A discrete simulated kalman filter optimizer for combinatorial optimization problems

Combinatorial optimization problems are ubiquitous in many fields, including healthcare, economics, engineering, manufacturing, and others. A solution to a combinatorial optimization problem is frequently expressed in terms of a permutation, arrangement, or combination of elements. Due to the practical significance of this problem in real-world issues, numerous algorithms have been proposed to solve it. These algorithms specifically refer to those that operate in discrete search space, often known as combinatorial algorithms. Another type of algorithm is called numerical algorithms. These algorithms were built specifically to address numerical optimization problems. In the last few decades, significant research effort has been spent on the development of numerical algorithms, particularly for solving combinatorial problems. An example of a numerical algorithm is the simulated Kalman filter (SKF). Various method has been introduced as an extension of a numerical algorithm to adapt it to a discrete search space. There are currently three extensions to the SKF, resulting in three combinatorial algorithms: the binary SKF (BSKF), the distance evaluated SKF (DESKF), and the angle modulated SKF (AMSKF). However, these extensions may result in increased execution times for the algorithm. In this research, a new combinatorial algorithm named discrete simulated Kalman filter optimizer (DSKFO) is proposed to solve combinatorial optimization problem. This new algorithm is originated by the concept of the simulated Kalman filter (SKF). Due to the limitation of the SKF algorithm which only able to operate in continuous search space, the proposed algorithm makes use of a new interpretation that incorporates mutation and Hamming distance, allowing the proposed algorithm to function in discrete search space. In this research, three combinatorial problems namely the travelling salesman problem (TSP), assembly sequence planning (ASP), and the hole drilling proble are used to evaluate the proposed algorithm. Two types of analysis are used to evaluate the proposed algorithm. First, the DSKFO algorithm is used to solve the travelling salesman problem (TSP), and then the algorithm's execution time is measured. Existing SKF methods are then compared to the findings of the DSKFO algorithm. DSKFO performs the fastest, requiring just 13 seconds to solve a small TSP instance such as eil51, whereas DESKF, AMSKF, BSKF, and SEDESKF require around 36, 42, 34, and 14 seconds, respectively. To solve larger TSP instance such as rl1889, DSKFO requires 139 seconds to execute a single run, whereas DESKF, AMSKF, BSKF, and SEDESKF require around 1587, 1590, 2418, and 208 seconds, respectively. For the second analysis, the performance of the proposed method is evaluated using three combinatorial problems: the travelling salesman problem (TSP), the assembly sequence planning (ASP), and the hole drilling problem. The results are compared to four previously published combinatorial SKFs: the BSKF, the AMSKF, the DESKF, and the SEDESKF. The DSKFO may be considered the best algorithm for solving the TSP and hole drilling problem, as it has the highest number of best performances. For solving the ASP, the DSKFO ranked third, while the AMSKF came in first, followed by the DESKF in second

Hybrid Simulated Annealing and Tabu Search Method for the Electric Travelling Salesman Problem with Time Windows and Mixed Charging Rates

The electric travelling salesman problem with time windows (ETSPTW) is an extension of the well-known travelling salesman problem with time windows (TSPTW). The ETSPTW additionally considers recharging operations of the electric vehicle at identical charging stations. However, different charging technologies used at public or private stations result in different charging times of the electric vehicles. Therefore, this study extends the ETSPTW by additionally considering charging operations at customer locations with different charging rates, called hereafter the electric travelling salesman problem with time windows and mixed charging rates (ETSPTW-MCR). To the best of our knowledge, this is the first study that considers both private and public charging stations for the ETSPTW. In addition to the extended version of the ETSPTW, this paper introduces a new and effective hybrid Simulated Annealing/Tabu Search (SA/TS) algorithm to solve the ETSPTW-MCR problem efficiently. Distinct from the existing hybridization of SA and TS, the proposed hybrid SA/TS algorithm employs efficient search procedures based on the TSPTW restrictions, a modified solution acceptance criterion, and an advanced tabu list structure. Moreover, an improved dynamic programming procedure is integrated to optimally find the charging station visits in shorter computational times. The proposed hybrid SA/TS is tested on several TSPTW and ETSPTW benchmark problems and compared with well-known solution approaches. Results of these experiments show that the proposed algorithm outperforms the other considered competitor algorithms both with regard to solution quality and computational time. Furthermore, 26 new best results are obtained for the ETSPTW instances. In addition, the hybrid algorithm is applied to a new problem set generated for the ETSPTW-MCR by extending the ETSPTW problems found in the literature. Comparisons with the ETSPTW results show that significant distance savings are found for most of the instances by charging the electric vehicle at customer locations. As a result of the computational studies, it should be concluded that the proposed algorithm is capable of finding efficient and more realistic route plans for the electric vehicles.status: Published onlin

