Using Differential Evolution for the Graph Coloring

Differential evolution was developed for reliable and versatile function optimization. It has also become interesting for other domains because of its ease to use. In this paper, we posed the question of whether differential evolution can also be used by solving of the combinatorial optimization problems, and in particular, for the graph coloring problem. Therefore, a hybrid self-adaptive differential evolution algorithm for graph coloring was proposed that is comparable with the best heuristics for graph coloring today, i.e. Tabucol of Hertz and de Werra and the hybrid evolutionary algorithm of Galinier and Hao. We have focused on the graph 3-coloring. Therefore, the evolutionary algorithm with method SAW of Eiben et al., which achieved excellent results for this kind of graphs, was also incorporated into this study. The extensive experiments show that the differential evolution could become a competitive tool for the solving of graph coloring problem in the future

Reinforcement learning based local search for grouping problems: A case study on graph coloring

Grouping problems aim to partition a set of items into multiple mutually disjoint subsets according to some specific criterion and constraints. Grouping problems cover a large class of important combinatorial optimization problems that are generally computationally difficult. In this paper, we propose a general solution approach for grouping problems, i.e., reinforcement learning based local search (RLS), which combines reinforcement learning techniques with descent-based local search. The viability of the proposed approach is verified on a well-known representative grouping problem (graph coloring) where a very simple descent-based coloring algorithm is applied. Experimental studies on popular DIMACS and COLOR02 benchmark graphs indicate that RLS achieves competitive performances compared to a number of well-known coloring algorithms

Algorithms for the minimum sum coloring problem: a review

The Minimum Sum Coloring Problem (MSCP) is a variant of the well-known vertex coloring problem which has a number of AI related applications. Due to its theoretical and practical relevance, MSCP attracts increasing attention. The only existing review on the problem dates back to 2004 and mainly covers the history of MSCP and theoretical developments on specific graphs. In recent years, the field has witnessed significant progresses on approximation algorithms and practical solution algorithms. The purpose of this review is to provide a comprehensive inspection of the most recent and representative MSCP algorithms. To be informative, we identify the general framework followed by practical solution algorithms and the key ingredients that make them successful. By classifying the main search strategies and putting forward the critical elements of the reviewed methods, we wish to encourage future development of more powerful methods and motivate new applications

Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

A Hybrid Artificial Bee Colony Algorithm for Graph 3-Coloring

The Artificial Bee Colony (ABC) is the name of an optimization algorithm that was inspired by the intelligent behavior of a honey bee swarm. It is widely recognized as a quick, reliable, and efficient methods for solving optimization problems. This paper proposes a hybrid ABC (HABC) algorithm for graph 3-coloring, which is a well-known discrete optimization problem. The results of HABC are compared with results of the well-known graph coloring algorithms of today, i.e. the Tabucol and Hybrid Evolutionary algorithm (HEA) and results of the traditional evolutionary algorithm with SAW method (EA-SAW). Extensive experimentations has shown that the HABC matched the competitive results of the best graph coloring algorithms, and did better than the traditional heuristics EA-SAW when solving equi-partite, flat, and random generated medium-sized graphs