I'm making a term project, I need something like this
x,te,ts decision variables,
if x[m,i]+x[m,j]-1 > 0
then
either te[i]+d-ts[j]<=0 or te[j]+d-ts[i]<=0;
If this was only either or I can make it with big M method, or I can convert an if then to either or, but I have a nested situtiation
is it possible to express this in a linear programming model? Or maybe my decision variables are wrong.
Related
I am trying to write a compiler for a domain-specific language, targeting a stack-machine based VM that is NOT a JVM.
I have already generated a parser for my language, and can readily produce an AST which I can easily walk. I also have had no problem converting many of the statements of my language into the appropriate instructions for this VM, but am facing an obstacle when it comes to the matter of handling the generation of appropriate branching instructions when complex conditionals are encountered, especially when they are combined with (possibly nested) 'and'-like or 'or' like operations which should use short-circuiting branching as applicable.
I am not asking anyone to write this for me. I know that I have not begun to describe my problem in sufficient detail for that. What I am asking for is pointers to useful material that can get me past this hurdle I am facing. As I said, I am already past the point of converting about 90% of the statements in my language into applicable instructions, but it is the handling of conditionals and generating the appropriate flow control instructions that has got me stumped. Much of the info that I have been able to find so far on generating code from an AST only seems to deal with the generation of code corresponding to simple imperative-like statements, but the handing of conditionals and flow control appears to be much more scarce.
Other than the short-circuiting/lazy-evaluation mechanism for 'and' and 'or' like constructs that I have described, I am not concerned with handling any other optimizations.
Every conditional control flow can be modelled as a flow chart (or flow graph) in which the two branches of the conditional have different targets. Given that boolean operators short-circuit, they are control flow elements rather than simple expressions, and they need to be modelled as such.
One way to think about this is to rephrase boolean operators as instances of the ternary conditional operator. So, for example, A and B becomes A ? B : false and A or B becomes A ? true : B [Note 1]. Note that every control flow diagram has precisely two output points.
To combine boolean expressions, just substitute into the diagram. For example, here's A AND (B OR C)
You implement NOT by simply swapping the meaning of the two out-flows.
If the eventual use of the boolean expression is some kind of conditional, such as an if statement or a conditional loop, you can use the control flow as is. If the boolean expression is to be saved into a variable or otherwise used as a value, you need to fill in the two outflows with code to create the relevant constant, usually a true or false boolean constant, or (in C-like languages) a 1 or 0.
Notes:
Another way to write this equivalence is A and B ⇒ A ? B : A; A or B ⇒ A ? A : B, but that is less useful for a control flow view, and also clouds the fact that the intent is to only evaluate each expression once. This form (modified to reuse the initial computation of A) is commonly used in languages with multiple "falsey" values (like Python).
I would like to use Pyomo's PySP framework to do some stochastic optimization. In this model, I have some variables that must be the same across scenarios (i.e., the standard root node variables). As part of the Progressive Hedging approach, PySP creates an augmented Lagrangian, whose multipliers are adjusted iteratively until all these variables are equal across scenarios. All good so far. But I also have some constraints that must be enforced on an expected value basis. In the extensive form, these look like this:
sum(probability[s] * use[s] for s in scenarios) == resource
This complicating constraint could be factored out with a Lagrangian relaxation. This would require adding a term like this to the main objective function (which would then become part of each scenario's objective function):
(
lambda * (sum(probability[s] * use[s] for s in scenarios) - resource)
+ mu/2 * (sum(probability[s] * use[s] for s in scenarios) - resource)**2
)
This is very similar to the Lagrangian terms for the nonanticipativity constraints that are already in the main objective function. At each iteration, the PySP framework automatically updates the multipliers for the nonanticipativity terms and then propagates their values into the individual scenarios.
So my question is, is there some way to add my terms to the standard Lagrangian managed by PySP, and have it automatically update my multipliers along with its own? I don't mind doing some heavy lifting, but I can't find any detailed documentation on how PySP is implemented, so I'm not sure where to start.
