scholarly journals An Improved Artificial Electric Field Algorithm for Multi-Objective Optimization

Processes ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 584
Author(s):  
Hemant Petwal ◽  
Rinkle Rani
Keyword(s):  
Electric Field ◽  
Density Estimation ◽  
Optimization Problems ◽  
Population Based ◽  
Population Diversity ◽  
Multi Objective Optimization ◽  
Local Optima ◽  
Multi Objective ◽  
Polynomial Mutation ◽  
Optimum Solution

Real-world problems such as scientific, engineering, mechanical, etc., are multi-objective optimization problems. In order to achieve an optimum solution to such problems, multi-objective optimization algorithms are used. A solution to a multi-objective problem is to explore a set of candidate solutions, each of which satisfies the required objective without any other solution dominating it. In this paper, a population-based metaheuristic algorithm called an artificial electric field algorithm (AEFA) is proposed to deal with multi-objective optimization problems. The proposed algorithm utilizes the concepts of strength Pareto for fitness assignment and the fine-grained elitism selection mechanism to maintain population diversity. Furthermore, the proposed algorithm utilizes the shift-based density estimation approach integrated with strength Pareto for density estimation, and it implements bounded exponential crossover (BEX) and polynomial mutation operator (PMO) to avoid solutions trapping in local optima and enhance convergence. The proposed algorithm is validated using several standard benchmark functions. The proposed algorithm’s performance is compared with existing multi-objective algorithms. The experimental results obtained in this study reveal that the proposed algorithm is highly competitive and maintains the desired balance between exploration and exploitation to speed up convergence towards the Pareto optimal front.

A Strength Pareto Gravitational Search Algorithm for Multi-Objective Optimization Problems

2015 ◽  
Vol 29 (06) ◽  
pp. 1559010 ◽  
Author(s):  
Xiaohui Yuan ◽  
Zhihuan Chen ◽  
Yanbin Yuan ◽  
Yuehua Huang ◽  
Xiaopan Zhang
Keyword(s):  
Optimization Problems ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Population Diversity ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Local Optima ◽  
Multi Objective ◽  
Fine Grained ◽  
Gravitational Search

A novel strength Pareto gravitational search algorithm (SPGSA) is proposed to solve multi-objective optimization problems. This SPGSA algorithm utilizes the strength Pareto concept to assign the fitness values for agents and uses a fine-grained elitism selection mechanism to keep the population diversity. Furthermore, the recombination operators are modeled in this approach to decrease the possibility of trapping in local optima. Experiments are conducted on a series of benchmark problems that are characterized by difficulties in local optimality, nonuniformity, and nonconvexity. The results show that the proposed SPGSA algorithm performs better in comparison with other related works. On the other hand, the effectiveness of two subtle means added to the GSA are verified, i.e. the fine-grained elitism selection and the use of SBX and PMO operators. Simulation results show that these measures not only improve the convergence ability of original GSA, but also preserve the population diversity adequately, which enables the SPGSA algorithm to have an excellent ability that keeps a desirable balance between the exploitation and exploration so as to accelerate the convergence speed to the true Pareto-optimal front.

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.

Optimization of Vehicle-Borne Radar Antenna Pedestal Based on Modified NSGA-II

2014 ◽  
Vol 945-949 ◽  
pp. 2241-2247
Author(s):  
De Gao Zhao ◽  
Qiang Li
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Population Diversity ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Sorting Process ◽  
Definition Of ◽  
Radar Antenna ◽  
Modified Algorithm

This paper deals with application of Non-dominated Sorting Genetic Algorithm with elitism (NSGA-II) to solve multi-objective optimization problems of designing a vehicle-borne radar antenna pedestal. Five technical improvements are proposed due to the disadvantages of NSGA-II. They are as follow: (1) presenting a new method to calculate the fitness of individuals in population; (2) renewing the definition of crowding distance; (3) introducing a threshold for choosing elitist; (4) reducing some redundant sorting process; (5) developing a self-adaptive arithmetic cross and mutation probability. The modified algorithm can lead to better population diversity than the original NSGA-II. Simulation results prove rationality and validity of the modified NSGA-II. A uniformly distributed Pareto front can be obtained by using the modified NSGA-II. Finally, a multi-objective problem of designing a vehicle-borne radar antenna pedestal is settled with the modified algorithm.

scholarly journals Comparative Study of Knee-Based Algorithms for Many-Objective Optimization Problems

2018 ◽  
Vol 12 (1) ◽  
pp. 7-16
Author(s):  
Saad M. Alzahrani ◽  
Naruemon Wattanapongsakorn
Keyword(s):  
Optimization Problems ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Trade Off ◽  
Knee Region ◽  
Multi Objective ◽  
Trade Offs ◽  
Conflicting Objectives ◽  
Small Set ◽  
Optimum Solution

