scholarly journals Uncrowded Hypervolume-based Multi-objective Optimization with Gene-pool Optimal Mixing

2021 ◽  
pp. 1-24
Author(s):  
S. C. Maree ◽  
T. Alderliesten ◽  
P. A. N. Bosman
Keyword(s):  
Gene Pool ◽  
Optimization Problems ◽  
State Of The Art ◽  
Hybrid Approach ◽  
Population Based ◽  
Multi Objective ◽  
Approximation Set ◽  
Direct Use ◽  
Optimal Mixing ◽  
Single Objective

Abstract Domination-based multi-objective (MO) evolutionary algorithms (EAs) are today arguably the most frequently used type of MOEA. These methods however stagnate when the majority of the population becomes non-dominated, preventing further convergence to the Pareto set. Hypervolume-based MO optimization has shown promising results to overcome this. Direct use of the hypervolume however results in no selection pressure for dominated solutions. The recently introduced Sofomore framework overcomes this by solving multiple interleaved single-objective dynamic problems that iteratively improve a single approximation set, based on the uncrowded hypervolume improvement (UHVI). It thereby however loses many advantages of population-based MO optimization, such as handling multimodality. Here, we reformulate the UHVI as a quality measure for approximation sets, called the uncrowded hypervolume (UHV), which can be used to directly solve MO optimization problems with a single-objective optimizer. We use the state-of-the-art gene-pool optimal mixing evolutionary algorithm (GOMEA) that is capable of efficiently exploiting the intrinsically available greybox properties of this problem. The resulting algorithm, UHV-GOMEA, is compared to Sofomore equipped with GOMEA, and the domination-based MO-GOMEA. In doing so, we investigate in which scenarios either domination-based or hypervolume-based methods are preferred. Finally, we construct a simple hybrid approach that combines MO-GOMEA with UHV-GOMEA and outperforms both.

Multi-Objective Evolutionary Algorithms

2011 ◽  
pp. 1145-1151 ◽  
Author(s):  
Sanjoy Das ◽  
Bijaya K. Panigrahi
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Population Based ◽  
Stochastic Methods ◽  
Local Minima ◽  
Multi Objective ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
Complex Optimization ◽  
Single Objective

Real world optimization problems are often too complex to be solved through analytical means. Evolutionary algorithms, a class of algorithms that borrow paradigms from nature, are particularly well suited to address such problems. These algorithms are stochastic methods of optimization that have become immensely popular recently, because they are derivative-free methods, are not as prone to getting trapped in local minima (as they are population based), and are shown to work well for many complex optimization problems. Although evolutionary algorithms have conventionally focussed on optimizing single objective functions, most practical problems in engineering are inherently multi-objective in nature. Multi-objective evolutionary optimization is a relatively new, and rapidly expanding area of research in evolutionary computation that looks at ways to address these problems. In this chapter, we provide an overview of some of the most significant issues in multi-objective optimization (Deb, 2001).

Multi-Objective Optimization Based on Brain Storm Optimization Algorithm

2013 ◽  
Vol 4 (3) ◽  
pp. 1-21 ◽  
Author(s):  
Yuhui Shi ◽  
Jingqian Xue ◽  
Yali Wu
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Solution Space ◽  
Population Based ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Brain Storm Optimization ◽  
Objective Space ◽  
Different Characteristics ◽  
Single Objective

In recent years, many evolutionary algorithms and population-based algorithms have been developed for solving multi-objective optimization problems. In this paper, the authors propose a new multi-objective brain storm optimization algorithm in which the clustering strategy is applied in the objective space instead of in the solution space in the original brain storm optimization algorithm for solving single objective optimization problems. Two versions of multi-objective brain storm optimization algorithm with different characteristics of diverging operation were tested to validate the usefulness and effectiveness of the proposed algorithm. Experimental results show that the proposed multi-objective brain storm optimization algorithm is a very promising algorithm, at least for solving these tested multi-objective optimization problems.

Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

2021 ◽  
Vol 12 (4) ◽  
pp. 98-116
Author(s):  
Noureddine Boukhari ◽  
Fatima Debbat ◽  
Nicolas Monmarché ◽  
Mohamed Slimane
Keyword(s):  
Convergence Rate ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Hybrid Approach ◽  
Optimization Methods ◽  
Global Optimum ◽  
Stochastic Methods ◽  
Local Optima ◽  
Portfolio Optimization Problem

Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.

scholarly journals Differential Evolution: A Survey and Analysis

2018 ◽  
Vol 8 (10) ◽  
pp. 1945 ◽  
Author(s):  
Tarik Eltaeib ◽  
Ausif Mahmood
Keyword(s):  
Global Optimization ◽  
Differential Evolution ◽  
Optimization Problems ◽  
State Of The Art ◽  
Population Based ◽  
Vital Role ◽  
Fine Tuning ◽  
Control Parameters ◽  
Hybrid Techniques ◽  
Global Optimizer

Differential evolution (DE) has been extensively used in optimization studies since its development in 1995 because of its reputation as an effective global optimizer. DE is a population-based metaheuristic technique that develops numerical vectors to solve optimization problems. DE strategies have a significant impact on DE performance and play a vital role in achieving stochastic global optimization. However, DE is highly dependent on the control parameters involved. In practice, the fine-tuning of these parameters is not always easy. Here, we discuss the improvements and developments that have been made to DE algorithms. In particular, we present a state-of-the-art survey of the literature on DE and its recent advances, such as the development of adaptive, self-adaptive and hybrid techniques.

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.

