Vector of Parameters: This is a set of variables or conditions that characterize the system or scenario. They can be input conditions, system states, or any other relevant metrics that describe the system. 

Objective Function: This is a mathematical function that quantifies how far the current system's performance is from the desired performance. The goal is usually to minimize or maximize this function. 

Constraints: These are the bounds or limitations within which the system operates. In engineering problems, constraints can arise from physical limitations, safety requirements, budgetary restrictions, etc. The solution must satisfy these constraints.

Mathematical Treatment of the Axioms of Physics

Rigorous Foundation of Schubert's Enumerative Calculus

Topology of Algebraic Curves and Surfaces

Analysis of Solutions of Variational Problems

Birch and Swinnerton-Dyer Conjecture

Hodge Conjecture

Navier–Stokes Existence and Smoothness

P vs NP Problem

Riemann Hypothesis

Yang–Mills Existence and Mass Gap

No Definitive Formulation

No Stopping Rule

Solutions Are Not True-or-False

No Immediate and No Ultimate Test

Every Solution is a 'One-Shot Operation'

No Enumerable (or Exhaustively Describable) Set of Potential Solutions

Every Wicked Problem is Essentially Unique

Every Wicked Problem Can Be Considered to Be a Symptom of Another Problem

The Existence of a Discrepancy Representing a Wicked Problem Can Be Explained in Numerous Ways

The Planner Has No Right to Be Wrong

Radioactive waste disposal

Liberation from fossil fuel dependency

Language extinction

Weltverständlichmachung

Unf*cking the Wohnungsmarkt

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The Clock Reform

https://github.com/python-constraint/python-constraint

https://github.com/timnon/pyschedule

Note: install the most recent fork, (e.g. pip3.10 install "pyschedule"@git+"https://github.com/ppoile/pyschedule/#subdirectory=src")

eight queen problems

map coloring problem

#Adam has one hour time on Monday and Wednesday, three hours time on Thursday and fours hours time on each weekend day, Eve has two hours on Tuesday, three hours on Friday and four hours on each weekend day.  Define pyschedule resources with correctly defined periods and horizons.

#Monday: Adam x 1
#Tuesday:  Eva x 2
#Wednesday: Adam x 1
#Thursday: Adam x 4
#Friday: Eva x 3
#Saturday: Both x 4
#Sunday : Both x 4

from pyschedule import Scenario, solvers, plotters, alt

# Define the scenario
S = Scenario('household_chores', horizon=15)  # Two weeks

# Define the resources, resource costs are not obligatory but it's more fun with them
adam = S.Resource('Adam',periods=[0,3,4,5,6,7,11,12,13,14])
eve = S.Resource('Eve',periods=[1,2,8,9,10,11,12,13,14])

kitchen=S.Resource('kitchen')

# Define the tasks and their durations
task_costs = {
    "meal1": {"length":1,"delay_cost":1},                # 1 hour, schedule towards beginning of the week
    "meal2": {"length":1,"delay_cost":1},             
    "meal3": {"length":1,"delay_cost":-1},               
    "meal4": {"length":1,"delay_cost":-1},               # 1 hour, schedule towards end of the week
    "bake": {"length":2,"delay_cost":0},                  # 2 hours (1 cake)
    "sleeping_room": {"length":2,"delay_cost":0},  # it seems there is a bug for tasks longer >1 
    #"CSR1": {"length":1,"delay_cost":0},          # one way how to address the bug is to split long tasks into sub-tasks coupled by tight preference constraints
    #"CSR2": {"length":1,"delay_cost":0},          # 
    "bathroom": {"length":2,"delay_cost":0},       # 2 hours
    "living_room": {"length":3,"delay_cost":0},    # 3 hours
    "clean_kitchen": {"length":3,"delay_cost":0}   # 3 hours
}

tasks={}
# Define alternative resources for each task
for task,costs in task_costs.items():
    print(task,costs)
    tasks[task] = S.Task(task,length=costs['length'],delay_cost=costs["delay_cost"])      #create new task
    tasks[task] += adam | eve               #assign resources to newly created task

#additional task-resource attributions
tasks["clean_kitchen"]+=kitchen
tasks["meal1"]+=kitchen
tasks["meal2"]+=kitchen
tasks["meal3"]+=kitchen
tasks["meal4"]+=kitchen
tasks["bake"]+=kitchen

#tight precedence constraints
#S += tasks['CSR1'] <= tasks['CSR2']

#optional tasks
#tasks['playground'] = S.Task('playground',length=2,schedule_cost=-1)
#tasks['playground'] += alt(adam,eve)

#additional constraints
S += tasks['meal1'] < tasks['clean_kitchen'] 
S += tasks['meal2'] < tasks['clean_kitchen'] 
S += tasks['meal3'] < tasks['clean_kitchen'] 
S += tasks['meal4'] < tasks['clean_kitchen'] 
S += tasks['bake'] < tasks['clean_kitchen'] 

# Solve the scenario
solvers.mip.solve(S,msg=1,kind='GUROBI')

print(S)
print(S.solution())
print(adam.periods)
# Plot the schedule
plotters.matplotlib.plot(S)

• Latin "solutio": Meaning a loosening or unbinding. This comes from the verb “solvere,” which means to loosen, untie, or dissolve.
• Latin "solvēre": This is a compound of “sol-,” a variant of “se-” (apart), and “luere” (to wash or to loosen).