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Iterated Local Search (ILS) is one of the classical metaheuristics that is frequently used for solving the Quadratic Assignment Problem (QAP), a commonly studied NP-hard combinatorial optimization problem. Despite the effectiveness shown by the ILS when solving the QAP, many possible enhancements can still be implemented, based on studies conducted on other combinatorial problems, for example vertex coloring problem, vehicle routing problem, network design optimization, and many others. Among possible approaches for improving the ILS are by implementing adaptive ILS and multi-start strategy. Adaptive ILS is implemented by dynamically changing the perturbation strength of ILS during the run, which focus on developing a robust algorithm that can solve a wide range of instances. Multi-start strategy on the other hand, focus on applying restart or diversification during ILS run to prevent early stagnation. Adaptive ILS with frequent and large perturbation strength change has shown the best overall result when it has obtained the lowest deviation to the best-known solution compared to others. Implementation of Multi-start strategy showed bad performance, except on Taillard75e instance, in which it frequently found the best-known solution compared to others. Both adaptive and multi-start strategy have shown interesting results that may be further studied for ILS improvement. [ABSTRACT FROM AUTHOR]

Quadratic Assignment Problem (QAP) is one of the famous combinatorial optimization problems in operational research field. In this problem, a set of facilities is assigned to a set of locations in form of one-to-one assignment with the goal to obtain minimum assignment cost. Since QAP is classified under NP-hard problem, a metaheuristics approach is more appropriate for finding a good solution especially when the problem size increased. Sine Cosine Algorithm (SCA) can be categorized under population-based method which shown such an excellent performance in solving various optimization problem. SCA came up with high quality solutions and performed well due to its ability in stabilizing between exploration and exploitation phases evenly during the search process for optimal solution. However, this approach is rarely used to solve discrete optimization problem such as QAP. This is because the nature of its solution search which produce continuous values for new solution based on the concept of sine cosine principle makes it challenging in solving discrete optimization problem. Hence, this study aims to modify the SCA on its acceptance criteria based on the concept of sine cosine to solve discrete optimization problem, to solve QAP and evaluate its solution performance. The instances from QAPLIB were tested. The computational results shows that the modified SCA is an effective and superior method in solving QAP when compared to the best-known solutions presented in previous studies. [ABSTRACT FROM AUTHOR]

The quadratic assignment problem is one of the most studied combinatorial optimization problems. Although many direct and heuristics methods exist for solving this problem, it takes a huge amount of time. Metaheuristics give an approximate solution in a feasible time. Therefore, we used a highly parallel iterated local search metaheuristic on a massively parallel graphics processing unit (GPU) to reduce the execution time. We utilized GPU spatial memory-global, local, constant, texture, and shared memory properties to further reduce the execution time. In this study, we found that using efficient utilization of GPU memory properties, and mixing different memory together we obtained better results from using only global memory. [ABSTRACT FROM AUTHOR]

Various Simulated Annealing (SA) variants have been proposed that differs from each other, mainly due to differences in their temperature schedule. Implementing different temperature schedules allow SAs to focus their intensification and diversification process at different regions in the search space. We focus on studying how the different temperature schedules proposed by different authors affect the performance of SA for solving selected Quadratic Assignment Problem instances. Results are presented in terms of percentage deviation compared to the best-known solutions already published. Our experimental results show that the temperature schedule does have a significant influence on the relative performance of different SA variants. [ABSTRACT FROM AUTHOR]

A stable set of a graph is a set of mutually non-adjacent vertices. The determination of a maximum size stable set, which is called maximum stable set, and the determination of its size, which is called stability number, are central combinatorial optimization problems. However, given a nonnegative integer k, to determine if a graph G has a stable set of size k is NP-complete. In this paper we deal with graphs for which the stability number can be determined by solving a convex quadratic programming problem. Such graphs were introduced in [13] and are called graphs with convex-QP stability number. A few algorithmic techniques for the recognition of this type of graphs in particular families are presented. [ABSTRACT FROM AUTHOR]