在质量和成本限制的情况下最大化运输利润的算法
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【中文标题】在质量和成本限制的情况下最大化运输利润的算法【英文标题】：Algorithm for maximizing shipping profit with limitations on mass and cost 【发布时间】：2021-12-07 19:36:00 【问题描述】：标题不是很有帮助，因为我不确定我要准确地说什么。我确信必须存在一个算法，但我不记得了。注意：不是作业问题，我很久以前就完成了学业。
那么问题来了：
我们正在从事运输和贸易工作，努力实现利润最大化 我们有一份可以用卡车运送的物品清单。每个项目都有： 买入价（来源） 销售价格（在目的地） 单位质量 可以购买的数量上限 我们的卡车可以承载的质量有限 我们对允许“投资”的金额（在源头上花费在项目上）有一个上限。 我们希望最大化我们工作的利润（在源头购买、运输、在目的地出售）。如果只有一个限制（总质量或总投资），那会很容易，但是当有两个限制时，我不知道如何处理。
计算利润的公式是：
profit = ItemA['quantity'] * (ItemA['sell_price'] - ItemA['buy_price']) + ItemB['quantity'] * (ItemB['sell_price'] - ItemB['buy_price']) + ...
所以我正在尝试选择应该购买哪些商品以及每件商品的数量以实现利润最大化。
是否有任何现有的已知算法可以解决这个问题？可能是某种mathematical optimization 问题？我正在使用 Python，所以我认为 mystic 包可能是合适的，但我不确定如何配置它。
【问题讨论】：
这是有界背包问题。项目的值为sell_price - buy_price。重量是每单位质量。而且你对每件商品的数量有限制，对总重量有限制。
这实际上是二维有界背包，因为我们的实际重量是一个二维向量（重量，buy_price），并且每个维度的总和都有一个限制。在计算上，它被认为比传统的一维背包更难近似。我们需要更多关于约束的信息：有多少物品，最大重量/价格，因为这是一个 NP 难题。它也可能更适合 cs.stackexchange
@kcsquared 我们可以将其限制为最多 10 个不同的项目。每件商品的重量和价格基本上没有限制，可能是 0.01 公斤到 1000 公斤，也可能是 0.01 美元到 1 毫米。
10 个不同的项目？只需向它扔一个整数程序求解器。我在工作中使用OR-Tools，但您可以选择。
@Erwin-Kalvelagen 在yetanothermathprogrammingconsultant.blogspot.com/2016/01/… 有一个多维背包模型示例
【参考方案1】：
您可以尝试框架optuna 进行超参数调优。
这是您可以尝试的示例代码。产品在 parameters.json 文件中被命名为 product1 等。数据值只是假设。
学习/优化会话现在保存在 sqlite db 中。这将支持中断和恢复。查看代码中的版本日志。
parameters.json
"study_name": "st5_tpe",
"sampler": "tpe",
"trials": 1000,
"max_purchase": 7000,
"min_weight_no_cost": 1000,
"high_weight_additional_cost": 0.5,
"trucks":
"smalltruck":
"maxmass": 1000,
"cost": 75
,
"mediumtruck":
"maxmass": 2000,
"cost": 150
,
"bigtruck":
"maxmass": 5000,
"cost": 400
,
"products":
"product1_qty":
"min": 20,
"max": 100,
"massperunit": 2,
"buyprice": 5,
"sellprice": 8
,
"product2_qty":
"min": 20,
"max": 100,
"massperunit": 4,
"buyprice": 6,
"sellprice": 10
,
"product3_qty":
"min": 20,
"max": 100,
"massperunit": 1,
"buyprice": 4,
"sellprice": 6
,
"product4_qty":
"min": 20,
"max": 100,
"massperunit": 2,
"buyprice": 7,
"sellprice": 10
,
"product5_qty":
"min": 20,
"max": 100,
"massperunit": 2,
"buyprice": 5,
"sellprice": 8
,
"product6_qty":
"min": 20,
"max": 100,
"massperunit": 1,
"buyprice": 5,
"sellprice": 7
,
"product7_qty":
"min": 20,
"max": 100,
"massperunit": 1,
"buyprice": 8,
"sellprice": 12
代码
"""
shipping_trading.py
version 0.7.0
* Calculate and show ROI (return of investment) and other info.
* Add user attribute to get other costs.
* Raise exception when max_purchase key is missing in parameters.json file.
* Continue the study even when trucks key is missing in parameters.json file.
version 0.6.0
* Save study/optimization session in sqlite db, with this it can now supports interrupt and resume.
When study session is interrupted it can be resumed later using data from previous session.
* Add study_name key in parameters.json file. Sqlite db name is based on study_name. If you
want new study/optimization session, modify the study_name. If you are re-running the
same study_name, it will run and continue from previous session. Example:
study_name=st8, sqlite_dbname=mydb_st8.db
By default study_name is example_study when you remove study_name key in parameters.json file.
* Remove printing in console on truck info.
version 0.5.0
* Replace kg with qty in parameters.json file.
* Add massperunit in the product.
* Optimize qty not mass.
* Refactor
version 0.4.0
* Add truck size optimization. It is contrained by the cost of using truck as well as the max kg capacity.
The optimizer may suggest a medium instead of a big truck if profit is higher as big truck is expensive.
profit = profit - truck_cost - other_costs
* Modify parameters.json file, trucks key is added.
version 0.3.0
* Read sampler, and number of trials from parameters.json file.
User inputs can now be processed from that file.
version 0.2.0
* Read a new parameters.json format.
* Refactor get_parameters().
version 0.1.0
* Add additional cost if total product weight is high.
"""
__version__ = '0.7.0'
import json
import optuna
def get_parameters():
"""
Read parameters.json file to get the parameters to optimize, etc.
