1. Taxonomy of Hybrid Metaheuristics Presented by: Xiaojun Bao & Lijun Wang Presented by: Xiaojun Bao & Lijun Wang School of Engineering School of Engineering University of Guelph University of Guelph Paper review for ENGG*6140 Optimization

2. Outline 1. Introduction 2. Design issues of Hybrid Metaheuristics 3. Implementation issues of Hybrid Metaheuristics 4. A Grammar for extended hybrid schemes 5. Conclusion 6. Reference

3. Introduction 1.1 Single-solution algorithms: - descent local search - descent local search - greedy heuristic - greedy heuristic - simulated annealing - simulated annealing - tabu search - tabu search

4. Introduction 1.2 Metaheuristic algorithms: - evolutionary algorithms - evolutionary algorithms EA: genetic algorithms evolution strategies genetic programming

5. Introduction - ant colonies - ant colonies - scater search - scater search - and so on. - and so on.

6. Hybridization 1.3 Hybrid Metaheuristics So far, many hybrid metaheuristic algorithms have been proposed and implemented to solve many combinatorial optimization problems, e.g. those known as NP-hard. So far, many hybrid metaheuristic algorithms have been proposed and implemented to solve many combinatorial optimization problems, e.g. those known as NP-hard. The best results found for various practical problems have proven that combination of different algorithms are very powerful, in case of large and difficult problems. The best results found for various practical problems have proven that combination of different algorithms are very powerful, in case of large and difficult problems.

7. Hybridization A taxonomy of hybrid algorithms is presented to provide a common terminology and classification mechanism A taxonomy of hybrid algorithms is presented to provide a common terminology and classification mechanism Based on the general taxonomy, we could make the comparison of the hybrid algorithms in a qualitative way. Based on the general taxonomy, we could make the comparison of the hybrid algorithms in a qualitative way.

8. Hybridization Hybridization of heuristics involves a few major issues which may be classified as design and implementation respectively. Hybridization of heuristics involves a few major issues which may be classified as design and implementation respectively. design functionality architecture

9. Hybridization implementation hardware platform programming model environment

10. Design issues 2.1 Hierarchical classification The structure of the hierarchical portion of the taxonomy is shown as follows: The structure of the hierarchical portion of the taxonomy is shown as follows:

11. Design issues Figure 1. Classification (design issues)

12. Hierarchical classification 2.1.1 Low-level versus High-level The low-level hybridization addresses the functional composition of a single optimization method. In this hybrid class, a given function of a metaheuristic is replaced by another metaheuristic. The low-level hybridization addresses the functional composition of a single optimization method. In this hybrid class, a given function of a metaheuristic is replaced by another metaheuristic.

13. Hierarchical classification In high-level hybrid algorithms, the different metaheuristics are self-contained. We have no direct relationship to the internal workings of a metaheuristic. In high-level hybrid algorithms, the different metaheuristics are self-contained. We have no direct relationship to the internal workings of a metaheuristic.

14. Hierarchical classification 2.1.2 Relay versus Co-evolutionary In relay hybridization, a set of meta- heuristics is applied one after another, each using the output of the previous as its input, acting in a pipeline fashion. In relay hybridization, a set of meta- heuristics is applied one after another, each using the output of the previous as its input, acting in a pipeline fashion.

15. Hierarchical classification Co-evolutionary hybridization represents cooperative optimization models, in which we have many parallel cooperating agents, each agent carries out a search in a solution space. Co-evolutionary hybridization represents cooperative optimization models, in which we have many parallel cooperating agents, each agent carries out a search in a solution space.

