Pareto archived simulated annealing for single machine job shop scheduling with multiple objectives

In this paper, the single machine job shop scheduling problem is studied with the objectives of minimizing the tardiness and the material cost of jobs. The simultaneous consideration of these objectives is the multi-criteria optimization problem under study. A metaheuristic procedure based on simulated annealing is proposed to find the approximate Pareto optimal (non-dominated) solutions. The two objectives are combined in one composite utility function based on the decision maker’s interest in having a schedule with weighted combination. In view of the unknown nature of the weights for the defined objectives, a priori approach is applied to search for the non-dominated set of solutions based on the Pareto dominance. The obtained solutions set is presented to the decision maker to choose the best solution according to his preferences. The performance of the algorithm is evaluated in terms of the number of non-dominated schedules generated and the proximity of the obtained non-dominated front to the true Pareto front. Results show that the produced solutions do not differ significantly from the optimal solutions.

Solving a multiobjective job shop scheduling problem using Pareto Archived Cuckoo Search

This paper investigates a new approach for solving the multiobjective job shop scheduling problem, namely the Cuckoo Search ( CS) approach. The requirement is to schedule jobs on a single machine so that the total material waste is minimised as well as the total tardiness time. The material waste is quantified in terms of saving factors to show the reduction in material that can be achieved when producing two jobs with the same materials in sequence. The estimated saving factor is used to calculate a cost savings for each job based on its material type. A formulation of multiobjective optimisation problems is adopted to generate the set of schedules that maximise the overall cost savings and minimise the total tardiness time. where all trade-offs are considered for the two conflicting objectives. A Pareto Archived Multiobjective Cuckoo Search (PAMOCS) is developed to find the set ofnondominated Pareto optimal solutions. The solution accuracy of PAMOCS is shown by comparing the closeness of the obtained solutions to the true Pareto front generated by the complete enumeration methad. Results shaw that CS is a very effective and promising technique to solve job shop scheduling problems.

Drying front in a sloping aquifier: nonlinear effects

The profiles for the water table height h(x, t) in a shallow sloping aquifer are reexamined with a solution of the nonlinear Boussinesq equation. We demonstrate that the previous anomaly first reported by Brutsaert [1994] that the point at which the water table h first becomes zero at x = L at time t = t c remains fixed at this point for all times t > t c is actually a result of the linearization of the Boussinesq equation and not, as previously suggested [ Brutsaert, 1994 ; Verhoest and Troch, 2000 ], a result of the Dupuit assumption. Rather, by examination of the nonlinear Boussinesq equation the drying front, i.e., the point x f at which h is zero for times t ≥ t c , actually recedes downslope as physically expected. This points out that the linear Boussinesq equation should be used carefully when a zero depth is obtained as the concept of an “average” depth loses meaning at that time.

The determination of the local conditions for void initiation in front of a crack tip for materials with second-phase particles

A procedure is proposed to determine, for second-phase particles near a crack tip, the maximum particle stresses at the moment of void initiation by either particle fracture or particle/matrix interface separation. A digital image analysis system is applied to perform a quantitative analysis of corresponding fracture surface regions from stereo image pairs taken in the scanning electron microscope. The fracture surface analysis is used to measure, for individual particles, the crack tip opening displacement at the moment of void initiation and the particle location with respect to the crack tip. From these data, the stress tensor at the moment of void initiation is calculated from the Hutchinson–Rice–Rosengren (HRR) field theory. The corresponding average local stresses within the particle are evaluated by a non-linear Mori–Tanaka-type approach. These stresses are compared to estimates according to the models by Argon et al. [A.S. Argon, J. Im, R. Safoglu, Metall. Trans. 6 (1975) 825] and Beremin [F.M. Beremin, Metall. Trans. 12 (1981) 723]. The procedure is demonstrated on an Al6061–10% Al2O3 metal matrix composite.

Group on the front steps of Ballara

Front row from left to right: Flora McIntosh, Mrs Jane McMillan (mother of soldier for whom a memorial cairn was erected at Arilpa), Wilfred Deakin Brookes; back row from left to right: Urquhart, Mr. McMillan, Ken Mitchell.