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

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 ◽  
Multi Objective Optimization ◽  
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.

Toward the Use of Pareto Performance Solutions and Pareto Robustness Solutions for Multi-Objective Robust Optimization Problems

2012 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis ◽  
Oscar Brito Augusto
Keyword(s):  
Robust Optimization ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Multi Objective Optimization ◽  
Robust Solutions ◽  
Multi Objective ◽  
Robust Optimization Problem ◽  
Design Solutions ◽  
Further Development

For Multi-Objective Robust Optimization Problem (MOROP), it is important to obtain design solutions that are both optimal and robust. To find these solutions, usually, the designer need to set a threshold of the variation of Performance Functions (PFs) before optimization, or add the effects of uncertainties on the original PFs to generate a new Pareto robust front. In this paper, we divide a MOROP into two Multi-Objective Optimization Problems (MOOPs). One is the original MOOP, another one is that we take the Robustness Functions (RFs), robust counterparts of the original PFs, as optimization objectives. After solving these two MOOPs separately, two sets of solutions come out, namely the Pareto Performance Solutions (PP) and the Pareto Robustness Solutions (PR). Make a further development on these two sets, we can get two types of solutions, namely the Pareto Robustness Solutions among the Pareto Performance Solutions (PR(PP)), and the Pareto Performance Solutions among the Pareto Robustness Solutions (PP(PR)). Further more, the intersection of PR(PP) and PP(PR) can represent the intersection of PR and PP well. Then the designer can choose good solutions by comparing the results of PR(PP) and PP(PR). Thanks to this method, we can find out the optimal and robust solutions without setting the threshold of the variation of PFs nor losing the initial Pareto front. Finally, an illustrative example highlights the contributions of the paper.

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.

Multi-Objective Optimization of Metal Forming Processes Based on the Kalai and Smorodinsky Solution

2015 ◽  
Vol 651-653 ◽  
pp. 1387-1393 ◽  
Author(s):  
Lorenzo Iorio ◽  
Lionel Fourment ◽  
Stephane Marie ◽  
Matteo Strano
Keyword(s):  
Optimization Problems ◽  
Good Method ◽  
Wire Drawing ◽  
Bargaining Problem ◽  
Mathematical Function ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Cooperative Approach ◽  
The Game Theory

The Game Theory is a good method for finding a compromise between two players in a bargaining problem. The Kalai and Smorodinsky (K-S) method is a solution the bargaining problem where players make decisions in order to maximize their own utility, with a cooperative approach. Interesting applications of the K-S method can be found in engineering multi-objective optimization problems, where two or more functions must be minimized. The aim of this paper is to develop an optimization algorithm aimed at rapidly finding the Kalai and Smorodinsky solution, where the objective functions are considered as players in a bargaining problem, avoiding the search for the Pareto front. The approach uses geometrical consideration in the space of the objective functions, starting from the knowledge of the so-called Utopia and Nadir points. An analytical solution is proposed and initially tested with a simple minimization problem based on a known mathematical function. Then, the algorithm is tested (thanks to a user friendly routine built-in the finite element code Forge®) for FEM optimization problem of a wire drawing operation, with the objective of minimizing the pulling force and the material damage. The results of the simulations are compared to previous works done with others methodologies.

An Improved Constrained Optimization Multi-Objective Genetic Algorithm and its Application in Engineering

2014 ◽  
Vol 962-965 ◽  
pp. 2903-2908
Author(s):  
Yun Lian Liu ◽  
Wen Li ◽  
Tie Bin Wu ◽  
Yun Cheng ◽  
Tao Yun Zhou ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Constrained Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Crossover Operator ◽  
Multi Objective Optimization ◽  
Constrained Optimization Problem ◽  
Great Ability ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm

