Vertex Descent is a local search algorithm which forms the basis of a wide spectrum of tabu search, simulated annealing and hybrid evolutionary algorithms for graph colouring. These algorithms are usually treated as experimental and provide strong results on established benchmarks. As a step towards studying these heuristics analytically, an analysis of the behaviour of Vertex Descent is provided. It is shown that Vertex Descent is able to find feasible colourings for several types of instances in expected polynomial time. This includes 2-colouring of paths and 3-colouring of graphs with maximum degree 3. The same also holds for 3-colouring of a subset of 3-colourable graphs with maximum degree 4. As a consequence, Vertex Descent finds a 3-colouring in expected polynomial time for the smallest graph for which Br 'elaz's heuristic DSATUR needs 4 colours. On the other hand, Vertex Descent may fail for forests with maximum degree 3 with high probability.
One of the most well-known hybrid evolutionary algorithms for GCP was introduced by Galinier and Hao @cite_25 . It used the tabu search algorithm TabuCol @cite_41 as an intensification subroutine. TabuCol practically represents the Vertex Descent algorithm enhanced by a tabu list to prevent it from cycling. Glass and Pr " u gel-Bennett investigated an adaptation of the hybrid algorithm by Galinier and Hao obtained by substituting TabuCol with Vertex Descent @cite_27 . They concluded that this version can perform comparably to the original variant but requires a larger population. Vertex Descent has also been used as a technique of search space sampling in an evaluation of different objective functions for the problem @cite_17 .
@cite_41 @cite_27 @cite_25 @cite_17
1582334898 2017565019 296030155 2027353299
A recent and very promising approach for combinatorial optimization is to embed local search into the framework of evolutionary algorithms. In this paper, we present such hybrid algorithms for the graph coloring problem. These algorithms combine a new class of highly specialized crossover operators and a well-known tabu search algorithm. Experiments of such a hybrid algorithm are carried out on large DIMACS Challenge benchmark graphs. Results prove very competitive with and even better than those of state-of-the-art algorithms. Analysis of the behavior of the algorithm sheds light on ways to further improvement. This paper considers a new variant of the two-dimensional bin packing problem where each rectangle is assigned a due date and each bin has a fixed processing time. Hence the objective is not only to minimize the number of bins, but also to minimize the maximum lateness of the rectangles. This problem is motivated by the cutting of stock sheets and the potential increased efficiency that might be gained by drawing on a larger pool of demand pieces by mixing orders, while also aiming to ensure a certain level of customer service. We propose a genetic algorithm for searching the solution space, which uses a new placement heuristic for decoding the gene based on the best fit heuristic designed for the strip packing problems. The genetic algorithm employs an innovative crossover operator that considers several different children from each pair of parents. Further, the dual objective is optimized hierarchically with the primary objective periodically alternating between maximum lateness and number of bins. As a result, the approach produces several non-dominated solutions with different trade-offs. Two further approaches are implemented. One is based on a previous Unified Tabu Search, suitably modified to tackle this revised problem. The other is randomized descent and serves as a benchmark for comparing the results. Comprehensive computational results are presented, which show that the Unified Tabu Search still works well in minimizing the bins, but the genetic algorithm performs slightly better. When also considering maximum lateness, the genetic algorithm is considerably better. This paper presents a tabu search and best-fit decreasing (BFD) algorithms to address a real-world steel cutting problem from a retail steel distributor. It consists of cutting large steel blocks in order to obtain smaller tailored blocks ordered by clients. The problem is addressed as a cutting & packing problem, formulated as a 3-dimensional residual bin packing problem for minimization of stock variation. The performance of the proposed approaches is compared to an heuristic and ant colony optimization (ACO) algorithms. The proposed algorithms were able to reduce the stock variation by up to 179 . The comparison of results between the tabu search and BFD algorithm shows that a multiple order joint analysis benefits the optimization of the addressed objective. To extend multiobjective evolutionary algorithm based on decomposition (MOEA D) in higher dimensional objective spaces, this paper proposes a new version of MOEA D with uniform design, named the uniform design multiobjective evolutionary algorithm based on decomposition (UMOEA D), and compares the proposed algorithm with MOEA D and NSGA-II on some scalable test problems with three to five objectives. UMOEA D adopts the uniform design method to set the aggregation coefficient vectors of the subproblems. Compared with MOEA D, distribution of the coefficient vectors is more uniform over the design space, and the population size neither increases nonlinearly with the number of objectives nor considers a formulaic setting. The experimental results indicate that UMOEA D outperforms MOEA D and NSGA-II on almost all these many-objective test instances, especially on problems with higher dimensional objectives and complicated Pareto set shapes. Experimental results also show that UMOEA D runs faster than NSGA-II for the problems used in this paper. In additional, the results obtained are very competitive when comparing UMOEA D with some other algorithm on the multiobjective knapsack problems.