scholarly journals Variation Rate to Maintain Diversity in Decision Space within Multi-Objective Evolutionary Algorithms

2019 ◽  
Vol 24 (3) ◽  
pp. 82 ◽  
Author(s):  
Oliver Cuate ◽  
Oliver Schütze
Keyword(s):  
Significant Loss ◽  
Selection Strategy ◽  
Benchmark Problems ◽  
Decision Space ◽  
Multi Objective ◽  
Approximation Quality ◽  
Selection Strategies ◽  
Objective Space ◽  
Variation Rate ◽  
Variable Space

The performance of a multi-objective evolutionary algorithm (MOEA) is in most cases measured in terms of the populations’ approximation quality in objective space. As a consequence, most MOEAs focus on such approximations while neglecting the distribution of the individuals of their populations in decision space. This, however, represents a potential shortcoming in certain applications as in many cases one can obtain the same or very similar qualities (measured in objective space) in several ways (measured in decision space). Hence, a high diversity in decision space may represent valuable information for the decision maker for the realization of a given project. In this paper, we propose the Variation Rate, a heuristic selection strategy that aims to maintain diversity both in decision and objective space. The core of this strategy is the proper combination of the averaged distance applied in variable space together with the diversity mechanism in objective space that is used within a chosen MOEA. To show the applicability of the method, we propose the resulting selection strategies for some of the most representative state-of-the-art MOEAs and show numerical results on several benchmark problems. The results demonstrate that the consideration of the Variation Rate can greatly enhance the diversity in decision space for all considered algorithms and problems without a significant loss in the approximation qualities in objective space.

On Benchmark Problems and Metrics for Decision Space Performance Analysis in Multi-Objective Optimization

2017 ◽  
Vol 16 (01) ◽  
pp. 1750006 ◽  
Author(s):  
Bin Zhang ◽  
Kamran Shafi ◽  
Hussein Abbass
Keyword(s):  
Performance Analysis ◽  
Fitness Landscape ◽  
Benchmark Problems ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Decision Space ◽  
Nsga Ii ◽  
Multi Objective ◽  
Objective Space ◽  
Problem Instances

A number of benchmark problems exist for evaluating multi-objective evolutionary algorithms (MOEAs) in the objective space. However, the decision space performance analysis is a recent and relatively less explored topic in evolutionary multi-objective optimization research. Among other implications, such analysis can lead to designing more realistic test problems, gaining better understanding about optimal and robust design areas, and design and evaluation of knowledge-based optimization algorithms. This paper complements the existing research in this area and proposes a new method to generate multi-objective optimization test problems with clustered Pareto sets in hyper-rectangular defined areas of decision space. The test problem is parametrized to control number of decision variables, number and position of optimal areas in the decision space and modality of fitness landscape. Three leading MOEAs, including NSGA-II, NSGA-III, and MOEA/D, are evaluated on a number of problem instances with varying characteristics. A new metric is proposed that measures the performance of algorithms in terms of their coverage of the optimal areas in the decision space. The empirical analysis presented in this research shows that the decision space performance may not necessarily be reflective of the objective space performance and that all algorithms are sensitive to population size parameter for the new test problems.

The Effect of Credit Definition and Aggregation Strategies on Multi-Objective Hyper-Heuristics

2015 ◽  
Author(s):  
Nozomi Hitomi ◽  
Daniel Selva
Keyword(s):  
Optimization Problems ◽  
Entire Population ◽  
Optimization Process ◽  
Selection Strategy ◽  
Credit Assignment ◽  
Multi Objective ◽  
Domain Specific ◽  
Combinatorial Optimization Problems ◽  
Pareto Ranking ◽  
Selection Strategies

