Cautious Non-Linear Optimisation: A New Technique for Allocation Problems

Abstract

Solutions of linear programming formulations of some problems may be unsatisfactory, because they inherently tend to be extreme, sparse, and ruthless. A method of non-linear optimisation is described which is cautious in the sense that a progressive restraint is imposed on departures from some reference solution. Constraints can be incorporated provided they are regarded as somewhat flexible. Multiple objectives may also be pursued. Large problems (more than 1000 variables) may be handled without difficulty by employing conjugate gradient methods of optimisation. Computing requirements are no greater than for an equivalent LP problem, and execution times to obtain satisfactory approximate solutions may be less.

The method has been successfully applied to a large fishery management problem, which is described. It yields stable, realistic solutions, and enables a range of solutions corresponding to different assumptions about the importance of various processes to be generated with confidence.