Abstract
An effective scheduling policy known as the Dynamic Cycle Lengths Heuristic was introduced by Leachman and Gascon in 1988 for the multi-item, single-machine production system facing stochastic, time-varying demands. In this article we develop a heuristic scheduling policy for the multi-machine extension of the same problem. We integrate the concepts of the Dynamic Cycle Lengths Heuristic with a nonlinear integer optimization model to obtain an overall scheduling policy that allocates items to machines and schedules production quantities during the next time period. We report promising performance in limited simulation tests of the policy.

Abstract
This paper presents a genetic algorithm for the Resource Constrained Project Scheduling Problem (RCPSP). The chromosome representation of the problem is based on random keys. The schedule is constructed using a heuristic priority rule in which the priorities of the activities are defined by the genetic algorithm. The heuristic generates parameterized active schedules. The approach was tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.

Abstract
This article addresses the problem of scheduling economic lots in a multi-product single-machine environment. A mixed integer non-linear programming formulation is developed, which finds the optimal sequence and economic lots. The model takes explicit account of initial inventories, setup times, allows setups to be scheduled at arbitrary epochs in continuous time and models backorders. To solve the problem we develop a hybrid approach, combining a genetic algorithm and linear programming. The approach is tested on a set of instances taken from the literature and compared with other approaches. The experimental results validate the quality of the solutions and the effectiveness of the proposed approach.

Abstract
We present a biased random-key genetic algorithm (BRKGA) for finding small covers of computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems. Using a parallel implementation of the BRKGA, we compute improved covers for the two largest instances in a standard set of test problems used to evaluate solution procedures for this problem. The new covers for instances A(405) and A(729) have sizes 335 and 617, respectively. On all other smaller instances our algorithm consistently produces covers of optimal size.

Abstract
This paper presents a new approach to solve the NP-complete minimum branch vertices problem (MBV) introduced by Gargano et. al[1]. In spite of being a recently proposed problem in the network optimization literature, there are some heuristics to solve it [3]. The main contribution of this paper consists in a new heuristic based on the iterative refinement approach proposed by Deo and Kumar [2]. The experimental results suggest that this approach is capable of finding solutions that are better than the best known in the literature. In this work, for instance, the proposed heuristic found better solutions for 78% of the instances tested. The heuristic looks very promising for the solution of problems related with constrained spanning trees.

Abstract
GRASP with path-relinking (GRASP+PR) is a metaheuristic for finding optimal or near-optimal solutions of combinatorial optimization problems. This paper proposes a new automatic parameter tuning procedure for GRASP+PR heuristics based on a biased random-key genetic algorithm (BRKGA). Given a GRASP+PR heuristic with n input parameters; the tuning procedure makes use of a BRKGA in a first phase to explore the parameter space and set the parameters with which the GRASP+PR heuristic will run in a second phase. The procedure is illustrated with a GRASP+PR for the generalized quadratic assignment problem with n = 30 parameters. Computational results show that the resulting hybrid heuristic is robust.