K-opt Local Search Research Articles

An Efficient Memetic Algorithm for the Minimum Load Coloring Problem

Given a graph G with n vertices and l edges, the load distribution of a coloring q: V → {red, blue} is defined as dq = (rq, bq), in which rq is the number of edges with at least one end-vertex colored red and bq is the number of edges with at least one end-vertex colored blue. The minimum load coloring problem (MLCP) is to find a coloring q such that the maximum load, lq = 1/l × max{rq, bq}, is minimized. This problem has been proved to be NP-complete. This paper proposes a memetic algorithm for MLCP based on an improved K-OPT local search and an evolutionary operation. Furthermore, a data splitting operation is executed to expand the data amount of global search, and a disturbance operation is employed to improve the search ability of the algorithm. Experiments are carried out on the benchmark DIMACS to compare the searching results from memetic algorithm and the proposed algorithms. The experimental results show that a greater number of best results for the graphs can be found by the memetic algorithm, which can improve the best known results of MLCP.

An Improved K-OPT Local Search Algorithm for the Vertex Separator Problem

An Improved K-OPT Local Search Algorithm for the Vertex Separator Problem

An Iterated Greedy Algorithm for the Binary Quadratic Programming Problem

In this paper, Iterated Greedy algorithm with K-opt Local Search (IGKLS) is proposed for the binary quadratic programming problem (BQP). The proposed iterated greedy algorithm consists of two central phases, construction and destruction phases. As a local search algorithm, k-opt local search is applied after the construction phase. The computational results showed that the proposed iterated greedy algorithm outperformed state-of-the-art methods for huge size BQP instances.

A low-complexity soft-input/soft-output multiuser detector based on local search algorithms

In this contribution, we consider iterative multiuser detection over coded code-division multiple-access (CDMA) channels from a combinatorial optimization viewpoint and propose a low-complexity soft-input/soft-output (SISO) multiuser detector based on the k-opt local search (LS) algorithm, which was previously used for solving the traveling salesperson problem (TSP). Simulation results and complexity analysis show that the proposed detector can approach closely the performance of the full-complexity a posteriori probability (APP) multiuser detector over highly correlated convolutionally coded channels.

An effective local search for the maximum clique problem

We propose a variable depth search based algorithm, called k-opt local search ( KLS), for the maximum clique problem. KLS efficiently explores the k-opt neighborhood defined as the set of neighbors that can be obtained by a sequence of several add and drop moves that are adaptively changed in the feasible search space. Computational results on DIMACS benchmark graphs indicate that KLS is capable of finding considerably satisfactory cliques with reasonable running times in comparison with those of state-of-the-art metaheuristics.

Memetic algorithms for the unconstrained binary quadratic programming problem

This paper presents a memetic algorithm, a highly effective evolutionary algorithm incorporating local search for solving the unconstrained binary quadratic programming problem (BQP). To justify the approach, a fitness landscape analysis is conducted experimentally for several instances of the BQP. The results of the analysis show that recombination-based variation operators are well suited for the evolutionary algorithms with local search. Therefore, the proposed approach includes — besides a highly effective randomized k-opt local search — a new variation operator that has been tailored specially for the application in the hybrid evolutionary framework. The operator is called innovative variation and is fundamentally different from traditional crossover operators, since new genetic material is included in the offspring which is not contained in one of the parents. The evolutionary heuristic is tested on 35 publicly available BQP instances, and it is shown experimentally that the algorithm is capable of finding best-known solutions to large BQPs in a short time and with a high frequency. In comparison to other approaches for the BQP, the approach appears to be much more effective, particularly for large instances of 1000 or 2500 binary variables.

An efficient local search heuristics for asynchronous multiuser detection

This letter considers the application of k-opt local search to the detection of data transmitted through the additive white Gaussian noise channel by K asynchronous users using direct-sequence code-division multiple access. The algorithm is based on a general approach to heuristics that is highly efficient in solving large combinatorial optimization problems. It is shown that the algorithm manages to produce optimum solutions with high frequency, in running time that grows about O(n/sup 2/).

Greedy and Local Search Heuristics for Unconstrained Binary Quadratic Programming

In this paper, a greedy heuristic and two local search algorithms, 1-opt local search and k-opt local search, are proposed for the unconstrained binary quadratic programming problem (BQP). These heuristics are well suited for the incorporation into meta-heuristics such as evolutionary algorithms. Their performance is compared for 115 problem instances. All methods are capable of producing high quality solutions in short time. In particular, the greedy heuristic is able to find near optimum solutions a few percent below the best-known solutions, and the local search procedures are sufficient to find the best-known solutions of all problem instances with n ≤ 100. The k-opt local searches even find the best-known solutions for all problems of size n ≤ 250 and for 11 out of 15 instances of size n e 500 in all runs. For larger problems (n e 500, 1000, 2500), the heuristics appear to be capable of finding near optimum solutions quickly. Therefore, the proposed heuristics—especially the k-opt local search—offer a great potential for the incorporation in more sophisticated meta-heuristics.

New Results on the Old k-opt Algorithm for the Traveling Salesman Problem

Local search with k-change neighborhoods is perhaps the oldest and most widely used heuristic method for the traveling salesman problem, yet almost no theoretical performance guarantees for it were previously known. This paper develops several results, some worst-case and some probabilistic, on the performance of 2- and k-opt local search for the traveling salesman problem, with respect to both the quality of the solution and the speed with which it is obtained.