Runtime Analysis of an Evolutionary Algorithm for Stochastic Multi-Objective Combinatorial Optimization

2012 ◽  
Vol 20 (3) ◽  
pp. 395-421 ◽  
Author(s):  
Walter J. Gutjahr
Keyword(s):  
Combinatorial Optimization ◽  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Fast Convergence ◽  
Runtime Analysis ◽  
Multi Objective ◽  
Complexity Results ◽  
Starting Point

For stochastic multi-objective combinatorial optimization (SMOCO) problems, the adaptive Pareto sampling (APS) framework has been proposed, which is based on sampling and on the solution of deterministic multi-objective subproblems. We show that when plugging in the well-known simple evolutionary multi-objective optimizer (SEMO) as a subprocedure into APS, ε-dominance has to be used to achieve fast convergence to the Pareto front. Two general theorems are presented indicating how runtime complexity results for APS can be derived from corresponding results for SEMO. This may be a starting point for the runtime analysis of evolutionary SMOCO algorithms.

QMAEA: A quantum multi-agent evolutionary algorithm for multi-objective combinatorial optimization

SIMULATION ◽  
2013 ◽  
Vol 90 (2) ◽  
pp. 182-204 ◽  
Author(s):  
F Tao ◽  
Y J Laili ◽  
L Zhang ◽  
Z H Zhang ◽  
AY C Nee
Keyword(s):  
Combinatorial Optimization ◽  
Evolutionary Algorithm ◽  
Multi Objective ◽  
Multi Agent

scholarly journals Solving the Path Planning Problem in Mobile Robotics with the Multi-Objective Evolutionary Algorithm

2018 ◽  
Vol 8 (9) ◽  
pp. 1425 ◽  
Author(s):  
Yang Xue ◽  
Jian-Qiao Sun
Keyword(s):  
Path Planning ◽  
Evolutionary Algorithm ◽  
Mobile Robotics ◽  
Good Choice ◽  
Target Point ◽  
Planning Problem ◽  
Multi Objective ◽  
Starting Point ◽  
Feasible Path ◽  
Path Planning Problem

Path planning problems involve finding a feasible path from the starting point to the target point. In mobile robotics, path planning (PP) is one of the most researched subjects at present. Since the path planning problem is an NP-hard problem, it can be solved by multi-objective evolutionary algorithms (MOEAs). In this article, we propose a multi-objective method for solving the path planning problem. It is a population evolutionary algorithm and solves three different objectives (path length, safety, and smoothness) to acquire precise and effective solutions. In addition, five scenarios and another existing method are used to test the proposed algorithm. The results show the advantages of the algorithm. In particular, different quality metrics are used to assess the obtained results. In the end, the research indicates that the proposed multi-objective evolutionary algorithm is a good choice for solving the path planning problem.

A many-objective evolutionary algorithm based on vector angle distance scaling

2021 ◽  
Vol 40 (5) ◽  
pp. 10285-10306
Author(s):  
Xin Li ◽  
Xiaoli Li ◽  
Kang Wang
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problems ◽  
Adaptive Strategy ◽  
Great Success ◽  
Multi Objective ◽  
Environmental Selection ◽  
Fitness Value ◽  
Vector Angle

In the past two decades, multi-objective evolutionary algorithms (MOEAs) have achieved great success in solving two or three multi-objective optimization problems. As pointed out in some recent studies, however, MOEAs face many difficulties when dealing with many-objective optimization problems(MaOPs) on account of the loss of the selection pressure of the non-dominant candidate solutions toward the Pareto front and the ineffective design of the diversity maintenance mechanism. This paper proposes a many-objective evolutionary algorithm based on vector guidance. In this algorithm, the value of vector angle distance scaling(VADS) is applied to balance convergence and diversity in environmental selection. In addition, tournament selection based on the aggregate fitness value of VADS is applied to generate a high quality offspring population. Besides, we adopt an adaptive strategy to adjust the reference vector dynamically according to the scales of the objective functions. Finally, the performance of the proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms on 52 instances of 13 MaOPs with diverse characteristics. Experimental results show that the proposed algorithm performs competitively when dealing many-objective with different types of Pareto front.

