New Method Developed to Find Optimal Solutions from Complex Combinations - Contributing to Efficiency in Logistics Routes and Work Shifts by Automatically Adjusting the Power of "Chaos"

【Research Summary and Key Points】

Determining delivery routes, creating work shifts, and similar tasks require finding optimal combinations that satisfy conditions from a vast number of options in a short amount of time.

This research has developed a new method that automatically adjusts key parameters during exploration by incorporating chaotic search methods into particle swarm optimization.

Numerical experiments targeting the capacitated vehicle routing problem have confirmed that the proposed method excels in solution quality and robustness compared to conventional chaotic search methods and feedback-based adjustment methods.

These achievements have the potential to enhance combinational optimization technology, which is needed in various aspects of society, including delivery routes, work shifts, production planning, IT, and communication networks.

【Research Overview】

A joint research group comprising Fengkai Guo (Doctoral Program 3rd year, scheduled for 2026) from the Department of Information Engineering, Graduate School of Engineering, Tokyo University of Science, Associate Professor Takafumi Matsuura from the Department of Data Science, Faculty of Advanced Engineering, Nippon Institute of Technology, Professor Takayuki Kimura from the Department of Intelligent Information Engineering, Faculty of Information Engineering, Tokyo City University, and Professor Tohru Ikeguchi from the Department of Information Engineering, Faculty of Engineering, Tokyo University of Science, has developed a chaotic search method incorporating particle swarm optimization to solve "combinatorial optimization problems" more stably.

Combinatorial optimization problems are involved in various aspects that support our lives, such as creating work shifts and production planning in factories. However, even a slight increase in the number of options causes the number of possible combinations to increase exponentially, necessitating methods to efficiently search for optimal solutions within a limited time. One such method is chaotic search, which utilizes chaotic dynamics. On the other hand, conventional chaotic search methods face the challenge that their performance is heavily influenced by the parameter settings of the chaotic neural network. Since appropriate parameters change depending on the problem type and the stage of exploration, it has been difficult to maintain consistently high performance through empirical parameter tuning alone.

To address this challenge, this research has integrated particle swarm optimization, a type of swarm intelligence optimization, into the chaotic search method. Particle swarm optimization is a method where multiple particles exploring search for better conditions by sharing information with each other. In the newly developed method, key parameters of the chaotic search method are automatically adjusted by particle swarm optimization according to the progress of the search, enabling stable exploration for optimal solutions.

The research group conducted numerical experiments targeting the "capacitated vehicle routing problem," which optimizes delivery routes under constraints on vehicle carrying capacity. The results confirmed that the proposed method can stably obtain better solutions compared to conventional chaotic search methods and feedback-based adjustment methods.

This achievement improves the parameter setting challenge, which affects the performance of chaotic search methods, through automatic adjustment during exploration. In the future, it has the potential to lead to technologies that enable more efficient operation of systems supporting our lives, such as logistics, work shifts, production planning, and communication networks.

This research result was published online on July 1, 2026, in the international academic journal "NOLTA, IEICE."

【Research Background】

Determining delivery routes, creating work shifts, production planning in factories, and designing/operating IT and communication networks all require finding optimal combinations that satisfy given constraints from a vast number of options. These problems are called "combinatorial optimization problems." However, as the number of options increases, the number of possible combinations grows explosively, making it impractical to find the optimal solution by examining all candidates.

To efficiently search for good solutions within a limited computation time, many heuristic and metaheuristic methods have been studied. Chaotic search, one of the metaheuristic methods, has the greatest strength in its ability to explore the solution space over a wide range using chaotic dynamics. It is particularly effective in situations where the number of solution candidates is enormous and exploration tends to stagnate due to the presence of many local optima. Therefore, it has been considered for application to various combinatorial optimization problems, including delivery planning problems, network route control, and sequence analysis in bioinformatics. On the other hand, its performance is strongly dependent on the parameter settings of the chaotic neural network. If the parameters are not appropriate, exploration may get stuck in the early stages, or search efficiency may decrease.