Nowadays, most real-world optimization problems consist of many and often conflicting objectives to be optimized simultaneously. Although, many current Multi-Objective optimization algorithms can efficiently solve problems with 3 or less objectives, their performance deteriorates proportionally with the increasing of the objectives number. Furthermore, in many situations the decision maker (DM) is not interested in all trade-off solutions obtained but rather interested in a single optimum solution or a small set of those trade-offs. Therefore, determining an optimum solution or a small set of trade-off solutions is a difficult task. However, an interesting method for finding such solutions is identifying solutions in the Knee region. Solutions in the Knee region can be considered the best obtained solution in the obtained trade-off set especially if there is no preference or equally important objectives. In this paper, a pruning strategy was used to find solutions in the Knee region of Pareto optimal fronts for some benchmark problems obtained by NSGA-II, MOEA/D-DE and a promising new Multi-Objective optimization algorithm NSGA-III. Lastly, those knee solutions found were compared and evaluated using a generational distance performance metric, computation time and a statistical one-way ANOVA test.

A DYNAMIC POLYNOMIAL MUTATION FOR EVOLUTIONARY MULTI-OBJECTIVE OPTIMIZATION ALGORITHMS

2011 ◽  
Vol 20 (01) ◽  
pp. 209-219 ◽  
Author(s):  
MOHAMMAD HAMDAN
Keyword(s):  
Performance Metrics ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Local Optima ◽  
Multi Objective ◽  
Multiobjective Optimization Problems ◽  
Evolutionary Optimization Algorithms ◽  
Dynamic Version ◽  
Polynomial Mutation ◽  
Multiobjective Algorithms

Polynomial mutation is widely used in evolutionary optimization algorithms as a variation operator. In previous work on the use of evolutionary algorithms for solving multi-objective problems, two versions of polynomial mutations were introduced. The first is non-highly disruptive that is not prone to local optima and the second is highly disruptive polynomial mutation. This paper looks at the two variants and proposes a dynamic version of polynomial mutation. The experimental results show that the proposed adaptive algorithm is doing well for three evolutionary multiobjective algorithms on well known multiobjective optimization problems in terms of convergence speed, generational distance and hypervolume performance metrics.

A CLUSTERING-BASED NICHING FRAMEWORK FOR THE APPROXIMATION OF EQUIVALENT PARETO-SUBSETS

2011 ◽  
Vol 10 (03) ◽  
pp. 295-311 ◽  
Author(s):  
OLIVER KRAMER ◽  
HOLGER DANIELSIEK
Keyword(s):  
Optimization Problems ◽  
Kernel Density ◽  
Population Based ◽  
Multi Objective Optimization ◽  
Decision Space ◽  
Multi Objective ◽  
Pareto Sets ◽  
Density Clustering ◽  
Different Characteristics ◽  
Different Parts

In many optimization problems in practice, multiple objectives have to be optimized at the same time. Some multi-objective problems are characterized by multiple connected Pareto-sets at different parts in decision space — also called equivalent Pareto-subsets. We assume that the practitioner wants to approximate all Pareto-subsets to be able to choose among various solutions with different characteristics. In this work, we propose a clustering-based niching framework for multi-objective population-based approaches that allows to approximate equivalent Pareto-subsets. Iteratively, the clustering process assigns the population to niches, and the multi-objective optimization process concentrates on each niche independently. Two exemplary hybridizations, rake selection and DBSCAN, as well as SMS-EMOA and kernel density clustering demonstrate that the niching framework allows enough diversity to detect and approximate equivalent Pareto-subsets.

Manufacturer Order Fulfillment Based on Multi-Objective Optimization NSGA II Model

2013 ◽  
Vol 340 ◽  
pp. 136-140
Author(s):  
Liang You Shu ◽  
Ling Xiao Yang
Keyword(s):  
Optimization Model ◽  
Optimization Problems ◽  
Population Based ◽  
Pareto Optimal ◽  
Order Fulfillment ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Pareto Optimal Front ◽  
Multi Objective ◽  
Local Search Procedure

The aim of this paper is to study the production and delivery decision problem in the Manufacturer Order Fulfillment. Owing to the order fulfillment optimization condition of the manufacturer, the multi-objective optimization model of manufacturers' production and delivery has been founded. The solution of the multi-objective optimization model is also very difficult. Fast and Elitist Non-dominated Sorting Genetic Algorithm (NSGA II) have been applied successfully to various test and real-world optimization problems. These population based the algorithm provide a diverse set of non-dominated solutions. The obtained non-dominated set is close to the true Pareto-optimal front. But its convergence to the true Pareto-optimal front is not guaranteed. Hence SBX is used as a local search procedure. The proposed procedure is successfully applied to a special case. The results validate that the algorithm is effective to the multi-objective optimization model.

scholarly journals Matrix Adaptation Evolution Strategy with Multi-Objective Optimization for Multimodal Optimization