16. Hierarchical classification Four classes are divided from this hierarchical taxonomy: Four classes are divided from this hierarchical taxonomy: LRH (Low-level Relay Hybrid). LRH (Low-level Relay Hybrid). This class of hybrids represents algorithms in which a given metaheuristic is embedded into a single-solution metaheuristic. Few examples from the literature belong to this class. This class of hybrids represents algorithms in which a given metaheuristic is embedded into a single-solution metaheuristic. Few examples from the literature belong to this class. Let us look at the following example: Let us look at the following example:

17. Hierarchical classification Figure 2. An example of LRH hybridization embedding local search in simulated annealing annealing

18. Hierarchical classification LCH (Low-level Co-evolutionary Hybrid) LCH (Low-level Co-evolutionary Hybrid) Two competing goals govern the design of a metaheuristic: exploration and exploitation. Two competing goals govern the design of a metaheuristic: exploration and exploitation. In order to achieve the best performance, most efficient population-based heuristics (i.e., genetic algorithms, scatter search, ant colonies, etc.) have been coupled with local search method such as hill-climbing, simulated annealing and tabu search. In order to achieve the best performance, most efficient population-based heuristics (i.e., genetic algorithms, scatter search, ant colonies, etc.) have been coupled with local search method such as hill-climbing, simulated annealing and tabu search.

19. Hierarchical classification An example: An example: Figure 3. LCH. For instance, a tabu search is used as a mutation operator and a greedy heuristic as a crossover operator in a genetic algorithm Figure 3. LCH. For instance, a tabu search is used as a mutation operator and a greedy heuristic as a crossover operator in a genetic algorithm GA Individuals individual Crossover mutation Greedy heuristic tabu

20. Hierarchical classification HRH (High-level Relay Hybrid). HRH (High-level Relay Hybrid). In HRH hybrid, self-contained metaheuristics are executed in a sequence. In HRH hybrid, self-contained metaheuristics are executed in a sequence. For example, evolutionary algorithms are not well suited for fine-tuning structures which are very close to optimal solutions. Instead, the strength of EA is in quickly locating the high performance regions of vast and complex search spaces. Once those regions are located, it may be useful to apply local search heuristics to the high performance structures evolved by the EA. For example, evolutionary algorithms are not well suited for fine-tuning structures which are very close to optimal solutions. Instead, the strength of EA is in quickly locating the high performance regions of vast and complex search spaces. Once those regions are located, it may be useful to apply local search heuristics to the high performance structures evolved by the EA.

21. Hierarchical classification GA Tabu Greedy heuristic GA Greedy heuristic GA Tabu Three instances of this hybridization scheme: Population to exploit Initial population Population to exploit

22. Hierarchical classification HCH (High-level Co-evolutionary Hybrid). HCH (High-level Co-evolutionary Hybrid). The HCH scheme involves several self- contained algorithms performing a search in parallel, and cooperating to find an optimum. Intuitively, HCH will ultimately perform at least as well as one algorithm alone, more often perform better, each algorithm providing information to the others to help them. The HCH scheme involves several self- contained algorithms performing a search in parallel, and cooperating to find an optimum. Intuitively, HCH will ultimately perform at least as well as one algorithm alone, more often perform better, each algorithm providing information to the others to help them.

23. Hierarchical classification An example of HCH based on GA is the island model: An example of HCH based on GA is the island model: Figure 4. The island model of genetic algorithms as an example of High-level Co-evolutionary Hybrid.

24. Hierarchical classification a) The population is partitioned into small subpopulations a) The population is partitioned into small subpopulations by geographic isolation. by geographic isolation. c) A GA evolves each subpopulation c) A GA evolves each subpopulation b) Individuals can migrate between subpopulations b) Individuals can migrate between subpopulations d) The model is controlled by several parameters: d) The model is controlled by several parameters: - topology - topology - migration rate - migration rate - replacement strategy - replacement strategy - migration interval - migration interval

25. Hierarchical classification e) The results of many experiment done based on this model show that: e) The results of many experiment done based on this model show that: the global optimum was found more often when migration (with cooperation) was used than in completely isolated cases (without cooperation). the global optimum was found more often when migration (with cooperation) was used than in completely isolated cases (without cooperation).