A Memetic Optimization Strategy Based on Dimension Reduction in Decision Space

2015 ◽  
Vol 23 (1) ◽  
pp. 69-100 ◽  
Author(s):  
Handing Wang ◽  
Licheng Jiao ◽  
Ronghua Shang ◽  
Shan He ◽  
Fang Liu
Keyword(s):  
Dimension Reduction ◽  
Optimization Problems ◽  
State Of The Art ◽  
Search Space ◽  
Optimization Strategy ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Decision Space ◽  
Multi Objective ◽  
Decision Variables

There can be a complicated mapping relation between decision variables and objective functions in multi-objective optimization problems (MOPs). It is uncommon that decision variables influence objective functions equally. Decision variables act differently in different objective functions. Hence, often, the mapping relation is unbalanced, which causes some redundancy during the search in a decision space. In response to this scenario, we propose a novel memetic (multi-objective) optimization strategy based on dimension reduction in decision space (DRMOS). DRMOS firstly analyzes the mapping relation between decision variables and objective functions. Then, it reduces the dimension of the search space by dividing the decision space into several subspaces according to the obtained relation. Finally, it improves the population by the memetic local search strategies in these decision subspaces separately. Further, DRMOS has good portability to other multi-objective evolutionary algorithms (MOEAs); that is, it is easily compatible with existing MOEAs. In order to evaluate its performance, we embed DRMOS in several state of the art MOEAs to facilitate our experiments. The results show that DRMOS has the advantage in terms of convergence speed, diversity maintenance, and portability when solving MOPs with an unbalanced mapping relation between decision variables and objective functions.

The Hybrid Differential Evolution with Dynamic Scaling Mutation and Wrapper Local Search for Optimization Problems

2013 ◽  
Vol 479-480 ◽  
pp. 989-995
Author(s):  
Chun Liang Lu ◽  
Shih Yuan Chiu ◽  
Chih Hsu Hsu ◽  
Shi Jim Yen
Keyword(s):  
Local Search ◽  
Differential Evolution ◽  
Job Shop ◽  
Job Shop Scheduling ◽  
Optimization Problems ◽  
Search Space ◽  
Dynamic Scaling ◽  
Multi Objective ◽  
Wide Range ◽  
Single Objective

In this paper, an improved hybrid Differential Evolution (DE) is proposed to enhance optimization performance by cooperating Dynamic Scaling Mutation (DSM) and Wrapper Local Search (WLS) schemes. When evolution speed is standstill, DSM can improve searching ability to achieve better balance between exploitation and exploration in the search space. Furthermore, WLS can disturb individuals to fine tune the searching range around and then properly find better solutions in the evolution progress. The effective particle encoding representation named Particle Segment Operation-Machine Assignment (PSOMA) that we previously published is also applied to always produce feasible candidate solutions for hybrid DE model to solve the Flexible Job-Shop Scheduling Problem (FJSP). To test the performance of the proposed hybrid method, the experiments contain five frequently used CEC 2005 numerical functions and three representative FJSP benchmarks for single-objective and multi-objective optimization verifications, respectively. Compare the proposed method with the other related published algorithms, the simulation results indicate that our proposed method exhibits better performance for solving most the test functions for single-objective problems. In addition, the wide range of Pareto-optimal solutions and the more Gantt chart diversities can be obtained for the multi-objective FJSP in practical decision-making considerations.

scholarly journals A NEW PROBABILISTIC ALGORITHM FOR SOLVING A CLASS OF SINGLE OR MULTI-OBJECTIVE OPTIMAL PROBLEMS

2009 ◽  
Vol 12 (11) ◽  
pp. 11-26
Author(s):  
Hao Van Tran ◽  
Thong Huu Nguyen
Keyword(s):  
Numerical Optimization ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Fixed Number ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Probabilistic Algorithm ◽  
Multi Objective ◽  
Single Objective

We consider a class of single-objective optimization problems which haves the character: there is a fixed number k (1≤k<n) that is independent of the size n of the problem such that if we only need to change values of k variables then it has the ability to find a better solution than the current one, let us call it Ok. In this paper, we propose a new numerical optimization technique, Search Via Probability (SVP) algorithm, for solving single objective optimization problems of the class Ok. The SVP algorithm uses probabilities to control the process of searching for optimal solutions. We calculate probabilities of the appearance of a better solution than the current one on each of iterations, and on the performance of SVP algorithm we create good conditions for its appearance. We tested this approach by implementing the SVP algorithm on some test single-objective and multi objective optimization problems, and we found good and very stable results.

scholarly journals An Overview of Few Nature Inspired Optimization Techniques and Its Reliability Applications

2020 ◽  
Vol 5 (4) ◽  
pp. 732-743
Author(s):  
Nitin Uniyal ◽  
Sangeeta Pant ◽  
Anuj Kumar
Keyword(s):  
Optimization Problems ◽  
Optimization Techniques ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Research Fields ◽  
Research Problems ◽  
Nature Inspired Algorithms ◽  
New Algorithms ◽  
Single Objective

Optimization has been a hot topic due to its inevitably in the development of new algorithms in almost every applied branch of Mathematics. Despite the broadness of optimization techniques in research fields, there is always an open scope of further refinement. We present here an overview of nature-inspired optimization with a subtle background of fundamentals and classification and their reliability applications. An attempt has been made to exhibit the contrast nature of multi objective optimization as compared to single objective optimization. Though there are various techniques to achieve the optimality in optimization problems but nature inspired algorithms have proved to be very efficient and gained special attention in modern research problems. The purpose of this article is to furnish the foundation of few nature inspired optimization techniques and their reliability applications to an interested researcher.

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