smoof: Single- and Multi-Objective Optimization Test Functions

Most real-world problems that have two or three objectives are dynamic, and the environment of the problems may change as time goes on. For the purpose of solving dynamic multi-objective problems better, two proposed strategies (second-order difference strategy and random strategy) were incorporated with NSGA-III, namely SDNSGA-III. When the environment changes in SDNSGA-III, the second-order difference strategy and random strategy are first used to improve the individuals in the next generation population, then NSGA-III is employed to optimize the individuals to obtain optimal solutions. Our experiments were conducted with two primary objectives. The first was to test the values of the metrics mean inverted generational distance (MIGD), mean generational distance (MGD), and mean hyper volume (MHV) on the test functions (Fun1 to Fun6) via the proposed algorithm and the four state-of-the-art algorithms. The second aim was to compare the metrics’ value of NSGA-III with single strategy and SDNSGA-III, proving the efficiency of the two strategies in SDNSGA-III. The comparative data obtained from the experiments demonstrate that SDNSGA-III has good convergence and diversity compared with four other evolutionary algorithms. What is more, the efficiency of second-order difference strategy and random strategy was also analyzed in this paper.

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Improving firefly-based multi-objective optimization based on attraction law and crowding distance

Statistics Optimization & Information Computing ◽

10.19139/soic-2310-5070-382 ◽

2020 ◽

Vol 8 (1) ◽

pp. 229-241

Author(s):

Farid Shayesteh ◽

Reihaneh Kardehi Moghaddam

Keyword(s):

Heuristic Algorithms ◽

Optimization Problems ◽

Differential Evolution Algorithm ◽

Bees Algorithm ◽

Test Functions ◽

Multi Objective Optimization ◽

Multi Objective ◽

Crowding Distance ◽

Simulation Results ◽

Law Of Attraction

Multi-objective optimization problems are so designed that they simultaneously minimize several objectives functions (which are sometimes contradictory). In most cases, the objectives are in conflict with each other such that optimization of one objective does not lead to the optimization of another ones. Therefore, we should achieve a certain balance of goals to solve these problems, which usually requires the application of an intelligent method. In this regard, use of meta-heuristic algorithms will be associated with resolved problems. In this paper, we propose a new multi-objective firefly optimization method which is designed based on the law of attraction and crowding distance. The proposed methods efficiency has been evaluated by three valid test functions containing convex, nonconvex and multi discontinuous convex Pareto fronts. Simulation results confirm the significant accuracy of proposed method in defining the Pareto front for all three test functions. In addition, the simulation results indicates that proposed algorithm has higher accuracy and greater convergence speed, compared to other well known multi-objective algorithms such as non-dominated sorting genetic algorithm, Bees algorithm, Differential Evolution algorithm and Strong Pareto Evolutionary Algorithm.

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On Test Functions for Evolutionary Multi-objective Optimization

Lecture Notes in Computer Science - Parallel Problem Solving from Nature - PPSN VIII ◽

10.1007/978-3-540-30217-9_80 ◽

2004 ◽

pp. 792-802 ◽

Cited By ~ 51

Author(s):

Tatsuya Okabe ◽

Yaochu Jin ◽

Markus Olhofer ◽

Bernhard Sendhoff

Keyword(s):

Test Functions ◽

Multi Objective Optimization ◽

Multi Objective

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Multi-objective colliding bodies optimization algorithm for design of trusses

Journal of Computational Design and Engineering ◽

10.1016/j.jcde.2018.04.001 ◽

2018 ◽

Vol 6 (1) ◽

pp. 49-59 ◽

Cited By ~ 4

Author(s):

Ali Kaveh ◽

Vahid Reza Mahdavi

Keyword(s):

Computational Cost ◽

Parameter Tuning ◽

Population Based ◽

Test Functions ◽

Objective Functions ◽

Multi Objective Optimization ◽

Simple Formulation ◽

Multi Objective ◽

Colliding Bodies Optimization ◽

Single Solution

Abstract This article presents a new population-based optimization algorithm to solve the multi-objective optimization problems of truss structures. This method is based on the recently developed single-solution algorithm proposed by the present authors, so called colliding bodies optimization (CBO), with each agent solution being considered as an object or body with mass. In the proposed multi-objective colliding bodies optimization (MOCBO) algorithm, the collision theory strategy as the search process is utilized and the Maximin fitness procedure is incorporated to the CBO for sorting the agents. A series of well-known test functions with different characteristics and number of objective functions are studied. In order to measure the accuracy and efficiency of the proposed algorithm, its results are compared to those of the previous methods available in the literature, such as SPEA2, NSGA-II and MOPSO algorithms. Thereafter, two truss structural examples considering bi-objective functions are optimized. The performance of the proposed algorithm is more accurate and requires a lower computational cost than the other considered algorithms. In addition, the present methodology uses simple formulation and does not require internal parameter tuning. Highlights A new population-based algorithm is presented for multi-objective optimization. The algorithm is based on the recently developed single-solution colliding bodies optimization (CBO). The proposed multi-objective colliding bodies optimization is abbreviated as MOCBO. MOCBO utilizes the maximin fitness procedure for sorting the agents. A series of well-known test functions and number of objective functions are studied. The MOCBO is more accurate and requires lower computational cost. The MOCBO method uses simple formulation and requires no internal parameter tuning.

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Study of Greedy Genetic Algorithm for Multi-Objective Optimization

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.291-294.2874 ◽

2013 ◽

Vol 291-294 ◽

pp. 2874-2877

Author(s):

Shi Fang Wang ◽

Li Tian ◽

Qiang Qiang Wang

Keyword(s):

Genetic Algorithm ◽

Pareto Front ◽

Optimization Problems ◽

Premature Convergence ◽

Mutation Operator ◽

Test Functions ◽

Multi Objective Optimization ◽

Multi Objective ◽

Crossover And Mutation

Based on greedy policies, the greedy genetic algorithm (GGA) is proposed for multi-objective optimization problems. In the process of evolution, the greedy policies are used to initialize population, generate crossover and mutation operator, and add new individuals to the population every a few generations. All these procedures are designed to prevent premature convergence and improve the performance of Pareto front，which can be showed by examples of six test functions.

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