Algorithms ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 56
Author(s):  
Wei Li
Keyword(s):  
Covariance Matrix ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Population Diversity ◽  
Evolution Strategy ◽  
Multimodal Optimization ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Covariance Matrix Adaptation ◽  
Adaptation Evolution

The standard covariance matrix adaptation evolution strategy (CMA-ES) is highly effective at locating a single global optimum. However, it shows unsatisfactory performance for solving multimodal optimization problems (MMOPs). In this paper, an improved algorithm based on the MA-ES, which is called the matrix adaptation evolution strategy with multi-objective optimization algorithm, is proposed to solve multimodal optimization problems (MA-ESN-MO). Taking advantage of the multi-objective optimization in maintaining population diversity, MA-ESN-MO transforms an MMOP into a bi-objective optimization problem. The archive is employed to save better solutions for improving the convergence of the algorithm. Moreover, the peaks found by the algorithm can be maintained until the end of the run. Multiple subpopulations are used to explore and exploit in parallel to find multiple optimal solutions for the given problem. Experimental results on CEC2013 test problems show that the covariance matrix adaptation with Niching and the multi-objective optimization algorithm (CMA-NMO), CMA Niching with the Mahalanobis Metric and the multi-objective optimization algorithm (CMA-NMM-MO), and matrix adaptation evolution strategy Niching with the multi-objective optimization algorithm (MA-ESN-MO) have overall better performance compared with the covariance matrix adaptation evolution strategy (CMA-ES), matrix adaptation evolution strategy (MA-ES), CMA Niching (CMA-N), CMA-ES Niching with Mahalanobis Metric (CMA-NMM), and MA-ES-Niching (MA-ESN).

scholarly journals A Novel Coupling Algorithm Based on Glowworm Swarm Optimization and Bacterial Foraging Algorithm for Solving Multi-Objective Optimization Problems

Algorithms ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 61 ◽  
Author(s):  
Yechuang Wang ◽  
Zhihua Cui ◽  
Wuchao Li
Keyword(s):  
Optimization Problems ◽  
Multi Objective Optimization ◽  
Swarm Optimization ◽  
Good Balance ◽  
Multi Objective ◽  
Bacterial Foraging ◽  
Glowworm Swarm Optimization ◽  
Bacterial Foraging Algorithm ◽  
Polynomial Mutation ◽  
Coupling Algorithm

In the real word, optimization problems in multi-objective optimization (MOP) and dynamic optimization can be seen everywhere. During the last decade, among various swarm intelligence algorithms for multi-objective optimization problems, glowworm swarm optimization (GSO) and bacterial foraging algorithm (BFO) have attracted increasing attention from scholars. Although many scholars have proposed improvement strategies for GSO and BFO to keep a good balance between convergence and diversity, there are still many problems to be solved carefully. In this paper, a new coupling algorithm based on GSO and BFO (MGSOBFO) is proposed for solving dynamic multi-objective optimization problems (dMOP). MGSOBFO is proposed to achieve a good balance between exploration and exploitation by dividing into two parts. Part I is in charge of exploitation by GSO and Part II is in charge of exploration by BFO. At the same time, the simulation binary crossover (SBX) and polynomial mutation are introduced into the MGSOBFO to enhance the convergence and diversity ability of the algorithm. In order to show the excellent performance of the algorithm, we experimentally compare MGSOBFO with three algorithms on the benchmark function. The results suggests that such a coupling algorithm has good performance and outperforms other algorithms which deal with dMOP.

scholarly journals Non-dominated sorting Harris’s hawk multi-objective optimizer based on reference point approach

2019 ◽  
Vol 15 (3) ◽  
pp. 1603 ◽  
Author(s):  
Shaymah Akram Yasear ◽  
Ku Ruhana Ku-Mahamud
Keyword(s):  
Reference Point ◽  
Pareto Front ◽  
Optimization Problems ◽  
Population Diversity ◽  
Experimental Results ◽  
Multi Objective Optimization ◽  
Next Generation ◽  
Multi Objective ◽  
Objective Space ◽  
Reference Point Approach

A non-dominated sorting Harris’s hawk multi-objective optimizer (NDSHHMO) algorithm is presented in this paper. The algorithm is able to improve the population diversity, convergence of non-dominated solutions toward the Pareto front, and prevent the population from trapping into local optimal. This was achieved by integrating fast non-dominated sorting with the original Harris’s hawk multi-objective optimizer (HHMO).  Non-dominated sorting divides the objective space into levels based on fitness values and then selects non-dominated solutions to produce the next generation of hawks. A set of well-known multi-objective optimization problems has been used to evaluate the performance of the proposed NDSHHMO algorithm. The results of the NDSHHMO algorithm were verified against the results of an HHMO algorithm. Experimental results demonstrate the efficiency of the proposed NDSHHMO algorithm in terms of enhancing the ability of convergence toward the Pareto front and significantly improve the search ability of the HHMO.

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