Heuristics and meta-heuristics are often used to solve complex real-world problems such as the non-linear, non-convex, and multi-objective combinatorial optimization problems that regularly appear in system design and architecture. Unfortunately, the performance of a specific heuristic is largely dependent on the specific problem at hand. Moreover, a heuristic’s performance can vary throughout the optimization process. Hyper-heuristics is one approach that can maintain relatively good performance over the course of an optimization process and across a variety of problems without parameter retuning or major modifications. Given a set of domain-specific and domain-independent heuristics, a hyper-heuristic adapts its search strategy over time by selecting the most promising heuristics to use at a given point. A hyper-heuristic must have: 1) a credit assignment strategy to rank the heuristics by their likelihood of producing improving solutions; and 2) a heuristic selection strategy based on the credits assigned to each heuristic. The literature contains many examples of hyper-heuristics with effective credit assignment and heuristic selection strategies for single-objective optimization problems. In multi-objective optimization problems, however, defining credit is less straightforward because there are often competing objectives. Therefore, there is a need to define and assign credit so that heuristics are rewarded for finding solutions with good trades between the objectives. This paper studies, for the first time, different combinations of credit definition, credit aggregation, and heuristic selection strategies. Credit definitions are based on different applications of the notion of Pareto dominance, namely: A1) dominance of the offspring with respect to the parent solutions; A2) ability to produce non-dominated solutions with respect to the entire population; A3) Pareto ranking with respect to the entire population. Two different credit aggregation strategies for assigning credit are also examined. A heuristic will receive credit for: B1) only the solutions it created in the current iteration or B2) all solutions it created that are in the current population. Different heuristic selection strategies are considered including: C1) probability matching; C2) dynamic multi-armed bandit; and C3) Hyper-GA. Thus, we conduct an experiment with three factors: credit definition (A1, A2, A3), credit aggregation (B1, B2), and heuristic selection (C1, C2, C3) and conduct a full factorial experiment. Performance is measured by hyper-volume of the last population. All algorithms are tested on a design problem for a climate monitoring satellite constellation instead of classical benchmarking problems to apply domain-specific heuristics within the hyper-heuristic.

Analytics on Fireworks Algorithm Solving Problems with Shifts in the Decision Space and Objective Space

2015 ◽  
Vol 6 (2) ◽  
pp. 52-86 ◽  
Author(s):  
Shi Cheng ◽  
Quande Qin ◽  
Junfeng Chen ◽  
Yuhui Shi ◽  
Qingyu Zhang
Keyword(s):  
Search Space ◽  
Population Diversity ◽  
Modular Arithmetic ◽  
Benchmark Problems ◽  
Search Range ◽  
Decision Space ◽  
Fireworks Algorithm ◽  
Mapping Strategy ◽  
Objective Space ◽  
Definition Of

Fireworks algorithms for solving problems with the optima shift in decision space and/or objective space are analyzed in this paper. The standard benchmark problems have several weaknesses in the research of swarm intelligence algorithms for solving single objective problems. The optimum is in the center of search range, and is the same at each dimension of the search space. The optimum shift in decision space and/or objective space could increase the difficulty of problem solving. A mapping strategy, modular arithmetic mapping, is utilized in the original fireworks algorithm to handle solutions out of search range. The solutions are implicitly guided to the center of search range for problems with symmetrical search range via this strategy. The optimization performance of fireworks algorithm on shift functions may be affected by this strategy. Four kinds of mapping strategies, which include mapping by modular arithmetic, mapping to the boundary, mapping to stochastic region, and mapping to limited stochastic region, are compared on problems with different dimensions and different optimum shift range. From experimental results, the fireworks algorithms with mapping to the boundary, or mapping to limited stochastic region obtain good performance on problems with the optimum shift. This is probably because the search tendency is kept in these two strategies. The definition of population diversity measurement is also proposed in this paper, from observation on population diversity changes, the useful information of fireworks algorithm solving different kinds of problems could be obtained.

Prediction of Pareto Dominance Using an Attribute Tendency Model for Expensive Multi-Objective Optimization

2019 ◽  
Vol 29 (02) ◽  
pp. 2050021
Author(s):  
Wenbin Li ◽  
Junqiang Jiang ◽  
Xi Chen ◽  
Guanqi Guo ◽  
Jianjun He
Keyword(s):  
Surrogate Model ◽  
Prediction Method ◽  
Optimization Methods ◽  
Black Box ◽  
Benchmark Problems ◽  
Pareto Dominance ◽  
Decision Space ◽  
Multi Objective ◽  
Decision Attributes ◽  
Coarse Model

This paper proposes a novel surrogate-assisted multi-objective evolutionary algorithm, MOEA-ATCM, to solve expensive or black-box multi-objective problems with small evaluation budgets. The proposed approach encompasses a state-of-the-art MOEA based on a nondominated sorting genetic algorithm assisted by multi-fidelity optimization methods. A high-fidelity attribute tendency (AT) surrogate model was used to construct a linear decision space by introducing the knowledge of the objective space. A coarse model (CM) based on the AT model and correlation analyses of the objective functions and decision attributes were used to predict the Pareto dominance for candidates in the new decision space constructed by the AT model. Two major roles of MOEA-ATCM were identified: (1) the development of a new multi-fidelity surrogate-model-based method to predict Pareto dominance in a decision space that was then applied to MOEA, which does not need to dynamically update surrogate models in the optimization process and (2) the development of a Pareto dominance prediction method to obtain good nondominated solutions of expensive or black box problems with relatively few objective function evaluations. The advantages of MOEA-ATCM were verified by mathematical benchmark problems and a real-world multi-objective parameter optimization problem.