"""
fn = 'parameters.json'
products, trucks = ,
with open(fn) as json_file:
values = json.load(json_file)
max_purchase = values.get('max_purchase', None)
if max_purchase is None:
raise Exception('Missing max_purchase, please specify max_purchase in json file, i.e "max_purchase": 1000')
study_name = values.get('study_name', "example_study")
sampler = values.get('sampler', "tpe")
trials = values.get('trials', 100)
min_weight_no_cost = values.get('min_weight_no_cost', None)
high_weight_additional_cost = values.get('high_weight_additional_cost', None)
products = values.get('products', None)
trucks = values.get('trucks', None)
return (products, trucks, sampler, trials, max_purchase, min_weight_no_cost, high_weight_additional_cost, study_name)
def objective(trial):
"""
Maximize profit.
"""
gp = get_parameters()
(products, trucks, _, _, max_purchase,
min_weight_no_cost, high_weight_additional_cost, _) = gp
# Ask the optimizer the product qty to use try.
new_param =
for k, v in products.items():
suggested_value = trial.suggest_int(k, v['min'], v['max']) # get suggested value from sampler
new_param.update(k: 'suggested': suggested_value,
'massperunit': v['massperunit'],
'buyprice': v['buyprice'],
'sellprice': v['sellprice'])
# Ask the sampler which truck to use, small, medium ....
truck_max_wt, truck_cost = None, None
if trucks is not None:
truck = trial.suggest_categorical("truck", list(trucks.keys()))
# Define truck limits based on suggested truck size.
truck_max_wt = trucks[truck]['maxmass']
truck_cost = trucks[truck]['cost']
# If total wt or total amount is exceeded, we return a 0 profit.
total_wt, total_buy, profit = 0, 0, 0
for k, v in new_param.items():
total_wt += v['suggested'] * v['massperunit']
total_buy += v['suggested'] * v['buyprice']
profit += v['suggested'] * (v['sellprice'] - v['buyprice'])
# (1) Truck mass limit
if truck_max_wt is not None:
if total_wt > truck_max_wt:
return 0
# (2) Purchase limit amount
if max_purchase is not None:
if total_buy > max_purchase:
return 0
# Cost for higher transport weight
cost_high_weight = 0
if min_weight_no_cost is not None and high_weight_additional_cost is not None:
excess_weight = total_wt - min_weight_no_cost
if excess_weight > 0:
cost_high_weight += (total_wt - min_weight_no_cost) * high_weight_additional_cost
# Cost for using a truck, can be small, medium etc.
cost_truck_usage = 0
if truck_cost is not None:
cost_truck_usage += truck_cost
# Total cost
other_costs = cost_high_weight + cost_truck_usage
trial.set_user_attr("other_costs", other_costs)
# Adjust profit
profit = profit - other_costs
# Send this profit to optimizer so that it will consider this value
# in its optimization algo and would suggest a better value next time we ask again.
return profit
def return_of_investment(study, products):
"""
Returns ROI.
ROI = Return Of Investment
ROI = 100 * profit/costs
"""
product_sales, product_costs = 0, 0
for (k, v), (k1, v1) in zip(products.items(), study.best_params.items()):
if k == 'truck':
continue
assert k == k1
product_sales += v1 * v['sellprice']
product_costs += v1 * v['buyprice']
other_costs = study.best_trial.user_attrs['other_costs']
total_costs = product_costs + other_costs
calculated_profit = product_sales - total_costs
study_profit = study.best_trial.values[0]
assert calculated_profit == study_profit
return_of_investment = 100 * calculated_profit/total_costs
return return_of_investment, product_sales, product_costs, other_costs
def main():
# Read parameters.json file for user data input.
gp = get_parameters()
(products, trucks, optsampler, num_trials,
max_purchase, _, _, study_name) = gp
# Location of sqlite db where optimization session data are saved.
sqlite_dbname = f'sqlite:///mydb_study_name.db'
# Available samplers to use:
# https://optuna.readthedocs.io/en/stable/reference/samplers.html
# https://optuna.readthedocs.io/en/stable/reference/generated/optuna.integration.SkoptSampler.html
# https://optuna.readthedocs.io/en/stable/reference/generated/optuna.integration.BoTorchSampler.html
if optsampler.lower() == 'cmaes':
sampler = optuna.samplers.CmaEsSampler(n_startup_trials=1, seed=100)
elif optsampler.lower() == 'tpe':
sampler = optuna.samplers.TPESampler(n_startup_trials=10, multivariate=False, group=False, seed=100, n_ei_candidates=24)
else:
print(f'Warning, optsampler is not supported, we will be using tpe sampler instead.')
optsampler = 'tpe'
sampler = optuna.samplers.TPESampler(n_startup_trials=10, multivariate=False, group=False, seed=100, n_ei_candidates=24)
# Store optimization in storage and supports interrupt/resume.
study = optuna.create_study(storage=sqlite_dbname, sampler=sampler, study_name=study_name, load_if_exists=True, direction='maximize')
study.optimize(objective, n_trials=num_trials)
# Show summary and best parameter values to maximize profit.
print()
print(f'study_name: study_name')
print(f'sqlite dbname: sqlite_dbname')
print(f'sampler: optsampler')
print(f'trials: num_trials')
print()
print(f'Max Purchase Amount: max_purchase')
print()
print('Products being optimized:')
for k, v in products.items():
print(f'k: v')
print()
if trucks is not None:
print('Trucks being optimized:')
for k, v in trucks.items():
print(f'k: v')
print()
print('Study/Optimization results:')
objective_name = 'profit'
print(f'best parameter value : study.best_params')
print(f'best value : study.best_trial.values[0]')
print(f'best trial : study.best_trial.number')
print(f'objective : objective_name')
print()
