desdeo.problem.toy

This module contains simple “toy” problems suitable for demonstrating different interactive multi-objective optimization methods.

class desdeo.problem.toy.CylinderProblem

Bases: desdeo.problem.porcelain.PorcelainProblem

In this problem consider a cell shaped like a cylinder with a circular cross-section.

The shape of the cell is here determined by two quantities, its radius r and its height h. We want to maximize the volume of the cylinder and minimize the surface area. In addition to this, cylinder’s height should be close to 15 units, i.e. we minimize the absolute difference between the height and 15.

Finally the cylinder’s height must be greater or equal to its width. Thus there are 2 decision variables, 3 objectives and 1 constraint in this problem.

__module__ = 'desdeo.problem.toy.cylinder'

_porc_constrs = []

_porc_name = 'Cylinder Problem'

_porc_objs = [('volume', <desdeo.problem.porcelain.Objective object>), ('surface_area', <desdeo.problem.porcelain.Objective object>), ('height_diff', <desdeo.problem.porcelain.Objective object>)]

_porc_vars = [('r', <desdeo.problem.porcelain.Variable object>), ('h', <desdeo.problem.porcelain.Variable object>)]

class desdeo.problem.toy.RiverPollution

Bases: desdeo.problem.porcelain.PorcelainProblem

River pollution problem by Narula and Weistroffer [NARULA1989].

The problem has four objectives and two variables

The problem describes a (hypothetical) pollution problem of a river, where a fishery and a city are polluting water. The decision variables represent the proportional amounts of biochemical oxygen demanding material removed from water in two treatment plants located after the fishery and after the city.

The first and second objective functions describe the quality of water after the fishery and after the city, respectively, while objective functions three and four represent the percent return on investment at the fishery and the addition to the tax rate in the city. respectively.

References

NARULA1989

Narula, S. & Weistroffer, H. A flexible method for nonlinear multicriteria decision-making problems Systems, IEEE Transactions on Man and Cybernetics, 1989, 19, 883-887.

__module__ = 'desdeo.problem.toy.river_pollution'

_porc_constrs = []

_porc_name = 'River pollution method'

_porc_objs = [('wq_fishery', <desdeo.problem.porcelain.Objective object>), ('wq_city', <desdeo.problem.porcelain.Objective object>), ('fishery_roi', <desdeo.problem.porcelain.Objective object>), ('city_tax', <desdeo.problem.porcelain.Objective object>)]

_porc_vars = [('bod_fishery', <desdeo.problem.porcelain.Variable object>), ('bod_city', <desdeo.problem.porcelain.Variable object>)]

class desdeo.problem.toy.RiverPollutionRobust

Bases: desdeo.problem.porcelain.PorcelainProblem

__module__ = 'desdeo.problem.toy.river_pollution_robust'

_porc_constrs = []

_porc_name = 'River pollution robust'

_porc_objs = [('wq_fishery', <desdeo.problem.porcelain.Objective object>), ('wq_city', <desdeo.problem.porcelain.Objective object>), ('fishery_roi', <desdeo.problem.porcelain.Objective object>), ('city_tax', <desdeo.problem.porcelain.Objective object>), ('robustness', <desdeo.problem.porcelain.Objective object>)]

_porc_vars = [('bod_fishery', <desdeo.problem.porcelain.Variable object>), ('bod_city', <desdeo.problem.porcelain.Variable object>)]