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Abstract.A strategy for solving an optimisation problem with a large number of objectives by transforming the original objective vector into a two-objective vector during survival selection is presented. The transformed objectives, referred to as preference objectives, consist of a winning score and a vicinity index. The winning score, a maximisation criterion, describes the difference of the number of superior and inferior objectives between two solutions. The minimisation vicinity index describes the level of solution clustering around a search location, particularly the best value of each individual objective, is used to encourage the results to spread throughout the Pareto front. With this strategy, a new multi-objective algorithm, the compressed-objective genetic algorithm (COGA), is introduced. COGA is subsequently benchmarked against a non-dominated sorting genetic algorithm II (NSGA-II) and an improved strength Pareto genetic algorithm (SPEA-II) in six scalable DTLZ benchmark problems with three to six objectives. The results reveal that the proposed strategy plays a crucial role in the generation of a superior solution set compared to the other two techniques in terms of the solution set coverage and the closeness to the true Pareto front. Furthermore, the spacing of COGA solutions is very similar to that of SPEA-II solutions. Overall, the functionality of the multi-objective evolutionary algorithm (MOEA) with preference objectives is effectively demonstrated.

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Vibration-based damage detection, a nondestructive method, is based on the fact that vibration characteristics such as natural frequencies and mode shapes of structures are changed when the damage happens. This paper presents cooperative coevolutionary genetic algorithm (CCGA), which is capable for an optimization problem with a large number of decision variables, as the optimizer for the vibration-based damage detection in beams. In the CCGA, a minimized objective function is a numerical indicator of differences between vibration characteristics of the actual damage and those of the anticipated damage. The damage detection in a uniform cross-section cantilever beam, a uniform strength cantilever beam, and a uniform cross-section simply supported beam is used as the test problems. Random noise in the vibration characteristics is also considered in the damage detection. In the simulation analysis, the CCGA provides the superior solutions to those that use standard genetic algorithms presented in previous works, although it uses less numbers of the generated solutions in solution search. The simulation results reveal that the CCGA can efficiently identify the occurred damage in beams for all test problems including the damage detection in a beam with a large number of divided elements such as 300 elements.

Ride quality and road holding capacity of a vehicle is significantly influenced by its suspension system. In the design process, a number of objective functions related to comfort and road holding capacity are taken into consideration. In this paper, the five-degree-of-freedom system of vehicle vibration model with passive suspension is investigated. This multiobjective optimization problem consists of five objective functions. Based on these five design objectives, this paper formulates four two-objective optimization problems by considering four pairs of design objectives and one five-objective optimization problem. This paper proposes the use of the improved compressed objective genetic algorithm (COGA-II) with convergence detection. COGA-II is intentionally designed for dealing with a problem having many optimized objectives. Furthermore, the performance of COGA-II was benchmarked with the multiobjective uniform-diversity genetic algorithm (MUGA) utilized in the previous study. From the simulation results, with equal population sizes, COGA-II employing the convergence detection for searching termination uses less numbers of generations for most sets of design objectives than MUGA whose termination condition is defined by the constant maximum number of generations. Moreover, the solutions obtained from COGA-II are obviously superior to those obtained from MUGA regardless of sets of design objective.