# Show other info like roi, etc.
roi, product_sales, product_costs, other_costs = return_of_investment(study, products)
print('Other info.:')
print(f'Return Of Investment : roi:0.2f%, profit/costs')
print(f'Product Sales : product_sales:0.2f')
print(f'Product Costs : product_costs:0.2f')
print(f'Other Costs : other_costs:0.2f')
print(f'Total Costs : product_costs + other_costs:0.2f')
print(f'Profit : product_sales - (product_costs + other_costs):0.2f')
print(f'Capital : max_purchase:0.2f')
print(f'Total Spent : product_costs + other_costs:0.2f (100*(product_costs + other_costs)/max_purchase:0.2f% of Capital)')
print(f'Capital Balance : max_purchase - product_costs - other_costs:0.2f')
print()
if __name__ == '__main__':
main()
输出
study_name: st5_tpe
sqlite dbname: sqlite:///mydb_st5_tpe.db
sampler: tpe
trials: 1000
Max Purchase Amount: 7000
Products being optimized:
product1_qty: 'min': 20, 'max': 100, 'massperunit': 2, 'buyprice': 5, 'sellprice': 8
product2_qty: 'min': 20, 'max': 100, 'massperunit': 4, 'buyprice': 6, 'sellprice': 10
product3_qty: 'min': 20, 'max': 100, 'massperunit': 1, 'buyprice': 4, 'sellprice': 6
product4_qty: 'min': 20, 'max': 100, 'massperunit': 2, 'buyprice': 7, 'sellprice': 10
product5_qty: 'min': 20, 'max': 100, 'massperunit': 2, 'buyprice': 5, 'sellprice': 8
product6_qty: 'min': 20, 'max': 100, 'massperunit': 1, 'buyprice': 5, 'sellprice': 7
product7_qty: 'min': 20, 'max': 100, 'massperunit': 1, 'buyprice': 8, 'sellprice': 12
Trucks being optimized:
smalltruck: 'maxmass': 1000, 'cost': 75
mediumtruck: 'maxmass': 2000, 'cost': 150
bigtruck: 'maxmass': 5000, 'cost': 400
Study/Optimization results:
best parameter value : 'product1_qty': 99, 'product2_qty': 96, 'product3_qty': 93, 'product4_qty': 96, 'product5_qty': 100, 'product6_qty': 100, 'product7_qty': 100, 'truck': 'mediumtruck'
best value : 1771.5
best trial : 865
objective : profit
Other info.:
Return Of Investment : 42.19%, profit/costs
Product Sales : 5970.00
Product Costs : 3915.00
Other Costs : 283.50
Total Costs : 4198.50
Profit : 1771.50
Capital : 7000.00
Total Spent : 4198.50 (59.98% of Capital)
Capital Balance : 2801.50
如果增加试验次数，程序或许能够找到更有利可图的参数值。
【讨论】：
我确实尝试过这个，但不幸的是它的速度非常慢。不过，感谢您提供出色的代码示例。 如果您有更多产品和大范围或（最大-最小），它确实会很慢。您能否举例说明参数数量和数量范围。卡车的选择也会导致优化速度变慢。您是否尝试过使用 scipy 的其他解决方案？ 我还没有尝试过 scipy，但我尝试了使用 OR-Tools 的 MIP（在对我最初问题的评论中建议），它进行得非常快。 对，我测试了ortools，确实很快。 scipy 也很快。【参考方案2】：另一个选项是使用scipy。 下面的示例包含 3 种产品，当然可以缩放。约束是购买和最大卡车质量。
代码
"""
shipping_trading_solver.py
Ref: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize
"""
from scipy.optimize import minimize
# Constants
sellprice = [8, 7, 10]
buyprice = [6, 5, 6]
mass_per_unit = [1, 2, 3]
purchase_limit = 100
truck_mass_limit = 70
def objective(x):
"""
objective, return value as negative to maximize.
x: quantity
"""
profit = 0
for (v, s, b) in zip(x, sellprice, buyprice):
profit += v * (s - b)
return -profit
def purchase_cons(x):
"""
Used for constrain
x: quantity
"""
purchases = 0
for (v, b) in zip(x, buyprice):
purchases += v * b
return purchase_limit - purchases # not negative
def mass_cons(x):
"""
Used for constrain
mass = qty * mass/qty
x: quantity
"""
mass = 0
for (v, m) in zip(x, mass_per_unit):
mass += v * m
return truck_mass_limit - mass # not negative
def profit_cons(x):
"""
Used for constrain
x: quantity
"""
profit = 0
for (v, s, b) in zip(x, sellprice, buyprice):
profit += v * (s - b)
return profit # not negative
def main():
# Define constrained. Note: ineq=non-negative, eq=zero
cons = (
'type': 'ineq', 'fun': purchase_cons,
'type': 'ineq', 'fun': mass_cons,
'type': 'ineq', 'fun': profit_cons
)
# Bounds of product quantity, (min,max)
bound = ((0, 50), (0, 20), (0, 30))
# Initial values
init_values = (0, 0, 0)
# Start minimizing
# SLSQP = Sequential Least Squares Programming
res = minimize(objective, init_values, method='SLSQP', bounds=bound, constraints=cons)
# Show summary
print('Results summary:')
print(f'optimization message: res.message')
print(f'success status: res.success')
print(f'profit: sum([(s-b) * int(x) for (x, s, b) in zip(res.x, sellprice, buyprice)]):0.1f')
print(f'best param values: [int(v) for v in res.x]')
print()
# Verify results
print('Verify purchase and mass limits:')
# (1) purchases
total_purchases = 0
for (qty, b) in zip(res.x, buyprice):
total_purchases += int(qty) * b
print(f'actual total_purchases: total_purchases:0.1f, purchase_limit: purchase_limit')
# (2) mass
total_mass = 0
for (qty, m) in zip(res.x, mass_per_unit):
total_mass += int(qty) * m
print(f'actual total_mass: total_mass:0.1f, truck_mass_limit: truck_mass_limit')
if __name__ == '__main__':
main()
输出
Results summary:
optimization message: Optimization terminated successfully
success status: True
profit: 64.0
best param values: [0, 0, 16]
Verify purchase and mass limits:
actual total_purchases: 96.0, purchase_limit: 100
actual total_mass: 48.0, truck_mass_limit: 70
【讨论】：
【参考方案3】：我是mystic 作者。首先，mystic 不是解决这个问题的最佳代码......像OR-Tools 中的一个好的线性 MIP 求解器将是更好的选择。 Mystic 将可靠地解决 MIP/LP 问题，只是不如 OR-Tools 快。在速度方面，mystic 与scipy.optimize 差不多快。随着约束变得更加非线性、复杂和受严格约束，Mystic 会放慢速度（请注意，在这种情况下，其他代码通常会失败，而 mystic 不会）。下面，我将使用差分进化求解器（它比 SLSQP 更慢，但更健壮）。
