Abstract
Aiming at the optimization problem of multiple objectives with contradictions and conflicts in the process of allocating the tolerance for complex products, taking advantage of the features of coordinating, and balancing contradictions and conflicts of cooperative game theory, this paper uses cooperative game theory to solve the multiobjective optimization problem of tolerance allocation. The quality requirements and cost requirements of assembly products are used as the game decision parties, and the fuzzy clustering method is used to group the design variables of tolerance allocation problem of the steam turbine to form the strategic space of game parties. Take the quality level and cost level of the assembly product as the optimization goals, complete the calculation of the utilities of the two game parties, and establish the multiobjective optimization model of tolerance allocation based on cooperative game theory. Finally, the Shapley value method based on cooperative game theory, the Nash equilibrium method based on noncooperative game theory, and the traditional single-objective optimization method with the quality as the constraint and the cost as the optimization objective are used to solve the tolerance allocation problem of steam turbine. The solution results show that the method of cooperative game realized the balance, coordination, and comprehensive optimization of the quality and cost from the perspective of collective interests, overcame the shortcomings of the traditional single-objective optimization method, and obtained better result than the Nash equilibrium method.
Highlights
Tolerance allocation is a core issue of tolerance design theory; it mainly studies how to scientifically and reasonably allocate the design tolerance of the closed ring to each component ring [1] and realizes the balanced coordination and comprehensive optimization of some indicators such as processing cost of the product, assembly quality, and assembly robustness under the premise of ensuring certain assembly success rate [1]. e key issue of tolerance allocation is how to establish a balance among its contradictory and conflicting goals, especially between the quality and cost, consider the mutual influence and conflict between the two goals, and get a scientific, reasonable, and balanced and coordinated tolerance allocation optimization program
The widely used tolerance allocation method is single-objective optimization method with quality as the constraint and cost as the optimization goal [2, 3], or both quality and cost are considered, and a multiobjective comprehensive weighted evaluation function is constructed to complete the establishment of the tolerance allocation optimization model
There are some more common algorithms, such as simulated annealing (SA) [9], genetic algorithm (GA) [10], particle swarm optimization (PSO) [11], and ant colony algorithm; besides, some less common algorithms are used for tolerance-cost optimization, such as the imperial competition algorithm [12], self-organizing migration algorithm [13], bat algorithm [14], artificial bee colony algorithm [15], and cuckoo search [16]
Summary
Tolerance allocation is a core issue of tolerance design theory; it mainly studies how to scientifically and reasonably allocate the design tolerance of the closed ring to each component ring [1] and realizes the balanced coordination and comprehensive optimization of some indicators such as processing cost of the product, assembly quality, and assembly robustness under the premise of ensuring certain assembly success rate [1]. e key issue of tolerance allocation is how to establish a balance among its contradictory and conflicting goals, especially between the quality and cost, consider the mutual influence and conflict between the two goals, and get a scientific, reasonable, and balanced and coordinated tolerance allocation optimization program. We took assembly quality and processing cost as the two game parties, adopted the fuzzy cluster analysis method to determine the strategy space of each game party, assembly quality level, and processing cost level as the optimization goals, calculated the utility of the two game parties, and established a set of tolerance distribution multiobjective optimization models for the steam turbines based on the cooperative game theory.
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