Archive of Useful Solutions for Directed Mating in Evolutionary Constrained Multiobjective Optimization

2014 ◽  
Vol 18 (2) ◽  
pp. 221-231 ◽  
Author(s):  
Minami Miyakawa ◽  
◽  
Keiki Takadama ◽  
Hiroyuki Sato
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Selection Process ◽  
Benchmark Problems ◽  
Search Performance ◽  
Next Generation ◽  
Multi Objective ◽  
Objective Space ◽  
Feasible Solutions ◽  
Constrained Multiobjective Optimization

As an evolutionary approach to solve multi-objective optimization problems involving several constraints, recently a multi-objective evolutionary algorithm (MOEA) using two-stage non-dominated sorting and directed mating (TNSDM) has been proposed. In TNSDM, directed mating utilizes infeasible solutions dominating feasible solutions in the objective space to generate offspring. In our previous studies, significant contribution of directed mating to the improvement of the search performancewas verified on several benchmark problems. However, in the conventional TNSDM, infeasible solutions utilized in directed mating are discarded in the selection process of parents (elites) population and cannot be utilized in the next generation. TNSDM has potential to further improve the search performance by archiving useful solutions for directed mating to the next generation and repeatedly utilizing them in directed mating. To further improve effects of directed mating in TNSDM, in this work, we propose an archiving strategy of useful solutions for directed mating. We verify the search performance of TNSDM using the proposed archive by varying the size of archive, and compare its search performance with the conventional CNSGA-II and RTS onmobjectiveskknapsacks problems. As results, we show that the search performance of TNSDM is improved by introducing the proposed archive in aspects of diversity of the obtained solutions in the objective space and convergence of solutions toward the optimal Pareto front.

EFFICIENCY INCREASE OF MULTI-OBJECTIVE GENETIC ALGORITHMS USING THE CLUSTERIZATION OF A POPULATION IN THE VARIABLE SPACE

2019 ◽  
pp. 13-20
Author(s):  
P. V. Kazakov
Keyword(s):  
Genetic Algorithm ◽  
Benchmark Problems ◽  
Additional Parameter ◽  
Nsga Ii ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Fitness Value ◽  
Efficiency Increase ◽  
Variable Space ◽  
Special Rule

The paper introduces a new manner for improving of obtained by MOGA (Multi-Objective Genetic Algorithm) solutions. It is based on the concept of dividing the population into set of clusters according to solutions similarity. In different of most MOGA the clusterization of population is implemented in the variable space, enables to enhance diversity of population and to increase the number of non-dominated solutions. The special procedures for the clustering of current population and copying the clusters in the next population were developed. The dominance principal by fitness-value is used for clustering. The number of clusters depends on additional parameter the radius of cluster’s hypersphere that is determined experimentally. By the special rule the individuals corresponded to centroids of clusters are copied in the new population. The clusters are recalculated for every population. The influence of the radius cluster to the number of non-dominated solutions variation was studied. The cluster modification should be integrated into any multi-objective genetic algorithm. By the analytical evaluation has been studied, this MOGA modification has additional computationally complexity from linear to quadratic. In experiments it was tested with the evolutionary algorithms SPEA2, NSGA-II on the special benchmark problems (DTLZ) with a various number of criteria using the set of performance indices. The used clustering in the variable space algorithms were achieved a better distribution and convergence to the true Paretofront in some cases.

An Analysis of Fireworks Algorithm Solving Problems With Shifts in the Decision Space and Objective Space

2020 ◽  
pp. 277-311
Author(s):  
Shi Cheng ◽  
Junfeng Chen ◽  
Quande Qin ◽  
Yuhui Shi
Keyword(s):  
Problem Solving ◽  
Swarm Intelligence ◽  
Modular Arithmetic ◽  
Benchmark Problems ◽  
Search Range ◽  
Decision Space ◽  
Fireworks Algorithm ◽  
Objective Space ◽  
Single Objective

Fireworks algorithms for solving problems with the optima shifts in the decision space and/or objective space are analyzed. The standard benchmark problems have several weaknesses in the research of swarm intelligence algorithms for solving single-objective problems. The optimum shift in decision space and/or objective space will increase the difficulty of problem-solving. Modular arithmetic mapping is utilized in the original fireworks algorithm to handle solutions out of the search range. The solutions are implicitly guided to the center of search range for problems with symmetrical search range via this strategy. The optimization performance of the fireworks algorithm on shift functions may be affected by this strategy. Four kinds of mapping strategies are compared with different problems. The fireworks algorithms with mapping to the boundary or mapping to a limited stochastic region obtain good performance on problems with the optimum shift.

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