请注意，一旦您有一个或多个非线性约束，您应该绝对使用mystic...，因为mystic 是为具有非线性约束的全局优化而构建的。或者，如果您没有固定定价模型，而是在模型中存在一些市场波动，从而产生不确定性......并且想要最大化预期利润，或者甚至更好地建立一个最小化风险的利润模型，那么您肯定应该使用mystic。 OR-tools 和其他 LP/QP 代码最多只能将问题近似为线性或二次 - 这可能不切实际。
无论如何。当您询问在此问题上使用 mystic 时，这是使用 mystic 解决问题的众多方法之一：
import mystic as my
import mystic.symbolic as ms
import mystic.constraints as mc
class item(object):
def __init__(self, id, mass, buy, net, limit):
self.id = id
self.mass = mass
self.buy = buy
self.net = net
self.limit = limit
def __repr__(self):
return 'item(%s, mass=%s, buy=%s, net=%s, limit=%s)' % (self.id, self.mass, self.buy, self.net, self.limit)
# data
masses = [10, 15, 20, 18, 34, 75, 11, 49, 68, 55]
buys = [123, 104, 149, 175, 199, 120, 164, 136, 194, 111]
nets = [13, 24, 10, 29, 29, 39, 28, 35, 33, 39]
limits = [300, 500, 200, 300, 200, 350, 100, 600, 1000, 50]
ids = range(len(limits))
# maxima
_load = 75000 # max limit on mass can carry
_spend = 350000 # max limit to spend at source
# items
items = [item(*i) for i in zip(ids, masses, buys, nets, limits)]
# profit
def fixnet(net):
def profit(x):
return sum(xi*pi for xi,pi in zip(x,net))
return profit
profit = fixnet([i.net for i in items])
# item constraints
load = [i.mass for i in items]
invest = [i.buy for i in items]
constraints = ms.linear_symbolic(G=[load, invest], h=[_load, _spend])
# bounds (on x)
bounds = [(0, i.limit) for i in items]
# bounds constraints
lo = 'x%s >= %s'
lo = '\n'.join(lo % (i,str(float(j[0])).lstrip('0')) for (i,j) in enumerate(bounds))
hi = 'x%s <= %s'
hi = '\n'.join(hi % (i,str(float(j[1])).lstrip('0')) for (i,j) in enumerate(bounds))
constraints = '\n'.join([lo, hi]).strip() + '\n' + constraints
pf = ms.generate_penalty(ms.generate_conditions(ms.simplify(constraints)))
# integer constraints
cf = mc.integers(float)(lambda x:x)
# solve
mon = my.monitors.VerboseMonitor(1, 10)
results = my.solvers.diffev2(lambda x: -profit(x), bounds, npop=400, bounds=bounds, ftol=1e-4, gtol=50, itermon=mon, disp=True, full_output=True, constraints=cf, penalty=pf)
print ('\nmax profit: %s' % -results[1])
print("load: %s <= %s" % (sum(i*j for i,j in zip(results[0], load)), _load))
print("spend: %s <= %s" % (sum(i*j for i,j in zip(results[0], invest)), _spend))
print('')
for item,quantity in enumerate(results[0]):
print("item %s: %s" % (item,quantity))
结果：
dude@borel>$ python knapsack.py
Generation 0 has ChiSquare: -58080.000000
Generation 0 has fit parameters:
[139.0, 413.0, 100.0, 271.0, 136.0, 344.0, 86.0, 404.0, 103.0, 5.0]
Generation 1 has ChiSquare: -58080.000000
Generation 2 has ChiSquare: -58080.000000
Generation 3 has ChiSquare: -58080.000000
Generation 4 has ChiSquare: -58080.000000
Generation 5 has ChiSquare: -58080.000000
Generation 6 has ChiSquare: -58080.000000
Generation 7 has ChiSquare: -58080.000000
Generation 8 has ChiSquare: -58080.000000
Generation 9 has ChiSquare: -58080.000000
Generation 10 has ChiSquare: -58080.000000
Generation 10 has fit parameters:
[139.0, 413.0, 100.0, 271.0, 136.0, 344.0, 86.0, 404.0, 103.0, 5.0]
Generation 11 has ChiSquare: -58603.000000
Generation 12 has ChiSquare: -58603.000000
Generation 13 has ChiSquare: -58603.000000
Generation 14 has ChiSquare: -58603.000000
Generation 15 has ChiSquare: -58603.000000
Generation 16 has ChiSquare: -58603.000000
Generation 17 has ChiSquare: -58603.000000
Generation 18 has ChiSquare: -58607.000000
Generation 19 has ChiSquare: -58607.000000
Generation 20 has ChiSquare: -58607.000000
Generation 20 has fit parameters:
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Generation 21 has ChiSquare: -59118.000000
Generation 22 has ChiSquare: -59944.000000
Generation 23 has ChiSquare: -59944.000000
Generation 24 has ChiSquare: -59944.000000
Generation 25 has ChiSquare: -59944.000000
Generation 26 has ChiSquare: -59944.000000
Generation 27 has ChiSquare: -59944.000000
Generation 28 has ChiSquare: -59944.000000
Generation 29 has ChiSquare: -60765.000000
Generation 30 has ChiSquare: -60765.000000
Generation 30 has fit parameters:
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Generation 31 has ChiSquare: -60765.000000
Generation 32 has ChiSquare: -60765.000000
Generation 33 has ChiSquare: -60765.000000
Generation 34 has ChiSquare: -60765.000000
Generation 35 has ChiSquare: -60765.000000
Generation 36 has ChiSquare: -61045.000000
Generation 37 has ChiSquare: -61045.000000
Generation 38 has ChiSquare: -61045.000000
Generation 39 has ChiSquare: -61045.000000
Generation 40 has ChiSquare: -61045.000000
Generation 40 has fit parameters:
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Generation 41 has ChiSquare: -61045.000000
Generation 42 has ChiSquare: -61045.000000
Generation 43 has ChiSquare: -61045.000000
Generation 44 has ChiSquare: -61045.000000
Generation 45 has ChiSquare: -61045.000000
Generation 46 has ChiSquare: -61045.000000
Generation 47 has ChiSquare: -61045.000000
Generation 48 has ChiSquare: -61045.000000
Generation 49 has ChiSquare: -62106.000000
Generation 50 has ChiSquare: -62106.000000
Generation 50 has fit parameters:
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Generation 51 has ChiSquare: -62106.000000
Generation 52 has ChiSquare: -62106.000000
Generation 53 has ChiSquare: -62106.000000
Generation 54 has ChiSquare: -62106.000000
Generation 55 has ChiSquare: -62106.000000
