Informed Reactive Tabu Search for Graph Coloring

Abstract

Tabu Search (TS) has always been a very popular algorithm for graph coloring, both as a stand-alone optimizer as well as a subroutine inside population-based hybrid methods. We present two TS extensions that could allow previous TS algorithms to improve their behavior at almost no additional computational cost. First, we integrate two new evaluation functions which employ supplementary (structural or dynamic) information in addition to the conventional objective function (the number of edges with both ends of the same color). These new evaluation functions allow the search process to differentiate configurations not distinguished by the conventional evaluation function. The second extension concerns a reactive mechanism for improving the tabu list management. Theoretical arguments show that this reactive component completely eliminates the risk of getting blocked looping on plateaus. Numerical experiments show that the two proposed TS extensions can be very useful inside a stand-alone TS optimizer, as well as inside TS subroutines of state-of-the-art hybrid methods.

A Distribution Evolutionary Algorithm for Graph Coloring

“…Besides tailored searching paradigms [11,12,13,14,15], performance of LS algorithms can be further improved by constructive generation of color assignments. Blöchliger and Zufferey [16] proposed a constructive strategy for GCPs based on the tabu search (TS) scheme, which constructed feasible but partial solutions and gradually increased its size to get the optimal coloring schemes.…”

“…Since a variety of state-of-the-art algorithms are dedicated to address the k-coloring problem [15,17,18,25,27,29,34,35,38], we first try to verify the ability of DEA-PPM to seek a k-coloring scheme, where k is set as the known number of colors for selected benchmark problems. Numerical results are collected for 30 independent runs with 500 generations, and the experimental results are shown in Table 2.…”

“…The competitiveness of DEA-PPM is demonstrated by comparing DEA-PPM with state-of-the-art algorithms [15,17,18,25,27,29,34,35,38]. It is shown in Tab.…”

“…It is shown in Tab. 3 that DEA-PPM performs slightly worse than HEAD [29], [15] ABAC [17] SDGC [18] CPFLS [25] HGA [27] HEAD [29] RLS [34] PLSCOL [35] TS [38] queen8. HGA [27] and PLSCOL [35], ranks the same as ABAC [17], and outperforms the remaining five state-of-the-art algorithms.…”