Interval optimization algorithms usually use local search methods to obtain a good upper bound of the global optimal value. These local methods are based on point evaluations. A new interval-genetic algorithm is presented that combines an interval arithmetic and a genetic algorithm in the paper. The proposed algorithm uses the improved upper bound of the global optimal value obtained by the genetic algorithm to delete the intervals not containing the global optimal solution from the work set at each iteration. Using the interval arithmetic, the new algorithm not only has the advantages of simplicity and less knowledge about problems as traditional interval optimization algorithms, but also produces the reliable domains where the genetic algorithm is applied to search. Moreover, with the direction provided by the genetic algorithm applied, the chance to divide the reliable interval is increased. A convergence is proved and numerical experiments shows that the proposed algorithm is more efficient than traditional interval optimization algorithms.
"Few approaches attempted to hybridize EC algorithms and Interval Branch and Bound algorithms. (Sotiropoulos, Stavropoulos, and Vrahatis 1997) and (Zhang and Liu 2007) devised integrative methods that embedded one algorithm Copyright c 2013, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. "
"It appears that most of the hybridization between metaheuristics and exact methods concern discrete or combinatorial optimization. IBBA and EA hybridizations were introduced by Sotiropoulos  in 1997 and used by Zhang  in 2007. Both approaches are integrative combinations, as described by Puchinger and Raidl . "
[Show abstract][Hide abstract] ABSTRACT: In this article, we introduce a global cooperative approach between an Interval Branch and Bound Algorithm and an Evolutionary Algorithm, that takes advantage of both methods to optimize a function for which an inclusion function can be expressed. The Branch and Bound algorithm deletes whole blocks of the search space whereas the Evolutionary Algorithm looks for the optimum in the remaining space and sends to the IBBA the best evaluation found in order to improve its Bound. The two algorithms run independently and update common information through shared memory. The cooperative algorithm prevents premature and local convergence of the evolutionary algorithm, while speeding up the convergence of the branch and bound algorithm. Moreover, the result found is the proved global optimum. In part 1, a short background is introduced. Part 2.1 describes the basic Interval Branch and Bound Algorithm and part 2.2 the Evolutionary Algorithm. Part 3 introduces the cooperative algorithm and part 4 gives the results of the algorithms on benchmark functions. The last part concludes and gives suggestions of avenues of further research.
[Show abstract][Hide abstract] ABSTRACT: Evolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality.
Biennial International Conference on Artificial Evolution (EA 2013), Bordeaux, France; 10/2013
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