Generation 56 has ChiSquare: -62224.000000
Generation 57 has ChiSquare: -62224.000000
Generation 58 has ChiSquare: -62224.000000
Generation 59 has ChiSquare: -62224.000000
Generation 60 has ChiSquare: -62224.000000
Generation 60 has fit parameters:
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Generation 61 has ChiSquare: -62224.000000
Generation 62 has ChiSquare: -62224.000000
Generation 63 has ChiSquare: -62224.000000
Generation 64 has ChiSquare: -62224.000000
Generation 65 has ChiSquare: -62224.000000
Generation 66 has ChiSquare: -62224.000000
Generation 67 has ChiSquare: -62224.000000
Generation 68 has ChiSquare: -62224.000000
Generation 69 has ChiSquare: -62224.000000
Generation 70 has ChiSquare: -62224.000000
Generation 70 has fit parameters:
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Generation 71 has ChiSquare: -63795.000000
Generation 72 has ChiSquare: -63795.000000
Generation 73 has ChiSquare: -63795.000000
Generation 74 has ChiSquare: -63795.000000
Generation 75 has ChiSquare: -63795.000000
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Generation 78 has ChiSquare: -63795.000000
Generation 79 has ChiSquare: -63795.000000
Generation 80 has ChiSquare: -63795.000000
Generation 80 has fit parameters:
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Generation 81 has ChiSquare: -63795.000000
Generation 82 has ChiSquare: -63795.000000
Generation 83 has ChiSquare: -63795.000000
Generation 84 has ChiSquare: -63795.000000
Generation 85 has ChiSquare: -63795.000000
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Generation 87 has ChiSquare: -63795.000000
Generation 88 has ChiSquare: -63795.000000
Generation 89 has ChiSquare: -63795.000000
Generation 90 has ChiSquare: -63795.000000
Generation 90 has fit parameters:
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Generation 91 has ChiSquare: -63795.000000
Generation 92 has ChiSquare: -63795.000000
Generation 93 has ChiSquare: -63795.000000
Generation 94 has ChiSquare: -63795.000000
Generation 95 has ChiSquare: -63795.000000
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Generation 97 has ChiSquare: -63795.000000
Generation 98 has ChiSquare: -63795.000000
Generation 99 has ChiSquare: -63795.000000
Generation 100 has ChiSquare: -63795.000000
Generation 100 has fit parameters:
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Generation 101 has ChiSquare: -63795.000000
Generation 102 has ChiSquare: -64252.000000
Generation 103 has ChiSquare: -64252.000000
Generation 104 has ChiSquare: -64252.000000
Generation 105 has ChiSquare: -64252.000000
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Generation 107 has ChiSquare: -64252.000000
Generation 108 has ChiSquare: -64252.000000
Generation 109 has ChiSquare: -64252.000000
Generation 110 has ChiSquare: -64252.000000
Generation 110 has fit parameters:
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Generation 111 has ChiSquare: -64252.000000
Generation 112 has ChiSquare: -64252.000000
Generation 113 has ChiSquare: -64252.000000
Generation 114 has ChiSquare: -64252.000000
Generation 115 has ChiSquare: -64252.000000
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Generation 117 has ChiSquare: -64252.000000
Generation 118 has ChiSquare: -64252.000000
Generation 119 has ChiSquare: -64252.000000
Generation 120 has ChiSquare: -64252.000000
Generation 120 has fit parameters:
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Generation 121 has ChiSquare: -64252.000000
Generation 122 has ChiSquare: -64252.000000
Generation 123 has ChiSquare: -64252.000000
Generation 124 has ChiSquare: -64368.000000
Generation 125 has ChiSquare: -64368.000000
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Generation 127 has ChiSquare: -64368.000000
Generation 128 has ChiSquare: -64368.000000
Generation 129 has ChiSquare: -64368.000000
Generation 130 has ChiSquare: -64368.000000
Generation 130 has fit parameters:
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Generation 131 has ChiSquare: -64368.000000
Generation 132 has ChiSquare: -64368.000000
Generation 133 has ChiSquare: -64368.000000
Generation 134 has ChiSquare: -64368.000000
Generation 135 has ChiSquare: -64368.000000
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Generation 137 has ChiSquare: -64368.000000
Generation 138 has ChiSquare: -64368.000000
Generation 139 has ChiSquare: -64735.000000
Generation 140 has ChiSquare: -64735.000000
Generation 140 has fit parameters:
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Generation 141 has ChiSquare: -64735.000000
Generation 142 has ChiSquare: -64735.000000
Generation 143 has ChiSquare: -64735.000000
Generation 144 has ChiSquare: -64735.000000
Generation 145 has ChiSquare: -64735.000000
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Generation 148 has ChiSquare: -64735.000000
Generation 149 has ChiSquare: -64735.000000
Generation 150 has ChiSquare: -64735.000000
Generation 150 has fit parameters:
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Generation 151 has ChiSquare: -64735.000000
Generation 152 has ChiSquare: -64735.000000
Generation 153 has ChiSquare: -64735.000000
Generation 154 has ChiSquare: -64735.000000
Generation 155 has ChiSquare: -64735.000000
