Abstract: A planning system includes an input device which accepts at least a given planning problem and values of variables required to solve the given planning problem; a display device which provides a visual display of an optimum plan obtained for the given planning problem; and a planner device which prepares an objective function representing items to be averaged and designs a plan to minimize a value of the objective function.

Abstract: A system for making an optimum plan for a given problem at high speed. The system sets a planning problem, etc., prepares an objective function and finalizes a plan for minimizing or maximizing the objective function value, and then stores necessary variables. The system prepares as many parent plans of a first generation as a given number (population), calculates objective function values, sorts plans in descending or ascending order of the objective function values of the plans, when selection numbers are assigned to plans in order of a ratio of the objective function value of each plan to the total of the objective function values of the plans, selects parent plans by using numbers indicated by as many constants as the population determined for each generation as the selection numbers, and replaces two elements, arranged at order positions specified by random numbers, with each other for each of the selected parent plans, to prepare child plans.

Abstract: A polarizing film comprising a uniaxially stretched film containing a polyvinyl alcohol having a degree of polymerization of at least about 2,500, and at least one polarizing agent selected from iodine and a dichroic dye, as well as a process for the production of the same. This polarizing film is superior in heat resistance and moist heat resistance to conventional films and has excellent optical properties, such as a high polarizing coefficient and transmittance.