26. Flat classification 2.2 Flat classification 2.2.1 Homogeneous versus Heterogeneous - In homogeneous hybrids, all the combined algorithms use the same metaheuristic. In general, different parameters are used for the algorithms. - In homogeneous hybrids, all the combined algorithms use the same metaheuristic. In general, different parameters are used for the algorithms. - In heterogeneous algorithms, different metaheuristics are used. - In heterogeneous algorithms, different metaheuristics are used.

27. Flat classification Figure 5. High-level Co-evolutionary Hybridization Figure 5. High-level Co-evolutionary Hybridization HCH(heterogeneous, global, general). Several search HCH(heterogeneous, global, general). Several search algorithms cooperate, co-adapt, and co-solve a solution. algorithms cooperate, co-adapt, and co-solve a solution.

28. Flat classification The GRASP method may be seen as an iterated heterogeneous HRH hybrid, in which local search is repeated from a number of initial solutions generated by randomized greedy heuristic. The GRASP method may be seen as an iterated heterogeneous HRH hybrid, in which local search is repeated from a number of initial solutions generated by randomized greedy heuristic.

29. Flat classification 2.2.2 Global versus Partial - In global hybrids, all the algorithms search in the whole research space. The goal is here to explore the space more thoroughly. - In global hybrids, all the algorithms search in the whole research space. The goal is here to explore the space more thoroughly. - In partial hybrids, the problem to be solved is decomposed into sub-problems, each one having its own search space. Then each algorithm is dedicated to the search in one of these sub-space. - In partial hybrids, the problem to be solved is decomposed into sub-problems, each one having its own search space. Then each algorithm is dedicated to the search in one of these sub-space.

30. Flat classification 2.2.3 Specialist versus General - In general hybrids, all the algorithms solve the same target optimization problem. All the above mentioned hybrids are general hybrids. - In general hybrids, all the algorithms solve the same target optimization problem. All the above mentioned hybrids are general hybrids. - Specialist hybrids combine algorithms which solve different problems. An example of such a HCH approach has been developed to solve the quadratic assignment problem(QAP). - Specialist hybrids combine algorithms which solve different problems. An example of such a HCH approach has been developed to solve the quadratic assignment problem(QAP).

31. Flat classification Figure 6. High-level Co-evolutionary hybridization HCH(Global, Heterogeneous, Specialist). Several search algorithms solve different problems

32. Flat classification Another approach of specialist hybrid HRH heuristic is to use an heuristic to optimize another heuristic, i.e. find the optimal values of the parameters of the heuristic. This approach has been used to optimize simulated annealing by GA, ant colonies by GA, and a GA by a GA. Another approach of specialist hybrid HRH heuristic is to use an heuristic to optimize another heuristic, i.e. find the optimal values of the parameters of the heuristic. This approach has been used to optimize simulated annealing by GA, ant colonies by GA, and a GA by a GA.

33. Implementation issues The structure of the taxonomy concerning implementation issues is shown in Figure 7. The structure of the taxonomy concerning implementation issues is shown in Figure 7.

34. Implementation issues Figure 7. Classification of hybrid metaheuristics(implementation issues).

35. Implementation issues Specific versus General-purpose computers Specific versus General-purpose computers - Application specific computers differ from general purpose ones in that they usually only solve a small range of problems, but often at much higher rates and lower costs. Their internal structure is tailored for a particular problem, and thus can achieve much higher efficiency and hardware utilization than a processor which must handle a wide range of tasks. - Application specific computers differ from general purpose ones in that they usually only solve a small range of problems, but often at much higher rates and lower costs. Their internal structure is tailored for a particular problem, and thus can achieve much higher efficiency and hardware utilization than a processor which must handle a wide range of tasks.

