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Determination of Expected Frequency01:08

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Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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A frequency distribution table can be constructed using the steps given below.
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A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).
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A New Frequency Analysis Operator for Population Improvement in Genetic Algorithms to Solve the Job Shop Scheduling

Monique Simplicio Viana1, Rodrigo Colnago Contreras2,3, Orides Morandin Junior1

  • 1Department of Computing, Federal University of Sao Carlos, Sao Carlos 13565-905, SP, Brazil.

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Summary

This study introduces a new guidance operator and genetic quality analysis for Genetic Algorithms to improve Job Shop Scheduling optimization. The method enhances population quality and significantly reduces solution errors for complex scheduling problems.

Keywords:
combinatorial optimizationevolutionary algorithmgenetic algorithmgenetic improvementjob shop scheduling problem

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Area of Science:

  • Operations Research
  • Computer Science
  • Artificial Intelligence

Background:

  • Job Shop Scheduling (JSSP) is an NP-Hard optimization problem.
  • Genetic Algorithms (GAs) are effective for JSSP but suffer from premature convergence and local optima.
  • Existing GA methods require improvements in population quality management.

Purpose of the Study:

  • To propose a novel guidance operator for modifying ill-adapted individuals in GAs.
  • To introduce a new method for determining individual genetic quality using frequency analysis.
  • To enhance the performance of GAs in solving JSSP instances.

Main Methods:

  • Development of a guidance operator that uses genetic material from well-adapted individuals.
  • Implementation of a genetic frequency analysis for assessing individual genetic quality.
  • Evaluation of the proposed methods on modern GAs and JSSP benchmarks.

Main Results:

  • The guidance operator effectively manages individuals with poor fitness, improving overall population quality.
  • The proposed methods lead to better solutions for JSSP instances.
  • A significant reduction in mean relative error (45.88%) was achieved on a leading GA-like method.

Conclusions:

  • The proposed guidance operator and genetic quality analysis are effective in overcoming GA limitations for JSSP.
  • These enhancements lead to improved solution accuracy and efficiency in complex scheduling problems.
  • The developed techniques offer a valuable contribution to the field of optimization and scheduling.