Handling Constrained Multi-objective Optimization By Ignoring Constraints and Using Two Evolutionary Frameworks

Multi Objective ◽

Real World Problem ◽

Conflicting Objectives ◽

Two Stages

Constrained multi-objective optimization problems exist widely in real-world applications, and they involve a simultaneous optimization of multiple and often conflicting objectives subject to several equality and/or inequality constraints. To deal with these problems, a crucial issue is how to handle constraints effectively. This paper proposes a simple yet effective constrained decomposition-based multi-objective evolutionary algorithm. In the proposal, the evolutionary process is divided into two stages in which constraints are handled differently. In the first stage, constraints are totally ignored and the population is pulled toward the unconstrained Pareto-optimal front (PF) by optimizing objectives only. This can help the proposed algorithm handle well problems with the following features, i.e., the constrained PF has an intersection with the unconstrained counterpart, and there are infeasible regions blocking the way of convergence. In the second stage, with the purpose of approximating the constrained PF well,constraint satisfaction is emphasized over objective minimization.Moreover, different evolutionary frameworks are adopted in the two stages to promote the performance of the algorithm as much as possible. The proposed algorithm is comprehensively compared with several state-of-the-art algorithms on 39 problems (with 266 test instances in total), including one real-world problem (with 36 instances) in search-based software engineering. As shown by the experimental results, the new algorithm performs best on the majority of these problems, particularly on those with the aforementioned features. In summary, the suggested algorithm provides an effective way of handling constrained multi-objective optimization problems.

Handling Constrained Multi-objective Optimization By Ignoring Constraints and Using Two Evolutionary Frameworks

10.36227/techrxiv.11792037.v3 ◽

2020 ◽

Author(s):

Xiang Yi ◽

Xiaowei Yang ◽

Han Huang ◽

Jiahai Wang

Keyword(s):

Real World ◽

Optimization Problems ◽

Evolutionary Process ◽

Inequality Constraints ◽

Multi Objective ◽

Real World Problem ◽

Conflicting Objectives ◽

Two Stages

Constrained multi-objective optimization problems exist widely in real-world applications, and they involve a simultaneous optimization of multiple and often conflicting objectives subject to several equality and/or inequality constraints. To deal with these problems, a crucial issue is how to handle constraints effectively. This paper proposes a simple yet effective constrained decomposition-based multi-objective evolutionary algorithm. In the proposal, the evolutionary process is divided into two stages in which constraints are handled differently. In the first stage, constraints are totally ignored and the population is pulled toward the unconstrained Pareto-optimal front (PF) by optimizing objectives only. This can help the proposed algorithm handle well problems with the following features, i.e., the constrained PF has an intersection with the unconstrained counterpart, and there are infeasible regions blocking the way of convergence. In the second stage, with the purpose of approximating the constrained PF well,constraint satisfaction is emphasized over objective minimization.Moreover, different evolutionary frameworks are adopted in the two stages to promote the performance of the algorithm as much as possible. The proposed algorithm is comprehensively compared with several state-of-the-art algorithms on 39 problems (with 266 test instances in total), including one real-world problem (with 36 instances) in search-based software engineering. As shown by the experimental results, the new algorithm performs best on the majority of these problems, particularly on those with the aforementioned features. In summary, the suggested algorithm provides an effective way of handling constrained multi-objective optimization problems.

Handling Constrained Multi-objective Optimization By Ignoring Constraints and Using Two Evolutionary Frameworks

10.36227/techrxiv.11792037 ◽

2020 ◽

Author(s):

Xiang Yi ◽

Xiaowei Yang ◽

Han Huang ◽

Jiahai Wang

Keyword(s):

