Hi Alex,

the answer might easily fill some books, but in short:

1. You have to know the contents of your toolbox. On the lowest level, it might contain less than 50 tools (like in robotics programming: speed, accel, move, moves, appro, appros, depart, departs, break, wait, delay etc.) On the physical level, you get to know your toolbox as a child; on the cognitive level, during your education (which is a lifelong process if you don't lead a boring life).

2. If you have done a similar task in the past: If the result was satisfactory then do it in the same way; if not then introduce some promising change.

3. If the task is new to you then search your memory for analogous tasks you have done successfully. (Cooking a soup might not be very different from cooking a pizza.)

4. If the task is completely new: Use your planning ability, i. e. simulate (in your mind) yourself and your environment based on your general experience. If you hit a solution then try to implement this solution in reality.

5. If the task is complex then apply "divide and conquer": Generate a hierarchy with the task as root and subtasks on lower levels. Stop when all subtasks forming leaves look feasible to you. It's the same as writing a program. If you don't know how to solve certain subtasks then you have to gain knowledge in this domain first before continuing the planning (or programming). In some cases, "outsourcing" might be a better option than solving certain problems yourself (in programming: find suitable procedures in existing libraries).

There are some problems like finding the exit of a labyrinth you are in where you cannot see further than the next bend; in this case, building a hierarchy isn't feasible, and the answer to your question regarding the next step is: You cannot know. With ideal tools, you could create a map while surveying the labyrinth but a) a helpful map must include the exit, and if you found it you don't need the map anymore, and b) to a well built labyrinth, the hierarchical approach cannot be applied even with a map because there aren't any obvious subgoals. The advantage of creating a map is that it protects you against walking in a closed loop forever.

6. If the task is not only new (to you and anyone else) but solving the problem involves obviously some creative processes then your picture with the virtually infinite toolbox is correct: Brute force (try systematically all options) could take centuries. The solving process might include a lot of dead ends, it might take weeks, years, or decades, and you might not succeed at all.

Thank you for your answer!

First, I thought planning because in theory the problem is fully new for somebody, I know the examples are every-day problems but these just examples so if we are looking in the "Pizza cooking" problem like a fully new problem then we have a theory how we solve the problem and why this way, we can easily check the exactness of the solution.

Second, the question is, how do you planning? (actually your 4. paragraph)

What systems/algorithm/method do you need to use that will lead to the next step and then the final step (so the whole step-by-step solution)

And this method should be universally applicable because the animals can solve problems with a very high diversity interval.

Hi

reinforcement learning can solve your problem in case you have a training dataset

Alex,

just to better understand where you're heading: Are you interested in the way humans solve problems consciously (e. g. as we would expect our students to improve in), or in theories about human problem solving, encompassing subconscious processes, or in machine based problem solving / learning?

As to animals, I seem to remember a setup which shows whether the animal can create a plan and act accordingly: Provide some nice smelling feed behind a straight barrier (like a fence) which is long but not unlimited. Without planning (just make one step and evaluate the change of your situation), the animal will never circumvent the barrier because that would mean to go on while the smell decreases . With planning (temporal goal: explore the barrier for holes etc.), the animal is ready to make a temporal sacrifice in order to reach the ultimate goal.

Accordingly, you don't start with the decision about your first physical step. First, you have to gain knowledge about the ingredients of pizzas and necessary tools for cooking. Then you could form the hypothesis that, for example, both the ingredients and the tools are located in your kitchen. So you have to test your hypothesis, and this involves moving physically to your kitchen.

There is a whole area of research on problem solving in Psychology and much of it is at the fuzzy boundary between Cognitive Psychology and Artificial Intelligence, such as the pioneering research of Herb Simon. Some examples of this earlier work include Herbert Simon’s “Models of Thought and Allen Newell’s “Unified Theories of Cognition.”  For problems in which the problem solver is experienced, you can use “domain specific problem solving strategies” well attuned to the particular kind of problem (e.g., for algebra, do the same thing to both sides).  In contrast, for problem solving situations in which the experience is new, you would use a “domain general problem solving strategy.”  These strategies include trial-and-error, analogical transfer, hill-climbing (i.e., choose an operator that reduces the discrepancy between the current state and the goal state, so in your example choose any action that moves you closer to the door), and means-ends analysis (i.e., identify sub-goals a recursively solving those problems).  Much of the research examines how the use of domain general problem solving by novices leads to expertise with experience.  Hope this helps some, Alex. ~ Kevin

Three ways:

1. If you have a teacher, ask them how to do it, then combine their general description with the specifics of your problem.

2. If you have done something similar or the same before, remember how you did it then and transfer the knowledge.

3. The hard scenario. You need to figure it out on your own. Even if you can't do 2, you should still aim to squeeze every bit of prior knowledge from your experience. Then, do local search. If you can measure how close you are to your goal, use this as a heuristic to guide your search. If you get stuck, expand your search, explore and try new things to gain new knowledge, then revise your heuristic. This process can be formalized as reinforcement learning, which has already been mentioned. In the end you wind up with a model for evaluating the expected utility of any state and the expected utility of a transition to a new state, which can now be used to guide your actions in similar scenarios you may encounter in the future.

But its important to recognize that in real life we rarely have to figure things out from scratch.

What about we just solve a problem backwards?

You know, back to the goal step by step to the start point...

I think its work universally and eliminate the unnecessary steps.

Alex Noel Szabó : This is the way I taught myself to tie my shoelaces myself: I slowly undid the shoe my mom had tied up, memorized how I did that it and then reversed everything. (Some time I must put my method on YouTube. All I know is that my wife and daughters have forbidden me to teach their children my unique method.) :-(

Alex Noel Szabó : "In many cases, problem solving is considerably facilitated by knowing the solution in advance." ;-) (source unknown)

A counterexample: Start point: You have a box with active and passive electronic components (transistors etc.), complete with datasheets, and all necessary tools; you don't have Internet access nor any electronics "cookbooks" (so, copying a published circuit diagram isn't possible). Goal: You want to have an amplifier (built of the available components) for a certain bandwidth with high linearity and high signal/noise ratio.