【Details of Research Results】

This research proposes a new chaotic search method that incorporates particle swarm optimization to address the challenge of chaotic search performance being dependent on parameter settings. Particle swarm optimization dynamically adjusts key parameters during exploration, leading to improvements in solutions for combinatorial optimization problems. This method consists of two layers: an outer layer for adjusting parameters and an inner layer for actually exploring solutions. In the outer layer, particle swarm optimization prepares multiple candidate parameters for the chaotic search method and evaluates how well each candidate leads to a good solution. In the inner layer, the chaotic search method is executed using each parameter to improve solutions such as delivery routes. By repeating this process, more suitable parameters can be found according to the progress of the search.

To verify the effectiveness of the proposed method, numerical experiments were conducted targeting the capacitated vehicle routing problem. In the experiments, conventional chaotic search methods, feedback-based adjustment methods, and the proposed chaotic search method incorporating particle swarm optimization were compared using standard benchmark data. The results confirmed that the proposed method can stably obtain optimal solutions compared to conventional methods. In particular, it reached known optimal solutions or solutions close to them for many small to medium-sized problems. Furthermore, the variation in results when solving the same problem multiple times was small, indicating high robustness to parameter settings.

On the other hand, the computation time was longer than with conventional feedback-based adjustment methods due to the addition of parameter search by particle swarm optimization. The paper also indicates that while the proposed method enhances solution quality and robustness, improving computational efficiency is a future challenge.

This achievement demonstrates a foundational technology for solving combinatorial optimization problems more stably by incorporating online parameter adjustment into chaotic search methods. In the future, it has the potential to lead to technologies that enable more efficient operation of systems supporting our lives, such as logistics, work shifts, production planning, and communication networks.

Professor Ikeguchi, who led this research, commented, "I have been continuously researching the application of chaotic dynamics to combinatorial optimization since the late 1990s. While we have verified its effectiveness in the capacitated vehicle routing problem this time, I believe these results can be applied to a wide range of fields such as shift scheduling, factory production planning, and IT and communication networks, and can greatly contribute to people's lives."

This research was supported by Grants-in-Aid for Scientific Research (JSPS) (20H00596, 22K04602, 22K18419, 23K04274, 23K21706, 25H00447, 25K08182) and the Tohoku University Research Project on Telecommunications (R05/A19, R05/B13, R06/B02).

【Glossary】

*1 Combinatorial Optimization Problem

A problem of finding the best combination that satisfies given conditions from a large number of options. For example, in delivery services, it is used to determine which truck goes to which household and in what order to minimize driving distance.

*2 Particle Swarm Optimization

An optimization method where multiple candidates, like flocks of birds or schools of fish, search for better conditions by sharing information with each other. In this research, it is used not for the delivery routes themselves, but to adjust key parameters that enable the chaotic search method to function effectively.

*3 Chaotic Search Method

Chaos refers to a phenomenon that exhibits complex and unpredictable behavior while following deterministic rules. This method aims to search for optimal solutions from a wider range, not just local optima, by utilizing this complex behavior.

*4 Chaotic Neural Network

A network combining neuron models that exhibit chaotic behavior. In this research, it is used as a mechanism to control which local search operation is executed.

*5 Parameter

Adjustment values that determine the operation of a computational method or model. In this research, the goal was to automatically adjust key parameters related to the ease and stability of exploration in the chaotic search method during the search process.

*6 Capacitated Vehicle Routing Problem

A problem in which multiple vehicles are used to deliver goods, aiming to minimize the total driving distance by visiting all delivery destinations while adhering to the carrying capacity limits of each vehicle. It is one of the representative combinatorial optimization problems related to the logistics field.

*7 Robustness

The property of working stably without significant performance degradation even when conditions change slightly. It is important for evaluating whether good solutions can be obtained stably regardless of changes in problem type or exploration stage.

【Paper Information】

Journal:

NOLTA, IEICE

Paper Title:

Adaptive parameter tuning of chaotic search using particle swarm

optimization

Authors:

Fengkai Guo, Takafumi Matsuura, Takayuki Kimura, and

Tohru Ikeguchi

DOI:

10.1587/nolta.17.1062

*Please note that due to the limitations of the PR TIMES system, superscript, subscript, and special characters may not be displayed correctly. For the official notation, please refer to the Tokyo University of Science webpage (https://www.tus.ac.jp/today/archive/20260708_8123.html).