Hybrid simulated annealing and tabu search method for the electric travelling salesman problem with time windows and mixed charging rates

The electric travelling salesman problem with time windows (ETSPTW) is an extension of the well-known travelling salesman problem with time windows (TSPTW). The ETSPTW additionally considers recharging operations of the electric vehicle at identical charging stations. However, different charging technologies used at public or private stations result in different charging times of the electric vehicles. Therefore, this study extends the ETSPTW by additionally considering charging operations at customer locations with different charging rates, called hereafter the electric travelling salesman problem with time windows and mixed charging rates (ETSPTW-MCR). To the best of our knowledge, this is the first study that considers both private and public charging stations for the ETSPTW. In addition to the extended version of the ETSPTW, this paper introduces a new and effective hybrid Simulated Annealing/Tabu Search (SA/TS) algorithm to solve the ETSPTW-MCR problem efficiently. Distinct from the existing hybridization of SA and TS, the proposed hybrid SA/TS algorithm employs efficient search procedures based on the TSPTW restrictions, a modified solution acceptance criterion, and an advanced tabu list structure. Moreover, an improved dynamic programming procedure is integrated to optimally find the charging station visits in shorter computational times. The proposed hybrid SA/TS is tested on several TSPTW and ETSPTW benchmark problems and compared with well-known solution approaches. Results of these experiments show that the proposed algorithm outperforms the other considered competitor algorithms both with regard to solution quality and computational time. Furthermore, 26 new best results are obtained for the ETSPTW instances. In addition, the hybrid algorithm is applied to a new problem set generated for the ETSPTW-MCR by extending the ETSPTW problems found in the literature. Comparisons with the ETSPTW results show that significant distance savings are found for most of the instances by charging the electric vehicle at customer locations. As a result of the computational studies, it should be concluded that the proposed algorithm is capable of finding efficient and more realistic route plans for the electric vehicles

ETSPTW and ETSPTW-MCR problem set, and details of the computational results

This file pack represents the supplemental data of the study "Hybrid Simulated Annealing and Tabu Search Method for the Electric Travelling Salesman Problem with Time Windows and Mixed Charging Rates" introduced by İ. Küçükoğlu, R. Dewil, and D. Cattrysse. Files include the data of the ETSPTW and ETSPTW-MCR instances, and the details of the computational results obtained by the authors. Description of the files is given in a "readme.txt" file for both of the problem and solution files. The problem and solution files are categorized with respect to instance groups given in the paper and named as follows: For problem files; ETSPTW problems -> "[instance_name].txt" ETSPTW-MCR(30%) problems -> "[instance_name]_MCR(30%).txt" ETSPTW-MCR(70%) problems -> "[instance_name]_MCR(70%).txt" ETSPTW-MCR(100%) problems -> "[instance_name]_MCR(100%).txt" For solution files; ETSPTW problems -> "route_[instance_name].txt" ETSPTW-MCR(30%) problems -> "route_[instance_name]_MCR(30%).txt" ETSPTW-MCR(70%) problems -> "route_[instance_name]_MCR(70%).txt" ETSPTW-MCR(100%) problems -> "route_[instance_name]_MCR(100%).txt" * The better solutions observed during the preliminary experiments are named as "route_[instance_name]_B.txt" or "route_[instance_name]_B_MCR(...).txt"