36. Implementation issues Sequential versus Parallel Sequential versus Parallel - Most of the proposed hybrid metaheuristics are sequential. - Most of the proposed hybrid metaheuristics are sequential. - According to the size of problems, parallel implementations of hybrid algorithms have been considered. Parallel hybrids may be classified using the different characteristics of the target parallel architecture: - According to the size of problems, parallel implementations of hybrid algorithms have been considered. Parallel hybrids may be classified using the different characteristics of the target parallel architecture: SIMD versus MIMD SIMD versus MIMD In SIMD (Single Instruction stream, Multiple Data Stream) parallel machines, the processors are restricted to execute the same program. They are very efficient in executing synchronized parallel algorithms that contain regular computations and regular data structure. In SIMD (Single Instruction stream, Multiple Data Stream) parallel machines, the processors are restricted to execute the same program. They are very efficient in executing synchronized parallel algorithms that contain regular computations and regular data structure.

37. Implementation issues In parallel MIMD (Multiple Instruction stream, Multiple data stream), the processors are allowed to perform different types of instructions on different data. HCH hybrids based respectively on tabu search, simulated annealing, and genetic algorithms have been implemented on networks of transputers. In parallel MIMD (Multiple Instruction stream, Multiple data stream), the processors are allowed to perform different types of instructions on different data. HCH hybrids based respectively on tabu search, simulated annealing, and genetic algorithms have been implemented on networks of transputers. Shared-memory versus Distributed-memory Shared-memory versus Distributed-memory Shared-memory parallel architecture simplicity Shared-memory parallel architecture simplicity Distributed-memory parallel architecture flexible and Distributed-memory parallel architecture flexible and fault-tolerant fault-tolerant programming programming platform platform

38. Implementation issues Homogeneous versus Heterogeneous Homogeneous versus Heterogeneous - Most of massively parallel machines (MPP) and cluster of processors such as IBM SP/2, Cray T3D, and DEC Alpha-farms are composed of homogeneous processors. - Most of massively parallel machines (MPP) and cluster of processors such as IBM SP/2, Cray T3D, and DEC Alpha-farms are composed of homogeneous processors. - Heterogeneous network of workstations comp up as platforms for high-performance computing due to the availability of powerful workstations and fast communication networks. - Heterogeneous network of workstations comp up as platforms for high-performance computing due to the availability of powerful workstations and fast communication networks. Look at the following example: Look at the following example:

39. Implementation issues Figure 8. Parallel implementation of heterogeneous HCH algorithms. Figure 8. Parallel implementation of heterogeneous HCH algorithms.

40. Implementation issues 3.3 Static, Dynamic or Adaptive static: This category represents parallel heuristics in which static: This category represents parallel heuristics in which both the number of tasks of the application and the both the number of tasks of the application and the location of the work (tasks or data) are generated at location of the work (tasks or data) are generated at compile time (static scheduling). The allocation of compile time (static scheduling). The allocation of processors to tasks (or data) remains unchanged processors to tasks (or data) remains unchanged during the execution of the application regardless of during the execution of the application regardless of the current state of the parallel machines. Most of the current state of the parallel machines. Most of the proposed parallel heuristics belong to this class. the proposed parallel heuristics belong to this class.

41. The major disadvantage When there are noticeable load or power differences between processors, a significant number of tasks are often idle waiting for other tasks to complete their work.

42. Implementation issues dynamic : To improve the performance of parallel static dynamic : To improve the performance of parallel static heuristics, dynamic load balancing must be heuristics, dynamic load balancing must be introduced. This class represents heuristics introduced. This class represents heuristics for which the number of tasks is fixed at for which the number of tasks is fixed at compile-time, but the location of work (tasks, compile-time, but the location of work (tasks, data) is determined and/or changed at run- data) is determined and/or changed at run- time. For example, load-balancing requirement time. For example, load-balancing requirement can be met by a dynamic redistribution of can be met by a dynamic redistribution of work between processors. work between processors.

43. Disadvantage When the number of tasks exceeds the number of idle nodes, multiple tasks are assigned to the same node. Moreover, when there are more idle nodes than tasks, some of them will not be used.

44. Implementation issues adaptive: Parallel adaptive programs are parallel adaptive: Parallel adaptive programs are parallel computations with a dynamically changing set of computations with a dynamically changing set of tasks. Tasks may be created or killed as a function tasks. Tasks may be created or killed as a function of the load state of the parallel machine. A task is of the load state of the parallel machine. A task is created automatically when a node become idle. created automatically when a node become idle. When a node becomes busy, the task is killed. When a node becomes busy, the task is killed.

