Hierarchical Optimization Algorithm Research Articles

Industrial Applications of Hierarchical Optomization Methods

A presentation of the possibility of using hierarchical optimization algorithms within practical systems for computer assisted production control is intended. It is shown how an optimization problem can be formulated in order to cope with the multiple objectives of the system. A practical large example is given. A computer package which uses multilevel algorithms is described.

Nonfeasible Hierarchical Multicriteria Methods

General nonfeasible (price-coordination, interaction balance) hierarchical optimization algorithms for large-scale systems with multiple objectives are considered. The systems studied consist of connected subsystems with multiple objectives (subgoals, indicators); the overall objectives are functions of the subsystem objectives. It is shown that, unlike in the single objective case, there is no general transformation, modification, of the objective vectors of the subsystems (cf. the additional price term in the single objective case). However, a series of transformed subproblems can be defined such that the limit solution can be taken as the subsystem solution. That is, in the general case where the way the decision-maker expresses his preference is free, an additional iteration is needed in each subproblem. A multicriteria duality theory is reviewed. Based on this theory a nonfeasible algorithm is rederived, where the subproblems are solved by multicriteria methods using explicit trade-offs (such as the SWT and Geoffrion's method). The derivation using the duality theory conveniently gives us a coordination algorithm, sufficient convexity properties, and a new suboptimal stopping rule.

Comments on “hierarchical optimization of nonlinear dynamical systems with nonquadratic objective functions”

It is shown that the fourth level of a four-level hierarchical optimization algorithm proposed by Fawzy is superfluous.

Implementation of a hierarchical optimization algorithm on a multimicrocomputer system

A hierarchical optimization method based on the interaction prediction principle is applied to the freeway traffic control problem. The solution method is implemented on a multimicrocomputer system. Both analytical and experimental results concerning certain properties of the decentralized computation structure such as computation time, storage space, and communication requirements are presented.

Different Approaches for the Production Control of a Pulp Mill

Three approaches to carry out the pulp mill production control calculations are discussed. These approaches are a simulation method, a hierarchical optimization algorithm and a network flow algorithm.In the simulation approach a general program package for the production control calculations was developed. The scheduling is based on a simulation model and some simple logical rules for production scheduling. It proceeds iteratively from a given production schedule to a production schedule that satisfies all the system constraints.The production schedules of both the pulp lines of the mill and the chemical recovery cycle can be calculated using Tamura’s time delay algorithm. This algorithm was modified so that the specific features of the problem can be taken into account. These include the compensation of planned shut-downs, identification of infeasible situations, etc.The use of standard linear programming algorithms to production control calculations is restricted by the fact that they need a considerable amount of core memory. However, for some special cases network flow algorithms that can solve LP-problems have been developed. In this connection Ford-Fulkerson out-of-kilter algorithm is considered.The applicability of these approaches was compared using simulations with UNIVAC 1100/20-computer of the University of Oulu. In the simulations the preselected simulation period of 48 hours was divided into intervals of 8 hours. Several kinds of test runs that correspond problems in the real plant environment were carried out.

Different approaches for the production control of a pulp mill

Three approaches to carry out the pulp mill production control calculations are discussed. These approaches are a simulation method, a hierarchical optimization algorithm and a network flow algorithm.In the simulation approach a general program package for the production control calculations was developed. The scheduling is based on a simulation model and some simple logical rules for production scheduling. It proceeds iteratively from a given production schedule to a production schedule that satisfies all the system constraints.The production schedules of both the pulp lines of the mill and the chemical recovery cycle can be calculated using Tamura’s time delay algorithm. This algorithm was modified so that the specific features of the problem can be taken into account. These include the compensation of planned shut-downs, identification of infeasible situations, etc.The use of standard linear programming algorithms to production control calculations is restricted by the fact that they need a considerable amount of core memory. However, for some special cases network flow algorithms that can solve LP-problems have been developed. In this connection Ford-Fulkerson out-of-kilter algorithm is considered.The applicability of these approaches was compared using simulations with UNIVAC 1100/20-computer of the University of Oulu. In the simulations the preselected simulation period of 48 hours was divided into intervals of 8 hours. Several kinds of test runs that correspond problems in the real plant environment were carried out.

Hierarchical optimisation for non-linear dynamical systems with non-separable cost functions

In this paper the previous hierarchical optimisation algorithm of Hassan and Singh for non-linear interconnected dynamical systems with separable cost functions is extended to the case of non-linear and non-separable cost functions. This ensures that any decomposition could be used and makes the new algorithm suitable for the optimisation of general non-linear problems.