GUIDED HYBRID GENETIC ALGORITHM FOR SOLVING GLOBAL OPTIMIZATION PROBLEMS
Keywords:nonlinear optimization, global minimum, randomized search heuristics, hybrid approach, genetic algorithm, deflation operator, guided local search.
Context. One of the leading problems in the world of artificial intelligence is the optimization of complex systems, which is often represented as a nonlinear function that needs to be minimized. Such functions can be multimodal, non-differentiable, and even set as a black box. Building effective methods for solving global optimization problems raises great interest among scientists.
Objective. Development of a new hybrid genetic algorithm for solving global optimization problems, which is faster than existing analogues.
Methods. One of the crucial challenges for hybrid methods in solving nonlinear global optimization problems is the rational use of local search, as its application is accompanied by quite expensive computational costs. This paper proposes a new GBOHGA hybrid genetic algorithm that reproduces guided local search and combines two successful modifications of genetic algorithms. The first one is BOHGA that establishes a qualitative balance between local and global search. The second one is HGDN that prevents reexploration of the previously explored areas of a search space. In addition, a modified bump-function and an adaptive scheme for determining one of its parameters – the radius of the “deflation” of the objective function in the vicinity of the already found local minimum – were presented to accelerate the algorithm.
Results. GBOHGA performance compared to other known stochastic search heuristics on a set of 33 test functions in 5 and 25dimensional spaces. The results of computational experiments indicate the competitiveness of GBOHGA, especially in problems with multimodal functions and a large number of variables.
Conclusions. The new GBOHGA hybrid algorithm, developed on the basis of the integration of guided local search ideas and BOHGA and HGDN algorithms, allows to save significant computing resources and speed up the solution process of the global optimization problem. It should be used to solve global optimization problems that arise in engineering design, solving organizational and management problems, especially when the mathematical model of the problem is complex and multidimensional.
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