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-Most optimization algorithms that use probabilistic models focus on extracting the information from good solutions found in the population. A selection method discards the below-average solutions. They do not contribute any information to be used to update the models. This work proposes a new algorithm, Combinatorial Optimization with Coincidence (COIN) that makes use of both good and not-good solutions. A Generator represents a probabilistic model of the required solution, is used to sample candidate solutions. Reward and punishment schemes are incorporated in updating the generator. The updating values are defined by selecting the good and not-good solutions. It has been observed that the notgood solutions contribute to avoid producing the bad solutions. The multi-objective version of COIN is also introduced. Several benchmarks of multi-objective problems of real world industrial applications are reported.

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The one-piece flow manufacturing line of single and customized products is usually organized as a U-shaped assembly layout. In this study, the characteristics of a single U-line are described and modeled. The worker allocation problem is hierarchically concerned with the task assignment into a U-line and allocate task to workers in sequence. Several products are assembled in 7-task to 297-task problems, and each problem is performed with a given cycle time. The primary purpose is to identify the impact of walking time on both symmetrical and rectangular U-shaped assembly layouts. The minor purpose is to compare the number of workers between two fixed layouts. Coincidence algorithm demonstrates clarifying solutions. To respond to two previous aims, the primary objective function of a number of workers is used. Finally, with the Pareto-optimal frontier between the deviation of operation times of workers and the walking time, its computational study is exemplified to identify good task assignment and walking path

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