Extremal optimization

About: Extremal optimization is a research topic. Over the lifetime, 1168 publications have been published within this topic receiving 104943 citations.

Experimental analysis of new heuristics for the TSP

Abstract: In this study, the three new heuristic algorithms which are proposed in [1] for the solution of traveling salesman problem is developed In addition, the new versions of 2-opt and 3-opt algorithms are proposed These algorithms are tested and their performances are compared with the well-known heuristic algorithms such as Nearest Neighbor, and Greedy algorithms

Multipoint-based tabu search using proximate optimality principle

Abstract: This paper presents a new method for combinatorial optimization problems. Most of the actual problems that have discrete structure can be formulated as combinatorial optimization problems. It is experientially known that proximate optimality principle (POP) holds in most of the actual combinatorial optimization problems. The concept of proximate optimality principle says that good solutions of most real combinatorial optimization problems have the structural similarity in parts of solution. In this paper, we propose a new optimization method based on tabu search. In the proposed algorithm, POP is taken into consideration. The proposed algorithm is applied to some knapsack problems and traveling salesman problems, which are typical combinatorial optimization problems in order to verify the performance of the proposed algorithm.

Heuristic Optimization of Physical Data Bases: Using a Generic and Abstract Design Model

Abstract: Designing efficient physical data bases is a complex activity, involving the consideration of a large number of factors. Mathematical programming-based optimization models for physical design make many simplifying assumptions; thus, their applicability is limited. In this article, we show that heuristic algorithms can be successfully used in the development of very good, physical data base designs. Two heuristic optimization algorithms are proposed in the contest of a genetic and abstract model for physical design. One algorithm is based on generic principles of heuristic optimization. The other is based on capturing and using problem-specific information in the heuristics. The goodness of the algorithms is demonstrated over a wide range of problems and factor values.

Solving the Traveling Salesman Problem through Extended Changing Crossover Operators

Abstract: In order to efficiently obtain an approximate solution of the traveling salesman problem (TSP), a new method of extended changing crossover operators (ECXO) which can change any crossover operator of both genetic algorithms (GAs) and ant colony optimization (ACO) for another crossover operator at any time is proposed. In ECXO, all the cyclic paths which are produced by some operator are not only able to be delivered to another operator and are but also able to be updated by it. Through ECXO, we can succeed to search for the global optimum solution while maintaining diversity of the cyclic paths. In this study, we investigate an ECXO which mainly controlls edge assembly crossover (EAX), since recently EAX is found to be powerful to find out the global optimum solution by preserving good edges of previous tours and maintaining diversity of cyclic paths in the population. EAX represents any tour as a set of edges that connect two cities. With EAX a parent can exchange his edges with another parent’s ones reciprocally to create sub-cyclic paths, before restructuring a cyclic path by combining them with making distances minimum. EAX is an extension of edge exchange crossover (EXX) with which a parent can change his edge for another parent’s edge and he can make arrangement of his edges reverse or foward. Our C experiments show that EAX is superior to both edge recombination crossover (EX) and ACO from points of view of ability to combine parents’ sub-paths together to create a global optimum solution if parents’ sub-paths are locally optimal, that with EAX alone any child spends much time on creating locally optimal sub-paths because he can not take into consideration of edges’ lengths when he generates sub-cyclic paths, that since with EX or ACO any child or any ant selects the next city he visits by edges’ lengths or by tours’ lengths deposited on edges as pheromone, he can only generate local optimum paths and can not select an optimum one by considering global links of edges, he is apt to fall into the local optimum solution. Hence we study ECXO (ACO(or EX)(→EXX)→EAX) in which we generate cyclic-paths which are locally optimum and which have variety of arranging edges with EX, ACO and EXX in early generations, and we generate cyclic-paths with EAX to create global optimum solution efficiently after generations, where EAX succeeds cyclic-paths EX, ACO and EXX generate. The efficiency of ECXO is verified by C experiments using the data of lin318 which is a midium sized TSP in TSPLIB. Table 1 demonstrates its verification. Table 1 shows best length, average length, the number of optimum trials, relative error which is defined as ((average length)/(optimal length) 1), computational time to find the best length, and average computational time to find it. The average length is the average value of fifteen best lengths. They are obtained from 15 independent runs by using different seed-ids which range from one to fifteen, where seed-id generates different initial random tours for lin318, where EAX has Ncross of 30. From Table 1, it has been shown that four ECXOs as well as EAX can find best lengths and their relative errors are low. Four ECXOs can find the best solution earlier than EAX and its improvement-ratio ranges from 10% to 30%. Among them ECXO (EX→EAX) has least amount of mean time to find the optimum one. In Fig. 1 we compare four ECXOs and EAX on the convergence speed to the optimal length of 42,029. The data is obtained from a trial of seed_id of one with Ncross of 100. It shows that firstly ECXO (EX → EXX → EAX) find the best solution at 2,224 sec and that secondly ECXO (EX → EAX), thirdly EAX, fourthly ECXO (ACO→EAX), and finally ECXO(ACO → EXX→EAX) find it at 3,055 sec. In this paper it has been also shown that we can select the optimal generation to change crossover operators based on diversity and convergence of chromosomes. The efficiency of ECXO is also verified by bench-mark test using d198 and pcb442 in TSPLIB. Table 1. Comparison of ECXOs with EAX, EX, EXX and ACO on best length, average length, the number of optimal trials, relative error, and computational time to find the best length. Results are obtained from fifteen independent trials. Ncross=30 in EAX. The optimum length of lin318 is 42,029 in TSPLIB

Managing combinatorial optimization problems by means of evolutionary computation and multi-agent system

Abstract: The necessity for solving a combinatorial optimization problem is very common. Evolutionary/genetic program could be used to deal with such situations. Unfortunately, depending on the complexity of the problem, high computational capabilities are required, primarily in those cases in which measuring the quality of a potential solution is very demanding. However, advances in Distributed Artificial Intelligence (DAI), Multi-Agent Systems (MAS) to be more specific, could help users to deal with this situation by parallelizing the evolutionary program aiming to distribute the computational capabilities required. This paper presents an inter-agent MAS protocol for parallelizing an evolutionary program aiming to reduce the communications requirements necessary as well as allowing a response within a reasonable period of time.