The PH implementation in PySP supports some level of customization through the use of user-defined extensions. These are classes you can implement whose methods are called by PH at different points in the algorithm. You can tell PH to use an extension by setting the command-line option "--user-defined-extension" to a file that contains an implementation. A number of examples can be found here (look for files that contain IPHExtension and copy what they do).
Unfortunately, there is not any specific code that will make what you want to do easy. You will have to look at source code to see how PH updates and manages these objective parameters (see ph.py for this and to see where different extension methods are called in the algorithm).
Traditional if > then relationship in pseudo code:
if (x>y) {
then print "x is greater than y."
}
There are also relational databases.
Or just visual if>then tables. A visual table representation.
There are also tree or hierarchical structure if>then programming aids.
I'm looking for any and all alternatives and flavors of if>then constructs, but preferably practical ones. Since most humans are better at using and remembering visual constructs (tables vs raw code) than symbolic constructs, I'm looking for the most intuitive way to theoretically construct an if>then rule engine, graphically.
Note: I'm not trying to implement this, I'm just trying to get an idea of what could theoretically be done.
I hope I've interpreted the question correctly.
Everything eventually boils down to comparisons, its just a matter of breaking up these comparisons in manageable chunks for humans. There are many techniques to reduce if-thens, or at least transform them into something easier to understand.
One example would be polymorphism. This frees the programmer from one instance of if/then (basically a switch statement). Another example is maps. The implementation of a map uses if/thens, but one might pre-populate the map with all the data and use one logical piece of code instead of using if/then to differentiate. This moves to a data-driven approach. Another example is SQL; it is just a language, a higher level construct, that enables us to express conditions and constraints differently. How you choose to express these conditions is dependent on the problem domain. Some problems work well with traditional procedural programming, some with logic programming, declarative programming etc. If there are many levels of nested if-thens, a state machine approach might work well. Aspect-oriented programming tries to solve the problem of duplicated code in modules that doesn't belong specifically to any one module; a concern that "cross-cuts".
I would do some reading on Programming Paradigms. Do lots of research and if you run into a recurring problem, see if another approach allows you to reduce the amount of if-thens. Most times someone else has run into the same problem and come up with a solution.
Your question is a bit broad and we could ramble from logical gates to mathematical functions. I'm going to focus on this particular bit:
"I'm looking for the most intuitive way to theoretically construct an if>then rule engine, graphically".
First, two caveats:
The best representation depends on the number of possible rules. What works for 3-4 rules probably won't work for 30-40.
I'm going to pretend that else conditions don't exist.
If "X then Y" boils down to: one condition and one instruction whose execution depends on the condition. Let's pretend X -> Y means that "If X is true then Y is executed". Let's create two sets: one is C that contains all the possible conditions. The other one is I which contains all the possible instructions.
With this is mind, X ∈ C and Y ∈ I. In your specific case, can Y ∈ C (can Y be a condition)? If so, you have nested ifs.
Nested ifs can be represented as chains of conditions joined by and operators:
if (x > 3) {
if (y > 5) {
# do something
}
}
Can be written as:
if (x > 3 and y > 5) {
# do something
}
If you're only thinking about code then the latter can become problematic when you have many nested conditions, but when you go graphical, nesting (probably using tree-like structures) can look cluttered while chaining usually looks like a sequence of instructions (which I think is better).
If you don't consider nesting (chaining) in your rules, then connecting elements (boxes, circles, etc) from X -> Y is trivial way to work. The representation of this depends on how graphical you want to get (see the links below for some examples).
If you're considering nesting then three random ideas come to my mind:
Venn Diagrams: Visually attractive, useless for more than 3-4 conditions. They have a good fit with database representations. See: http://share.mheroin.com/image/3i3l1y0S2F39
Flowcharts: Highly functional and easy to read, not too cumbersome to create. Can get out of hand with 10+ elements. See: http://share.mheroin.com/image/2g071j3U1u29
Tables: As you mentioned, tables are a decent way to represent conditionals as long as you can restrain the set of applicable rules. This is an example taken from iTunes: http://share.mheroin.com/image/390y2G18123q. The "Match [all/any] of the following rules" works as a replacement for if/else.