Real World ◽

Optimization Problems ◽

Evolutionary Process ◽

Inequality Constraints ◽

Multi Objective ◽

Real World Problem ◽

Conflicting Objectives ◽

Two Stages

Constrained multi-objective optimization problems exist widely in real-world applications, and they involve a simultaneous optimization of multiple and often conflicting objectives subject to several equality and/or inequality constraints. To deal with these problems, a crucial issue is how to handle constraints effectively. This paper proposes a simple yet effective constrained decomposition-based multi-objective evolutionary algorithm. In the proposal, the evolutionary process is divided into two stages in which constraints are handled differently. In the first stage, constraints are totally ignored and the population is pulled toward the unconstrained Pareto-optimal front (PF) by optimizing objectives only. This can help the proposed algorithm handle well problems with the following features, i.e., the constrained PF has an intersection with the unconstrained counterpart, and there are infeasible regions blocking the way of convergence. In the second stage, with the purpose of approximating the constrained PF well,constraint satisfaction is emphasized over objective minimization.Moreover, different evolutionary frameworks are adopted in the two stages to promote the performance of the algorithm as much as possible. The proposed algorithm is comprehensively compared with several state-of-the-art algorithms on 39 problems (with 266 test instances in total), including one real-world problem (with 36 instances) in search-based software engineering. As shown by the experimental results, the new algorithm performs best on the majority of these problems, particularly on those with the aforementioned features. In summary, the suggested algorithm provides an effective way of handling constrained multi-objective optimization problems.

Efficient Computation of Probabilistic Dominance in Multi-objective Optimization

ACM Transactions on Evolutionary Learning and Optimization ◽

10.1145/3469801 ◽

2021 ◽

Vol 1 (4) ◽

pp. 1-26

Author(s):

Faramarz Khosravi ◽

Alexander Rass ◽

Jürgen Teich

Keyword(s):

Optimization Problems ◽

Statistical Tests ◽

Optimization Techniques ◽

Sampled Data ◽

Efficient Computation ◽

Multi Objective ◽

Conflicting Objectives ◽

Comparison Operator

Real-world problems typically require the simultaneous optimization of multiple, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables or objective functions. To cope with such uncertainties, stochastic and robust optimization techniques are widely studied aiming to distinguish candidate solutions with uncertain objectives specified by confidence intervals, probability distributions, sampled data, or uncertainty sets. In this scope, this article first introduces a novel empirical approach for the comparison of candidate solutions with uncertain objectives that can follow arbitrary distributions. The comparison is performed through accurate and efficient calculations of the probability that one solution dominates the other in terms of each uncertain objective. Second, such an operator can be flexibly used and combined with many existing multi-objective optimization frameworks and techniques by just substituting their standard comparison operator, thus easily enabling the Pareto front optimization of problems with multiple uncertain objectives. Third, a new benchmark for evaluating uncertainty-aware optimization techniques is introduced by incorporating different types of uncertainties into a well-known benchmark for multi-objective optimization problems. Fourth, the new comparison operator and benchmark suite are integrated into an existing multi-objective optimization framework that features a selection of multi-objective optimization problems and algorithms. Fifth, the efficiency in terms of performance and execution time of the proposed comparison operator is evaluated on the introduced uncertainty benchmark. Finally, statistical tests are applied giving evidence of the superiority of the new comparison operator in terms of \epsilon -dominance and attainment surfaces in comparison to previously proposed approaches.

Advances in Data Mining and Database Management - Developing a Keyword Extractor and Document Classifier ◽

Dynamic Template Generation

10.4018/978-1-7998-3772-5.ch001 ◽

2021 ◽

pp. 1-37

Keyword(s):

Optimization Problems ◽

Real Life ◽

Dynamic Test ◽

Test Paper ◽

Multi Objective ◽

Life Problems ◽

Conflicting Objectives ◽

Complex Optimization ◽

Dynamic Template

A test blueprint/test template, also known as the table of specifications, represents the structure of a test. It has been highly recommended in assessment textbook to carry out the preparation of a test with a test blueprint. This chapter focuses on modeling a dynamic test paper template using multi-objective optimization algorithm and makes use of the template in dynamic generation of examination test paper. Multi-objective optimization-based models are realistic models for many complex optimization problems. Modeling a dynamic test paper template, similar to many real-life problems, includes solving multiple conflicting objectives satisfying the template specifications.

