New meta-heuristic for combinatorial optimization problems: Intersection based scaling

Zou, Peng; Zhou, Zhi; Wan, Yingyu; Chen, Guoliang; Gu, Jun

doi:10.1007/bf02973434

Cited by 5 publications

(4 citation statements)

References 25 publications

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“…, where a and b are the boundaries of X. e dynamic opposite number X DO can be defined as equation (16), where a and b are the boundaries and rand is a random number between 0 and 1. Moreover, w is a positive weighting factor, and X O is the opposite number defined as equation ( 14):…”

Section: Dynamic Opposite Number X Is a Real Number In [A B]mentioning

confidence: 99%

“…Check the boundaries; (7) end for (8) end for (9) Select N number of the fittest individuals from X ∪ X DO ; (10) Set G � 0; (11) while G ≤ maximal iteration do (12) Evaluate all learners by the fitness function f(. ); (13) if G � 1 then (14) Sort individuals by the fitness value to get the best grasshopper X best in the first population; (15) else (16) for i � 1; i ≤ Np; i + + do (17) Update the position of the individuals X i according to update mechanism (equation ( 12)); (18) Check the boundaries; (19) Evaluate the fitness values of the new individuals X′; (20) if f(X i ′ ) < f(X best ) then (21) Replace X best with X i ′ ; (22) end if (23) end for (24) end if (25)…”

Section: Analysis Of Convergencementioning

confidence: 99%

“…Global optimization algorithms mainly consist of two classes: deterministic mathematical programming method [7][8][9][10] and metaheuristic algorithms (MAs) [11][12][13][14]. MAs have simple structure and strong adaptability, which is very advantageous in solving complex problems [15,16]. In recent decades, inspired by nature, MAs with many different characteristics have been proposed by researchers.…”

Section: Introductionmentioning

confidence: 99%

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A Dynamic Opposite Learning Assisted Grasshopper Optimization Algorithm for the Flexible JobScheduling Problem

et al. 2020

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Job shop scheduling problem (JSP) is one of the most difficult optimization problems in manufacturing industry, and flexible job shop scheduling problem (FJSP) is an extension of the classical JSP, which further challenges the algorithm performance. In FJSP, a machine should be selected for each process from a given set, which introduces another decision element within the job path, making FJSP be more difficult than traditional JSP. In this paper, a variant of grasshopper optimization algorithm (GOA) named dynamic opposite learning assisted GOA (DOLGOA) is proposed to solve FJSP. The recently proposed dynamic opposite learning (DOL) strategy adopts the asymmetric search space to improve the exploitation ability of the algorithm and increase the possibility of finding the global optimum. Various popular benchmarks from CEC 2014 and FJSP are used to evaluate the performance of DOLGOA. Numerical results with comparisons of other classic algorithms show that DOLGOA gets obvious improvement for solving global optimization problems and is well-performed when solving FJSP.

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Section: Dynamic Opposite Number X Is a Real Number In [A B]mentioning

confidence: 99%

Section: Analysis Of Convergencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Dynamic Opposite Learning Assisted Grasshopper Optimization Algorithm for the Flexible JobScheduling Problem

et al. 2020

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“…For large instances, many heuristics offering very good near optimal solutions in a reasonable time have been developed [14][15][16][17][18] . Yet there still lack theoretical analysis results of the backbone for the GBP except that Zou et al [19] developed a heuristic with the approximate backbone. For the GBP, there exist two major problems: (i) A serious disadvantage exists in those widely used methods to approximate the backbone, i.e.…”

mentioning

confidence: 99%

Unique optimal solution instance and computational complexity of backbone in the graph bi-partitioning problem

2007

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As an important tool for heuristic design of NP-hard problems, backbone analysis has become a hot spot in theoretical computer science in recent years. Due to the difficulty in the research on computational complexity of the backbone, many researchers analyzed the backbone by statistic ways. Aiming to increase the backbone size which is usually very small by the existing methods, the unique optimal solution instance construction (UOSIC) is proposed for the graph bi-partitioning problem (GBP). Also, we prove by using the UOSIC that it is NP-hard to obtain the backbone, i.e. no algorithm exists to obtain the backbone of a GBP in polynomial time under the assumption that P ≠ NP. Our work expands the research area of computational complexity of the backbone. And the UOSIC provides a new way for heuristic design of NP-hard problems.graph bi-partitioning problem, NP-hard, backbone analysis, unique optimal solution instance, computational complexity Backbone analysis [1] has been a hot spot in the research of NP-hard problems [2] in recent years. The backbone, the shared common part of all optimal solutions for an NP-hard problem instance, is important to the evaluation of the hardness and phase transition of NP-hard problems. Monasson et al. [3] investigated the effect of the backbone on the hardness and phase transition of the satisfiability problem (SAT) in 1998. Zhang [4] analyzed the effect of the backbone size on the asymmetric traveling salesman problem (ATSP). Moreover, backbone analysis has been currently an important way to design heuristics for NP-hard problems. Schneider [5] and Zou et al. [6] proposed multilevel reduction algorithms for the TSP by using the intersection of local optimal solutions as the approximate backbone, respectively. Zhang et al. [7] presented a backbone guided LK algorithm for the TSP. Zhang [8] , Dubois et al. [9] , and Valnir et al. [10] gave backbone guided local search algorithms for the SAT, respectively. Zou et al. [11] developed the approximate backbone-guided fant (ABFANT) for the quadratic assignment problem (QAP). However, backbone analysis is still in the beginning state using experimental statistic methods. Also, there are few theoretical analysis results concerning the backbone. As to our knowledge, the only theoretical result is that Kilby et al. [12] proved that it is NP-hard to obtain the backbone of the TSP.The graph bi-partitioning problem (GBP) [2] is one of the classical NP-hard problems, with extensive applications in parallel computing, very large scale integration (VLSI), transportation scheduling, and data mining. According to the computational complexity theory [13] , there exists no exact algorithm to solve NP-hard problems in polynomial time unless P=NP. For large instances, many heuristics offering very good near optimal solutions in a reasonable time have been developed [14][15][16][17][18] . Yet there

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A Puzzle-Based Genetic Algorithm with Block Mining and Recombination Heuristic for the Traveling Salesman Problem

Chang

Huang

Zhang

2012

J. Comput. Sci. Technol.

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New meta-heuristic for combinatorial optimization problems: Intersection based scaling

Cited by 5 publications

References 25 publications

A Dynamic Opposite Learning Assisted Grasshopper Optimization Algorithm for the Flexible JobScheduling Problem

A Dynamic Opposite Learning Assisted Grasshopper Optimization Algorithm for the Flexible JobScheduling Problem

Unique optimal solution instance and computational complexity of backbone in the graph bi-partitioning problem

A Puzzle-Based Genetic Algorithm with Block Mining and Recombination Heuristic for the Traveling Salesman Problem

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