scholarly journals An Entropy-Based Multiobjective Evolutionary Algorithm with an Enhanced Elite Mechanism

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yufang Qin ◽  
Junzhong Ji ◽  
Chunnian Liu
Keyword(s):  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problem ◽  
State Of The Art ◽  
Early Stage ◽  
Test Problems ◽  
Multiobjective Optimization Problem ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective

Multiobjective optimization problem (MOP) is an important and challenging topic in the fields of industrial design and scientific research. Multi-objective evolutionary algorithm (MOEA) has proved to be one of the most efficient algorithms solving the multi-objective optimization. In this paper, we propose an entropy-based multi-objective evolutionary algorithm with an enhanced elite mechanism (E-MOEA), which improves the convergence and diversity of solution set in MOPs effectively. In this algorithm, an enhanced elite mechanism is applied to guide the direction of the evolution of the population. Specifically, it accelerates the population to approach the true Pareto front at the early stage of the evolution process. A strategy based on entropy is used to maintain the diversity of population when the population is near to the Pareto front. The proposed algorithm is executed on widely used test problems, and the simulated results show that the algorithm has better or comparative performances in convergence and diversity of solutions compared with two state-of-the-art evolutionary algorithms: NSGA-II, SPEA2 and the MOSADE.

A MULTI-OBJECTIVE HW–SW CO-SYNTHESIS ALGORITHM BASED ON QUANTUM-INSPIRED EVOLUTIONARY ALGORITHM

2008 ◽  
Vol 07 (02) ◽  
pp. 129-148 ◽  
Author(s):  
WENLONG WEI ◽  
BIN LI ◽  
YI ZOU ◽  
WENCONG ZHANG ◽  
ZHENQUAN ZHUANG
Keyword(s):  
Embedded System ◽  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Solution Space ◽  
Quantum Probability ◽  
Multiple Quantum ◽  
Synthesis Algorithm ◽  
Multi Objective ◽  
Key Steps ◽  
Slot Filling

Hardware–Software (HW–SW) co-synthesis is one of the key steps in modern embedded system design. Generally, HW–SW co-synthesis is to optimally allocate processors, assign tasks to processors, and schedule the processing of tasks to achieve a good balance among performance, cost, power consumption, etc. Hence, it is a typical multi-objective optimization problem. In this paper, a new multi-objective HW–SW co-synthesis algorithm based on the quantum-inspired evolutionary algorithm (MQEAC) is proposed. MQEAC utilizes multiple quantum probability amplitude vectors to model the promising areas of solution space. Meanwhile, this paper presents a new crossover operator to accelerate the convergence to the Pareto front and introduces a PE slot-filling strategy to improve the efficiency of scheduling. Experimental results show that the proposed algorithm can solve the typical multi-objective co-synthesis problems effectively and efficiently.

scholarly journals Maximum Diversity Problem. A Multi-Objective Approach

2018 ◽  
Vol 21 (2) ◽  
Author(s):  
Katherine Dahiana Vera Escobar ◽  
Fabio Lopez-Pires ◽  
Benjamin Baran ◽  
Fernando Sandoya
Keyword(s):  
Evolutionary Algorithm ◽  
Pareto Front ◽  
A Priori ◽  
Experimental Results ◽  
Simultaneous Optimization ◽  
Optimization Models ◽  
Decision Variable ◽  
Multi Objective ◽  
Diversity Measures ◽  
First Time