Multi-objective particle swarm optimization using Pareto-based set and aggregation approach

Modern Physics Letters B ◽

10.1142/s0217984917400735 ◽

2017 ◽

Vol 31 (19-21) ◽

pp. 1740073 ◽

Cited By ~ 3

Author(s):

Song Huang ◽

Yan Wang ◽

Zhicheng Ji

Keyword(s):

Particle Swarm Optimization ◽

Local Search ◽

Real World ◽

Optimization Problems ◽

Particle Swarm ◽

Pareto Set ◽

Particle Swarm Optimizer ◽

Swarm Optimization ◽

Multi Objective

Multi-objective optimization problems (MOPs) need to be solved in real world recently. In this paper, a multi-objective particle swarm optimization based on Pareto set and aggregation approach was proposed to deal with MOPs. Firstly, velocities and positions were updated similar to PSO. Then, global-best set was defined in particle swarm optimizer to preserve Pareto-based set obtained by the population. Specifically, a hybrid updating strategy based on Pareto set and aggregation approach was introduced to update the global-best set and local search was carried on global-best set. Thirdly, personal-best positions were updated in decomposition way, and global-best position was selected from global-best set. Finally, ZDT instances and DTLZ instances were selected to evaluate the performance of MULPSO and the results show validity of the proposed algorithm for MOPs.

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

Applied Sciences ◽

10.3390/app11199153 ◽

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 ◽

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.

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

ECTI Transactions on Computer and Information Technology (ECTI-CIT) ◽

10.37936/ecti-cit.2018121.98549 ◽

2018 ◽

Vol 12 (1) ◽

pp. 7-16

Author(s):

Saad M. Alzahrani ◽

Naruemon Wattanapongsakorn

Keyword(s):

Optimization Problems ◽

Benchmark Problems ◽

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 Multi-Objective Robust Preference Genetic Algorithm Based on Decision Variable Perturbation

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.211-212.818 ◽

2011 ◽

Vol 211-212 ◽

pp. 818-822 ◽

Cited By ~ 2

Author(s):

Bing Kun Zhu ◽

Li Hong Xu ◽

Hai Gen Hu

Keyword(s):

Fitness Function ◽

Latin Hypercube Sampling ◽

Function Parameter ◽

Decision Variable ◽

Robust Solution ◽

Robust Solutions ◽

Multi Objective ◽

Conflicting Objectives

Multi-objective optimization is a challenging research topic because it involves the simultaneous optimization of several complex and conflicting objectives. However multi-objectivity is only one aspect of real-world applications and there is a growing interest in the optimization of solutions that are insensitive to parametric variations as well. A new robust preference multi-objective optimization algorithm is proposed in this paper, and the robust measurement of solution is designed based on Latin Hypercube Sampling, which is embedded in the optimization process to guide the optimization direction and help the better robust solution have more chance to survive. In order to obtain different preference of the robust solutions, a new fitness scheme is also presented. Through the adjustment of fitness function parameter preference, robust solutions can be obtained. Results suggest that the proposed algorithm has a bias towards the region where the preference robust solutions lie.

An Ensemble Framework of Evolutionary Algorithm for Constrained Multi-Objective Optimization

Symmetry ◽

10.3390/sym14010116 ◽

2022 ◽

Vol 14 (1) ◽

pp. 116

Author(s):

Junhua Ku ◽

Fei Ming ◽

Wenyin Gong

Keyword(s):

Evolutionary Algorithms ◽

Real World ◽

Optimization Problems ◽

State Of The Art ◽

The Real ◽

Multi Objective ◽

The Past ◽

Hypervolume Indicator ◽

Real World Problems

In the real-world, symmetry or asymmetry widely exists in various problems. Some of them can be formulated as constrained multi-objective optimization problems (CMOPs). During the past few years, handling CMOPs by evolutionary algorithms has become more popular. Lots of constrained multi-objective optimization evolutionary algorithms (CMOEAs) have been proposed. Whereas different CMOEAs may be more suitable for different CMOPs, it is difficult to choose the best one for a CMOP at hand. In this paper, we propose an ensemble framework of CMOEAs that aims to achieve better versatility on handling diverse CMOPs. In the proposed framework, the hypervolume indicator is used to evaluate the performance of CMOEAs, and a decreasing mechanism is devised to delete the poorly performed CMOEAs and to gradually determine the most suitable CMOEA. A new CMOEA, namely ECMOEA, is developed based on the framework and three state-of-the-art CMOEAs. Experimental results on five benchmarks with totally 52 instances demonstrate the effectiveness of our approach. In addition, the superiority of ECMOEA is verified through comparisons to seven state-of-the-art CMOEAs. Moreover, the effectiveness of ECMOEA on the real-world problems is also evaluated for eight instances.