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Generation 157 has ChiSquare: -64735.000000
Generation 158 has ChiSquare: -64735.000000
Generation 159 has ChiSquare: -64735.000000
Generation 160 has ChiSquare: -64735.000000
Generation 160 has fit parameters:
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Generation 161 has ChiSquare: -64735.000000
Generation 162 has ChiSquare: -64897.000000
Generation 163 has ChiSquare: -65223.000000
Generation 164 has ChiSquare: -65223.000000
Generation 165 has ChiSquare: -65223.000000
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Generation 168 has ChiSquare: -65223.000000
Generation 169 has ChiSquare: -65223.000000
Generation 170 has ChiSquare: -65223.000000
Generation 170 has fit parameters:
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Generation 171 has ChiSquare: -65223.000000
Generation 172 has ChiSquare: -65223.000000
Generation 173 has ChiSquare: -65223.000000
Generation 174 has ChiSquare: -65223.000000
Generation 175 has ChiSquare: -65223.000000
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Generation 177 has ChiSquare: -65223.000000
Generation 178 has ChiSquare: -65223.000000
Generation 179 has ChiSquare: -65223.000000
Generation 180 has ChiSquare: -65223.000000
Generation 180 has fit parameters:
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Generation 181 has ChiSquare: -65223.000000
Generation 182 has ChiSquare: -65223.000000
Generation 183 has ChiSquare: -65223.000000
Generation 184 has ChiSquare: -65223.000000
Generation 185 has ChiSquare: -65223.000000
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Generation 187 has ChiSquare: -65223.000000
Generation 188 has ChiSquare: -65223.000000
Generation 189 has ChiSquare: -65223.000000
Generation 190 has ChiSquare: -65223.000000
Generation 190 has fit parameters:
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Generation 191 has ChiSquare: -65223.000000
Generation 192 has ChiSquare: -65223.000000
Generation 193 has ChiSquare: -65223.000000
Generation 194 has ChiSquare: -65223.000000
Generation 195 has ChiSquare: -65223.000000
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Generation 198 has ChiSquare: -65223.000000
Generation 199 has ChiSquare: -65223.000000
Generation 200 has ChiSquare: -65223.000000
Generation 200 has fit parameters:
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Generation 201 has ChiSquare: -65340.000000
Generation 202 has ChiSquare: -65340.000000
Generation 203 has ChiSquare: -65340.000000
Generation 204 has ChiSquare: -65340.000000
Generation 205 has ChiSquare: -65340.000000
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Generation 209 has ChiSquare: -65340.000000
Generation 210 has ChiSquare: -65340.000000
Generation 210 has fit parameters:
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Generation 211 has ChiSquare: -65340.000000
Generation 212 has ChiSquare: -65340.000000
Generation 213 has ChiSquare: -65340.000000
Generation 214 has ChiSquare: -65340.000000
Generation 215 has ChiSquare: -65340.000000
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Generation 217 has ChiSquare: -65340.000000
Generation 218 has ChiSquare: -65340.000000
Generation 219 has ChiSquare: -65340.000000
Generation 220 has ChiSquare: -65340.000000
Generation 220 has fit parameters:
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Generation 221 has ChiSquare: -65340.000000
Generation 222 has ChiSquare: -65340.000000
Generation 223 has ChiSquare: -65340.000000
Generation 224 has ChiSquare: -65340.000000
Generation 225 has ChiSquare: -65340.000000
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Generation 230 has ChiSquare: -65449.000000
Generation 230 has fit parameters:
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Generation 231 has ChiSquare: -65449.000000
Generation 232 has ChiSquare: -65449.000000
Generation 233 has ChiSquare: -65449.000000
Generation 234 has ChiSquare: -65449.000000
Generation 235 has ChiSquare: -65449.000000
Generation 236 has ChiSquare: -65449.000000
Generation 237 has ChiSquare: -65449.000000
Generation 238 has ChiSquare: -65449.000000
Generation 239 has ChiSquare: -65449.000000
Generation 240 has ChiSquare: -65449.000000
Generation 240 has fit parameters:
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Generation 241 has ChiSquare: -65449.000000
Generation 242 has ChiSquare: -65449.000000
Generation 243 has ChiSquare: -65449.000000
Generation 244 has ChiSquare: -65449.000000
Generation 245 has ChiSquare: -65449.000000
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Generation 248 has ChiSquare: -65456.000000
Generation 249 has ChiSquare: -65456.000000
Generation 250 has ChiSquare: -65456.000000
Generation 250 has fit parameters:
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Generation 251 has ChiSquare: -65456.000000
Generation 252 has ChiSquare: -65456.000000
Generation 253 has ChiSquare: -65456.000000
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Generation 255 has ChiSquare: -65622.000000
Generation 256 has ChiSquare: -65622.000000
Generation 257 has ChiSquare: -65622.000000
Generation 258 has ChiSquare: -65622.000000
Generation 259 has ChiSquare: -65622.000000
