scholarly journals Running Time Analysis of MOEA/D with Crossover on Discrete Optimization Problem

2019 ◽  
Vol 33 ◽  
pp. 2296-2303 ◽  
Author(s):  
Zhengxin Huang ◽  
Yuren Zhou ◽  
Zefeng Chen ◽  
Xiaoyu He
Keyword(s):  
Discrete Optimization ◽  
Optimization Problems ◽  
Theoretical Aspect ◽  
Weight Vector ◽  
Future Research ◽  
Discrete Optimization Problem ◽  
Time Analysis ◽  
Running Time ◽  
Running Time Analysis ◽  
The One

Decomposition-based multiobjective evolutionary algorithms (MOEAs) are a class of popular methods for solving multiobjective optimization problems (MOPs), and have been widely studied in numerical experiments and successfully applied in practice. However, we know little about these algorithms from the theoretical aspect. In this paper, we present a running time analysis of a simple MOEA with crossover based on the MOEA/D framework (MOEA/D-C) on four discrete optimization problems. Our rigorous theoretical analysis shows that the MOEA/D-C can obtain a set of Pareto optimal solutions to cover the Pareto front of these problems in expected running time apparently lower than the one without crossover. Moreover, the MOEA/D-C only needs to decompose an MOP into a few scalar optimization subproblems according to several simple weight vectors. This result suggests that the use of crossover in decomposition-based MOEA can simplify the setting of weight vector for different problems and make the algorithm more efficient. This study theoretically explains why some decomposition-based MOEAs work well in computational experiments and provides insights in design of MOEAs for MOPs in future research.

scholarly journals A General Approach to Running Time Analysis of Multi-objective Evolutionary Algorithms

2018 ◽  
Author(s):  
Chao Bian ◽  
Chao Qian ◽  
Ke Tang
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Theoretical Aspect ◽  
Combinatorial Problems ◽  
Time Analysis ◽  
Running Time ◽  
Asymptotic Bounds ◽  
Multi Objective ◽  
Running Time Analysis ◽  
Empirical Performance

Evolutionary algorithms (EAs) have been widely applied to solve multi-objective optimization problems. In contrast to great practical successes, their theoretical foundations are much less developed, even for the essential theoretical aspect, i.e., running time analysis. In this paper, we propose a general approach to estimating upper bounds on the expected running time of multi-objective EAs (MOEAs), and then apply it to diverse situations, including bi-objective and many-objective optimization as well as exact and approximate analysis. For some known asymptotic bounds, our analysis not only provides their leading constants, but also improves them asymptotically. Moreover, our results provide some theoretical justification for the good empirical performance of MOEAs in solving multi-objective combinatorial problems.

Discrete Social Spider Algorithm for Solving Traveling Salesman Problem

2021 ◽  
pp. 2150020
Author(s):  
Asieh Khosravanian ◽  
Mohammad Rahmanimanesh ◽  
Parviz Keshavarzi
Keyword(s):  
Genetic Algorithm ◽  
Discrete Optimization ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Fitness Function ◽  
Traveling Salesman ◽  
The Other ◽  
Discrete Optimization Problem ◽  
Social Spider ◽  
Social Spider Algorithm

The Social Spider Algorithm (SSA) was introduced based on the information-sharing foraging strategy of spiders to solve the continuous optimization problems. SSA was shown to have better performance than the other state-of-the-art meta-heuristic algorithms in terms of best-achieved fitness values, scalability, reliability, and convergence speed. By preserving all strengths and outstanding performance of SSA, we propose a novel algorithm named Discrete Social Spider Algorithm (DSSA), for solving discrete optimization problems by making some modifications to the calculation of distance function, construction of follow position, the movement method, and the fitness function of the original SSA. DSSA is employed to solve the symmetric and asymmetric traveling salesman problems. To prove the effectiveness of DSSA, TSPLIB benchmarks are used, and the results have been compared to the results obtained by six different optimization methods: discrete bat algorithm (IBA), genetic algorithm (GA), an island-based distributed genetic algorithm (IDGA), evolutionary simulated annealing (ESA), discrete imperialist competitive algorithm (DICA) and a discrete firefly algorithm (DFA). The simulation results demonstrate that DSSA outperforms the other techniques. The experimental results show that our method is better than other evolutionary algorithms for solving the TSP problems. DSSA can also be used for any other discrete optimization problem, such as routing problems.

Running-time Analysis of Ant System Algorithms with Upper-bound Comparison

2017 ◽  
Vol 8 (4) ◽  
pp. 1-17
Author(s):  
Han Huang ◽  
Hongyue Wu ◽  
Yushan Zhang ◽  
Zhiyong Lin ◽  
Zhifeng Hao
Keyword(s):  
Optimal Solution ◽  
Numerical Results ◽  
Ant System ◽  
Time Analysis ◽  
Traveling Salesman Problems ◽  
Running Time ◽  
Cycle System ◽  
Running Time Analysis ◽  
Global Optimal

Running-time analysis of ant colony optimization (ACO) is crucial for understanding the power of the algorithm in computation. This paper conducts a running-time analysis of ant system algorithms (AS) as a kind of ACO for traveling salesman problems (TSP). The authors model the AS algorithm as an absorbing Markov chain through jointly representing the best-so-far solutions and pheromone matrix as a discrete stochastic status per iteration. The running-time of AS can be evaluated by the expected first-hitting time (FHT), the least number of iterations needed to attain the global optimal solution on average. The authors derive upper bounds of the expected FHT of two classical AS algorithms (i.e., ant quantity system and ant-cycle system) for TSP. They further take regular-polygon TSP (RTSP) as a case study and obtain numerical results by calculating six RTSP instances. The RTSP is a special but real-world TSP where the constraint of triangle inequality is stringently imposed. The numerical results derived from the comparison of the running time of the two AS algorithms verify our theoretical findings.

scholarly journals Running Time Analysis of the ( $$1+1$$ 1 + 1 )-EA for OneMax and LeadingOnes Under Bit-Wise Noise

Algorithmica ◽  
2018 ◽  
Vol 81 (2) ◽  
pp. 749-795 ◽  
Author(s):  
Chao Qian ◽  
Chao Bian ◽  
Wu Jiang ◽  
Ke Tang
Keyword(s):  
Time Analysis ◽  
Running Time ◽  
Running Time Analysis

scholarly journals Partial Quicksort and Quickpartitionsort

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Conrado Martínez ◽  
Uwe Rösler
Keyword(s):  
Lower Bound ◽  
Time Analysis ◽  
Information Theoretic ◽  
Running Time ◽  
Running Time Analysis ◽  
International Audience

International audience Partial Quicksort sorts the $l$ smallest elements in a list of length $n$. We provide a complete running time analysis for this combination of Find and Quicksort. Further we give some optimal adapted versions, called Partition Quicksort, with an asymptotic running time $c_1l\ln l+c_2l+n+o(n)$. The constant $c_1$ can be as small as the information theoretic lower bound $\log_2 e$.

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