まだ PuLPのdocumentに載っていない(執筆時)関数ですが sequentialSolveという多段階最適化を行う関数が実装されています
import pulp from pulp import LpVariable # 問題の宣言 problem = pulp.LpProblem() # 変数の宣言(連続変数, 上限2) x = LpVariable('x', upBound=2, cat='Continuous') y = LpVariable('y', upBound=2, cat='Continuous') z = LpVariable('z', upBound=2, cat='Continuous') # 制約の追加 problem.addConstraint(x + y + z >= 3) # 多段階最適化(obj1→obj2) # つまり出てきた解x*はobj1をf1, obj2をf2とすると # f1(x*) ≤ f1(x) (for all x in feasible solution) # f2(x*) ≤ f2(x) (for all x in feasible solution such that f1(x) = f1(x*)) # を満たしている obj1 = x + y obj2 = y + z problem.sequentialSolve(objectives=[obj1, obj2]) # 最適解を表示 for v in [x, y, z]: print(f'{v.name}={v.value()}') > x=2.0 > y=-1.0 > z=2.0
documentに載っていないのは, まだ開発中だからのようです.
心配な方は下記の関数を参考に自分で処理を書くとよいでしょう.
中身の処理は単純で, まず第一目的関数で問題を解き目的関数値O1を取得したら, 次は, その目的関数をO1以下とする制約を追加して, 第二目的関数で問題を解きます. その後はこれの繰り返しです. なのでobjectivesの長さ(=目的関数の個数)の回数だけ問題の生成とソルバによる求解が行われます.
ソースコードは: https://github.com/coin-or/pulp/blob/68c70ec33a03e0fadeab50d69b0da106edaa345f/pulp/pulp.py から
def sequentialSolve(self, objectives, absoluteTols = None, relativeTols = None, solver = None, debug = False): """ Solve the given Lp problem with several objective functions. This function sequentially changes the objective of the problem and then adds the objective function as a constraint :param objectives: the list of objectives to be used to solve the problem :param absoluteTols: the list of absolute tolerances to be applied to the constraints should be +ve for a minimise objective :param relativeTols: the list of relative tolerances applied to the constraints :param solver: the specific solver to be used, defaults to the default solver. """ #TODO Add a penalty variable to make problems elastic #TODO add the ability to accept different status values i.e. infeasible etc if not(solver): solver = self.solver if not(solver): solver = LpSolverDefault if not(absoluteTols): absoluteTols = [0] * len(objectives) if not(relativeTols): relativeTols = [1] * len(objectives) #time it self.solutionTime = -clock() statuses = [] for i,(obj,absol,rel) in enumerate(zip(objectives, absoluteTols, relativeTols)): self.setObjective(obj) status = solver.actualSolve(self) statuses.append(status) if debug: self.writeLP("%sSequence.lp"%i) if self.sense == LpMinimize: self += obj <= value(obj)*rel + absol,"%s_Sequence_Objective"%i elif self.sense == LpMaximize: self += obj >= value(obj)*rel + absol,"%s_Sequence_Objective"%i self.solutionTime += clock() self.solver = solver return statuses