Generation 260 has ChiSquare: -65622.000000
Generation 260 has fit parameters:
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Generation 261 has ChiSquare: -65622.000000
Generation 262 has ChiSquare: -65622.000000
Generation 263 has ChiSquare: -65622.000000
Generation 264 has ChiSquare: -65622.000000
Generation 265 has ChiSquare: -65622.000000
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Generation 267 has ChiSquare: -65622.000000
Generation 268 has ChiSquare: -65622.000000
Generation 269 has ChiSquare: -65622.000000
Generation 270 has ChiSquare: -65622.000000
Generation 270 has fit parameters:
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Generation 271 has ChiSquare: -65622.000000
Generation 272 has ChiSquare: -65622.000000
Generation 273 has ChiSquare: -65622.000000
Generation 274 has ChiSquare: -65622.000000
Generation 275 has ChiSquare: -65622.000000
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Generation 278 has ChiSquare: -65622.000000
Generation 279 has ChiSquare: -65622.000000
Generation 280 has ChiSquare: -65622.000000
Generation 280 has fit parameters:
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Generation 281 has ChiSquare: -65622.000000
Generation 282 has ChiSquare: -65622.000000
Generation 283 has ChiSquare: -65622.000000
Generation 284 has ChiSquare: -65622.000000
Generation 285 has ChiSquare: -65622.000000
Generation 286 has ChiSquare: -65622.000000
Generation 287 has ChiSquare: -65622.000000
Generation 288 has ChiSquare: -65622.000000
Generation 289 has ChiSquare: -65622.000000
Generation 290 has ChiSquare: -65622.000000
Generation 290 has fit parameters:
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Generation 291 has ChiSquare: -65644.000000
Generation 292 has ChiSquare: -65644.000000
Generation 293 has ChiSquare: -65691.000000
Generation 294 has ChiSquare: -65691.000000
Generation 295 has ChiSquare: -65691.000000
Generation 296 has ChiSquare: -65691.000000
Generation 297 has ChiSquare: -65691.000000
Generation 298 has ChiSquare: -65691.000000
Generation 299 has ChiSquare: -65691.000000
Generation 300 has ChiSquare: -65691.000000
Generation 300 has fit parameters:
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Generation 301 has ChiSquare: -65691.000000
Generation 302 has ChiSquare: -65691.000000
Generation 303 has ChiSquare: -65703.000000
Generation 304 has ChiSquare: -65703.000000
Generation 305 has ChiSquare: -65703.000000
Generation 306 has ChiSquare: -65703.000000
Generation 307 has ChiSquare: -65703.000000
Generation 308 has ChiSquare: -65703.000000
Generation 309 has ChiSquare: -65703.000000
Generation 310 has ChiSquare: -65703.000000
Generation 310 has fit parameters:
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Generation 311 has ChiSquare: -65703.000000
Generation 312 has ChiSquare: -65703.000000
Generation 313 has ChiSquare: -65703.000000
Generation 314 has ChiSquare: -65703.000000
Generation 315 has ChiSquare: -65703.000000
Generation 316 has ChiSquare: -65703.000000
Generation 317 has ChiSquare: -65773.000000
Generation 318 has ChiSquare: -65773.000000
Generation 319 has ChiSquare: -65773.000000
Generation 320 has ChiSquare: -65773.000000
Generation 320 has fit parameters:
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Generation 321 has ChiSquare: -65773.000000
Generation 322 has ChiSquare: -65773.000000
Generation 323 has ChiSquare: -65773.000000
Generation 324 has ChiSquare: -65773.000000
Generation 325 has ChiSquare: -65773.000000
Generation 326 has ChiSquare: -65773.000000
Generation 327 has ChiSquare: -65773.000000
Generation 328 has ChiSquare: -65773.000000
Generation 329 has ChiSquare: -65773.000000
Generation 330 has ChiSquare: -65773.000000
Generation 330 has fit parameters:
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Generation 331 has ChiSquare: -65773.000000
Generation 332 has ChiSquare: -65773.000000
Generation 333 has ChiSquare: -65773.000000
Generation 334 has ChiSquare: -65773.000000
Generation 335 has ChiSquare: -65773.000000
Generation 336 has ChiSquare: -65773.000000
Generation 337 has ChiSquare: -65773.000000
Generation 338 has ChiSquare: -65774.000000
Generation 339 has ChiSquare: -65774.000000
Generation 340 has ChiSquare: -65774.000000
Generation 340 has fit parameters:
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Generation 341 has ChiSquare: -65774.000000
Generation 342 has ChiSquare: -65774.000000
Generation 343 has ChiSquare: -65774.000000
Generation 344 has ChiSquare: -65774.000000
Generation 345 has ChiSquare: -65774.000000
Generation 346 has ChiSquare: -65774.000000
Generation 347 has ChiSquare: -65774.000000
Generation 348 has ChiSquare: -65774.000000
Generation 349 has ChiSquare: -65774.000000
Generation 350 has ChiSquare: -65774.000000
Generation 350 has fit parameters:
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Generation 351 has ChiSquare: -65774.000000
Generation 352 has ChiSquare: -65774.000000
Generation 353 has ChiSquare: -65774.000000
Generation 354 has ChiSquare: -65779.000000
Generation 355 has ChiSquare: -65779.000000
Generation 356 has ChiSquare: -65779.000000
Generation 357 has ChiSquare: -65779.000000
Generation 358 has ChiSquare: -65779.000000