The Maximum Diversity (MD) problem is the process of selecting a subset of elements where the diversity among selected elements is maximized. Several diversity measures were already studied in the literature, optimizing the problem considered in a pure mono-objective approach. This work presents for the first time multi-objective approaches for the MD problem, considering the simultaneous optimization of the following five diversity measures: (i) Max-Sum, (ii) Max-Min, (iii) Max-MinSum, (iv) Min-Diff and (v) Min-P-center. Two different optimization models are proposed: (i) Multi-Objective Maximum Diversity (MMD) model, where the number of elements to be selected is defined a-priori, and (ii) Multi-Objective Maximum Average Diversity (MMAD) model, where the number of elements to be selected is also a decision variable. To solve the formulated problems, a Multi-Objective Evolutionary Algorithm (MOEA) is presented. Experimental results demonstrate that the proposed MOEA found good quality solutions, i.e. between 98.85% and 100% of the optimal Pareto front when considering the hypervolume for comparison purposes.

scholarly journals Stratification for Constraint-Based Multi-Objective Combinatorial Optimization

2018 ◽  
Author(s):  
Miguel Terra-Neves ◽  
Inês Lynce ◽  
Vasco Manquinho
Keyword(s):  
Combinatorial Optimization ◽  
Experimental Evaluation ◽  
Pareto Front ◽  
Stochastic Methods ◽  
Objective Functions ◽  
Minimal Models ◽  
Multi Objective ◽  
New Methods ◽  
Constraint Set

New constraint-based algorithms have been recently proposed to solve Multi-Objective Combinatorial Optimization (MOCO) problems. These new methods are based on Minimal Correction Subsets (MCSs) or P-minimal models and have shown to be successful at solving MOCO instances when the constraint set is hard to satisfy. However, if the constraints are easy to satisfy, constraint-based tools usually do not perform as well as stochastic methods. For solving such instances, algorithms should focus on dealing with the objective functions. This paper proposes the integration of stratification techniques in constraint-based algorithms for MOCO. Moreover, it also shows how to diversify the stratification among the several objective criteria in order to better approximate the Pareto front of MOCO problems. An extensive experimental evaluation on publicly available MOCO instances shows that the new algorithm is competitive with stochastic methods and it is much more effective than existing constraint-based methods.

scholarly journals Improved Lebesgue Indicator-Based Evolutionary Algorithm: Reducing Hypervolume Computations

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 19
Author(s):  
Saúl Zapotecas-Martínez ◽  
Abel García-Nájera ◽  
Adriana Menchaca-Méndez
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Lebesgue Measure ◽  
Pareto Front ◽  
Optimization Problems ◽  
State Of The Art ◽  
Computational Cost ◽  
Computational Time ◽  
Multi Objective Optimization ◽  
Multi Objective

One of the major limitations of evolutionary algorithms based on the Lebesgue measure for multi-objective optimization is the computational cost required to approximate the Pareto front of a problem. Nonetheless, the Pareto compliance property of the Lebesgue measure makes it one of the most investigated indicators in the designing of indicator-based evolutionary algorithms (IBEAs). The main deficiency of IBEAs that use the Lebesgue measure is their computational cost which increases with the number of objectives of the problem. On this matter, the investigation presented in this paper introduces an evolutionary algorithm based on the Lebesgue measure to deal with box-constrained continuous multi-objective optimization problems. The proposed algorithm implicitly uses the regularity property of continuous multi-objective optimization problems that has suggested effectiveness when solving continuous problems with rough Pareto sets. On the other hand, the survival selection mechanism considers the local property of the Lebesgue measure, thus reducing the computational time in our algorithmic approach. The emerging indicator-based evolutionary algorithm is examined and compared versus three state-of-the-art multi-objective evolutionary algorithms based on the Lebesgue measure. In addition, we validate its performance on a set of artificial test problems with various characteristics, including multimodality, separability, and various Pareto front forms, incorporating concavity, convexity, and discontinuity. For a more exhaustive study, the proposed algorithm is evaluated in three real-world applications having four, five, and seven objective functions whose properties are unknown. We show the high competitiveness of our proposed approach, which, in many cases, improved the state-of-the-art indicator-based evolutionary algorithms on the multi-objective problems adopted in our investigation.

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