45. A grammar for extended hybrids | | | | | | LRH ( ( )) LRH ( ( )) LCH ( ( )) LCH ( ( )) HRH ( + ) HRH ( + ) HCH ( ) HCH ( ) HCH (, ) HCH (, ) (,, ) (,, ) homogeneous | heterogeneous homogeneous | heterogeneous global | partial global | partial

46. A grammar for extended hybrids general | specialist general | specialist sequential | parallel sequential | parallel static | dynamic | adaptive static | dynamic | adaptive LS | TS | SA | GA | ES | GP | NN | LS | TS | SA | GA | ES | GP | NN | GH | AC | SS | NM | CLP | GH | AC | SS | NM | CLP | Figure 9. A grammar for extended hybridization schemes

47. A grammar for extended hybrids Some hybridization examples: HCH(HRH(GH+LCH(GA(LS)))) hierarchical scheme was used to solve set partitioning problem. HCH(HRH(GH+LCH(GA(LS)))) hierarchical scheme was used to solve set partitioning problem. HRH(GH+LS+LCH(GA(GH+LS))) scheme was used for traveling salesman problem. HRH(GH+LS+LCH(GA(GH+LS))) scheme was used for traveling salesman problem. Three metaheuristics, GA, SA, and TS have been combined in a LCH(GA(HRH(SA+TS))) scheme to solve a scheduling problem. Three metaheuristics, GA, SA, and TS have been combined in a LCH(GA(HRH(SA+TS))) scheme to solve a scheduling problem.

48. Conclusion A taxonomy for hybrid metaheuristics has been presented. A taxonomy for hybrid metaheuristics has been presented. It considers solutions to design and implementation issues. It considers solutions to design and implementation issues. Treating the two problems orthogonally is beneficial because it allows one to study, understand, classify and evaluate the algorithms using a well defined set of criteria. Treating the two problems orthogonally is beneficial because it allows one to study, understand, classify and evaluate the algorithms using a well defined set of criteria.

49. Conclusion Hybrid metaheuristics that hybridize population-based metaheuristics with local search heuristics have been proved to be very efficient for large size and hard optimization problem. Hybrid metaheuristics that hybridize population-based metaheuristics with local search heuristics have been proved to be very efficient for large size and hard optimization problem. The HCH proposes natural way to efficiently implement algorithms on heterogeneous computer environment The HCH proposes natural way to efficiently implement algorithms on heterogeneous computer environment

50. References E-G. Talbi. A Taxonomy of Hybrid Metaheuristics. Journal of Combinatorial Optimization, 1-45, 1999 E-G. Talbi. A Taxonomy of Hybrid Metaheuristics. Journal of Combinatorial Optimization, 1-45, 1999 V. Bachelet, P. Preux, and E-G. Talbi. Parallel Hybrid Meta-heuristics: Application to the Quadratic Assignment Problem. May, 1996 V. Bachelet, P. Preux, and E-G. Talbi. Parallel Hybrid Meta-heuristics: Application to the Quadratic Assignment Problem. May, 1996 Olivier C. Martin, and Steve W. Otto. Combining Simulated Annealing with Local Search Heuristics. Annals of Operations Research, 1996 Olivier C. Martin, and Steve W. Otto. Combining Simulated Annealing with Local Search Heuristics. Annals of Operations Research, 1996 D.E. Brown, C. L. Huntley, and A. R. Spillane. A parallel genetic heuristic for the quadratic assignment problem. In Third Int. Conf. On Genetic Algorithms ICGA’ 89, San Mateo, USA, July 1989 D.E. Brown, C. L. Huntley, and A. R. Spillane. A parallel genetic heuristic for the quadratic assignment problem. In Third Int. Conf. On Genetic Algorithms ICGA’ 89, San Mateo, USA, July 1989

51. The End Thank you ! Thank you !