Generation 359 has ChiSquare: -65779.000000
Generation 360 has ChiSquare: -65779.000000
Generation 360 has fit parameters:
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Generation 361 has ChiSquare: -65888.000000
Generation 362 has ChiSquare: -65888.000000
Generation 363 has ChiSquare: -65888.000000
Generation 364 has ChiSquare: -65888.000000
Generation 365 has ChiSquare: -65888.000000
Generation 366 has ChiSquare: -65888.000000
Generation 367 has ChiSquare: -65895.000000
Generation 368 has ChiSquare: -65895.000000
Generation 369 has ChiSquare: -65895.000000
Generation 370 has ChiSquare: -65895.000000
Generation 370 has fit parameters:
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Generation 371 has ChiSquare: -65895.000000
Generation 372 has ChiSquare: -65895.000000
Generation 373 has ChiSquare: -65895.000000
Generation 374 has ChiSquare: -65895.000000
Generation 375 has ChiSquare: -65895.000000
Generation 376 has ChiSquare: -65895.000000
Generation 377 has ChiSquare: -65895.000000
Generation 378 has ChiSquare: -65895.000000
Generation 379 has ChiSquare: -65895.000000
Generation 380 has ChiSquare: -65895.000000
Generation 380 has fit parameters:
[300.0, 500.0, 50.0, 300.0, 198.0, 231.0, 99.0, 599.0, 12.0, 49.0]
Generation 381 has ChiSquare: -65895.000000
Generation 382 has ChiSquare: -65895.000000
Generation 383 has ChiSquare: -65895.000000
Generation 384 has ChiSquare: -65895.000000
Generation 385 has ChiSquare: -65895.000000
Generation 386 has ChiSquare: -65895.000000
Generation 387 has ChiSquare: -65895.000000
Generation 388 has ChiSquare: -65895.000000
Generation 389 has ChiSquare: -65895.000000
Generation 390 has ChiSquare: -65895.000000
Generation 390 has fit parameters:
[300.0, 500.0, 50.0, 300.0, 198.0, 231.0, 99.0, 599.0, 12.0, 49.0]
Generation 391 has ChiSquare: -65895.000000
Generation 392 has ChiSquare: -65895.000000
Generation 393 has ChiSquare: -65895.000000
Generation 394 has ChiSquare: -65895.000000
Generation 395 has ChiSquare: -65895.000000
Generation 396 has ChiSquare: -65966.000000
Generation 397 has ChiSquare: -65966.000000
Generation 398 has ChiSquare: -65966.000000
Generation 399 has ChiSquare: -65966.000000
Generation 400 has ChiSquare: -65966.000000
Generation 400 has fit parameters:
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Generation 401 has ChiSquare: -65966.000000
Generation 402 has ChiSquare: -65966.000000
Generation 403 has ChiSquare: -65966.000000
Generation 404 has ChiSquare: -65966.000000
Generation 405 has ChiSquare: -65966.000000
Generation 406 has ChiSquare: -65966.000000
Generation 407 has ChiSquare: -65966.000000
Generation 408 has ChiSquare: -65966.000000
Generation 409 has ChiSquare: -65966.000000
Generation 410 has ChiSquare: -65966.000000
Generation 410 has fit parameters:
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Generation 411 has ChiSquare: -65966.000000
Generation 412 has ChiSquare: -65966.000000
Generation 413 has ChiSquare: -65966.000000
Generation 414 has ChiSquare: -65966.000000
Generation 415 has ChiSquare: -65966.000000
Generation 416 has ChiSquare: -65966.000000
Generation 417 has ChiSquare: -65966.000000
Generation 418 has ChiSquare: -65966.000000
Generation 419 has ChiSquare: -65966.000000
Generation 420 has ChiSquare: -65966.000000
Generation 420 has fit parameters:
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Generation 421 has ChiSquare: -65966.000000
Generation 422 has ChiSquare: -65966.000000
Generation 423 has ChiSquare: -65966.000000
Generation 424 has ChiSquare: -65966.000000
Generation 425 has ChiSquare: -65966.000000
Generation 426 has ChiSquare: -65966.000000
Generation 427 has ChiSquare: -65966.000000
Generation 428 has ChiSquare: -65966.000000
Generation 429 has ChiSquare: -65966.000000
Generation 430 has ChiSquare: -65966.000000
Generation 430 has fit parameters:
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Generation 431 has ChiSquare: -65966.000000
Generation 432 has ChiSquare: -65966.000000
Generation 433 has ChiSquare: -65966.000000
Generation 434 has ChiSquare: -65966.000000
Generation 435 has ChiSquare: -65966.000000
Generation 436 has ChiSquare: -65966.000000
Generation 437 has ChiSquare: -65966.000000
Generation 438 has ChiSquare: -65966.000000
Generation 439 has ChiSquare: -65966.000000
Generation 440 has ChiSquare: -65966.000000
Generation 440 has fit parameters:
[299.0, 499.0, 21.0, 299.0, 200.0, 249.0, 100.0, 597.0, 2.0, 50.0]
Generation 441 has ChiSquare: -65966.000000
Generation 442 has ChiSquare: -65966.000000
Generation 443 has ChiSquare: -65966.000000
Generation 444 has ChiSquare: -65966.000000
Generation 445 has ChiSquare: -65966.000000
STOP("ChangeOverGeneration with 'tolerance': 0.0001, 'generations': 50")
Optimization terminated successfully.
Current function value: -65966.000000
Iterations: 445
Function evaluations: 178400
max profit: 65966.0
load: 74991.0 <= 75000
spend: 317337.0 <= 350000
item 0: 299.0
item 1: 499.0
item 2: 21.0
item 3: 299.0
item 4: 200.0
item 5: 249.0
item 6: 100.0
item 7: 597.0
item 8: 2.0
item 9: 50.0
这是我第一次尝试获得解决方案，并且未调整求解器，您可以看到可能仍有一些小的摆动空间需要改进，因为最后的收敛是尖锐而不是超级平滑 - 但是，我假设解决方案接近最优（基于约束检查）。我会尝试设置以及如何施加约束/惩罚，看看解决方案是否可以进一步改进。
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