optimization problems. This paper novel presents a novel cross-domain evaluation for multi-objective optimization: we investigate how four state-of-the-art online hyper-heuristics with different characteristics perform in order to find solutions for eighteen real-world multi-objective optimization problems. These hyper-heuristics were designed in previous studies and tackle the algorithm selection problem from different perspectives: Election-Based, based on Reinforcement Learning and based on a mathematical function. All studied hyper-heuristics control a set of five Multi-Objective Evolutionary Algorithms (MOEAs) as Low-Level (meta-)Heuristics (LLHs) while finding solutions for the optimization problem. To our knowledge, this work is the first to deal conjointly with the following issues: (i) selection of meta-heuristics instead of simple operators (ii) focus on multi-objective optimization problems, (iii) experiments on real world problems and not just function benchmarks. In our experiments, we computed, for each algorithm execution, Hypervolume and IGD+ and compared the results considering the Kruskal–Wallis statistical test. Furthermore, we ranked all the tested algorithms considering three different Friedman Rankings to summarize the cross-domain analysis. Our results showed that hyper-heuristics have a better cross-domain performance than single meta-heuristics, which makes them excellent candidates for solving new multi-objective optimization problems.

scholarly journals APPLICATION OF POPULATION EVOLVABILITY IN A HYPER-HEURISTIC FOR DYNAMIC MULTI-OBJECTIVE OPTIMIZATION

2019 ◽  
Vol 25 (5) ◽  
pp. 951-978 ◽  
Author(s):  
Teodoro Macias-Escobar ◽  
Laura Cruz-Reyes ◽  
Bernabé Dorronsoro ◽  
Héctor Fraire-Huacuja ◽  
Nelson Rangel-Valdez ◽  
...  
Keyword(s):  
Dynamic Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Dynamic Properties ◽  
Selection Method ◽  
Multiobjective Evolutionary Algorithms ◽  
Multi Objective Optimization ◽  
Selection Methods ◽  
Dynamic Optimization Problems ◽  
Multi Objective

It is important to know the properties of an optimization problem and the difficulty an algorithm faces to solve it. Population evolvability obtains information related to both elements by analysing the probability of an algorithm to improve current solutions and the degree of those improvements. DPEM_HH is a dynamic multi-objective hyper-heuristic that uses low-level heuristic (LLH) selection methods that apply population evolvability. DPEM_HH uses dynamic multiobjective evolutionary algorithms (DMOEAs) as LLHs to solve dynamic multi-objective optimization problems (DMOPs). Population evolvability is incorporated in DPEM_HH by calculating it on each candidate DMOEA for a set of sampled generations after a change is detected, using those values to select which LLH will be applied. DPEM_HH is tested on multiple DMOPs with dynamic properties that provide several challenges. Experimental results show that DPEM_HH with a greedy LLH selection method that uses average population evolvability values can produce solutions closer to the Pareto optimal front with equal to or better diversity than previously proposed heuristics. This shows the effectiveness and feasibility of the application of population evolvability on hyperheuristics to solve dynamic optimization problems.

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