An improved multi-objective genetic algorithm is proposed to solve constrained optimization problems. The constrained optimization problem is converted into a multi-objective optimization problem. In the evolution process, our algorithm is based on multi-objective technique, where the population is divided into dominated and non-dominated subpopulation. Arithmetic crossover operator is utilized for the randomly selected individuals from dominated and non-dominated subpopulation, respectively. The crossover operator can lead gradually the individuals to the extreme point and improve the local searching ability. Diversity mutation operator is introduced for non-dominated subpopulation. Through testing the performance of the proposed algorithm on 3 benchmark functions and 1 engineering optimization problems, and comparing with other meta-heuristics, the result of simulation shows that the proposed algorithm has great ability of global search. Keywords: multi-objective optimization;genetic algorithm;constrained optimization problem;engineering application

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

2017 ◽  
Vol 31 (19-21) ◽  
pp. 1740073 ◽  
Author(s):  
Song Huang ◽  
Yan Wang ◽  
Zhicheng Ji
Keyword(s):  
Particle Swarm Optimization ◽  
Local Search ◽  
Real World ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Pareto Set ◽  
Multi Objective Optimization ◽  
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.

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

2020 ◽  
Author(s):  
Xiang Yi ◽  
Xiaowei Yang ◽  
Han Huang ◽  
Jiahai Wang
Keyword(s):  
Real World ◽  
Optimization Problems ◽  
Evolutionary Process ◽  
Inequality Constraints ◽  
Simultaneous Optimization ◽  
Multi Objective Optimization ◽  
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.

scholarly journals APPLICATION OF POPULATION EVOLVABILITY IN A HYPER-HEURISTIC FOR DYNAMIC MULTI-OBJECTIVE OPTIMIZATION

2019 ◽  
Vol 25 (5) ◽  
pp. 951-978 ◽  
Author(s):  
Teodoro Macias-Escobar ◽  
Laura Cruz-Reyes ◽  
Bernabé Dorronsoro ◽  
Héctor Fraire-Huacuja ◽  
Nelson Rangel-Valdez ◽  
...  
Keyword(s):  
Dynamic Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Dynamic Properties ◽  
Selection Method ◽  
Multiobjective Evolutionary Algorithms ◽  
Multi Objective Optimization ◽  
Selection Methods ◽  
Dynamic Optimization Problems ◽  
Multi Objective

It is important to know the properties of an optimization problem and the difficulty an algorithm faces to solve it. Population evolvability obtains information related to both elements by analysing the probability of an algorithm to improve current solutions and the degree of those improvements. DPEM_HH is a dynamic multi-objective hyper-heuristic that uses low-level heuristic (LLH) selection methods that apply population evolvability. DPEM_HH uses dynamic multiobjective evolutionary algorithms (DMOEAs) as LLHs to solve dynamic multi-objective optimization problems (DMOPs). Population evolvability is incorporated in DPEM_HH by calculating it on each candidate DMOEA for a set of sampled generations after a change is detected, using those values to select which LLH will be applied. DPEM_HH is tested on multiple DMOPs with dynamic properties that provide several challenges. Experimental results show that DPEM_HH with a greedy LLH selection method that uses average population evolvability values can produce solutions closer to the Pareto optimal front with equal to or better diversity than previously proposed heuristics. This shows the effectiveness and feasibility of the application of population evolvability on hyperheuristics to solve dynamic optimization problems.

scholarly journals An approximation algorithm for multi-objective optimization problems using a box-coverage

2021 ◽  
Author(s):  
Gabriele Eichfelder ◽  
Leo Warnow
Keyword(s):  
Approximation Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Nondominated Set ◽  
Common Technique ◽  
Nondominated Points ◽  
Nondominated Point ◽  
Do So

AbstractFor a continuous multi-objective optimization problem, it is usually not a practical approach to compute all its nondominated points because there are infinitely many of them. For this reason, a typical approach is to compute an approximation of the nondominated set. A common technique for this approach is to generate a polyhedron which contains the nondominated set. However, often these approximations are used for further evaluations. For those applications a polyhedron is a structure that is not easy to handle. In this paper, we introduce an approximation with a simpler structure respecting the natural ordering. In particular, we compute a box-coverage of the nondominated set. To do so, we use an approach that, in general, allows us to update not only one but several boxes whenever a new nondominated point is found. The algorithm is guaranteed to stop with a finite number of boxes, each being sufficiently thin.

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

Symmetry ◽  
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 ◽  
Multi Objective Optimization ◽  
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.

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