I am considering the problem of validating real numbers of various formats, because this is very similar to a problem I am facing in design.
Real numbers may come in different combinations of formats, for example:
1. with/without sign at the front
2. with/without a decimal point (if no decimal point, then perhaps number of decimals can be agreed beforehand)
3. base 10 or base 16
We need to allow for each combination, so there are 2x2x2=8 combinations. You can see that the complexity increases exponentially with each new condition imposed.
In OO design, you would normally allocate a class for each number format (e.g. in this case, we have 8 classes), and each class would have a separate validation function. However, with each new condition, you have to double the number of classes required and it soon becomes a nightmare.
In procedural programming, you use 3 flags (i.e. has_sign, has_decimal_point and number_base) to identify the property of the real number you are validating. You have a single function for validation. In there, you would use the flags to control its behaviour.
// This is part of the validation function
if (has_sign)
check_sign();
for (int i = 0; i < len; i++)
{
if (has_decimal_point)
// Check if number[i] is '.' and do something if it is. If not, continue
if (number_base = BASE10)
// number[i] must be between 0-9
else if (number_base = BASE16)
// number[i] must be between 0-9, A-F
}
Again, the complexity soon gets out of hand as the function becomes cluttered with if statements and flags.
I am sure that you have come across design problems of this nature before - a number of independent differences which result in difference in behaviour. I would be very interested to hear how have you been able to implement a solution without making the code completely unmaintainable.
Would something like the bridge pattern have helped?
In OO design, you would normally
allocate a class for each number
format (e.g. in this case, we have 8
classes), and each class would have a
separate validation function.
No no no no no. At most, you'd have a type for representing Numeric Input (in case String doesn't make it); another one for Real Number (in most languages you'd pick a built-in type, but anyway); and a Parser class, which has the knowledge to take a Numeric Input and transform it into a Real Number.
To be more general, one difference of behaviour in and by itself doesn't automatically map to one class. It can just be a property inside a class. Most importantly, behaviours should be treated orthogonally.
If (imagining that you write your own parser) you may have a sign or not, a decimal point or not, and hex or not, you have three independent sources of complexity and it would be ok to find three pieces of code, somewhere, that treat one of these issues each; but it would not be ok to find, anywhere, 2^3 = 8 different pieces of code that treat the different combinations in an explicit way.
Imagine that add a new choice: suddenly, you remember that numbers might have an "e" (such as 2.34e10) and want to be able to support that. With the orthogonal strategy, you'll have one more independent source of complexity, the fourth one. With your strategy, the 8 cases would suddenly become 16! Clearly a no-no.
I don't know why you think that the OO solution would involve a class for each number pattern. My OO solution would be to use a regular expression class. And if I was being procedural, I would probably use the standard library strtod() function.
You're asking for a parser, use one:
http://www.pcre.org/
http://www.complang.org/ragel/
sscanf
boost::lexical_cast
and plenty of other alternatives...
Also: http://en.wikipedia.org/wiki/Parser_generator
Now how do I handle complexity for this kind of problems ? Well if I can, I reformulate.
In your case, using a parser generator (or regular expression) is using a DSL (Domain Specific Language), that is a language more suited to the problem you're dealing with.
Design pattern and OOP are useful, but definitely not the best solution to each and every problem.
Sorry but since i use vb, what i do is a base function then i combine a evaluator function
so ill fake code it out the way i have done it
function getrealnumber(number as int){ return getrealnumber(number.tostring) }
function getrealnumber(number as float){ return getrealnumber(number.tostring) }
function getrealnumber(number as double){ return getrealnumber(number.tostring) }
function getrealnumber(number as string){
if ishex(){ return evaluation()}
if issigned(){ return evaluation()}
if isdecimal(){ return evaluation()}
}
and so forth up to you to figure out how to do binary and octal
You don't kill a fly with a hammer.
I realy feel like using a Object-Oriented solution for your problem is an EXTREME overkill. Just because you can design Object-Oriented solution , doesn't mean you have to force such one to every problem you have.
From my experience , almost every time there is a difficulty in finding an OOD solution to a problem , It probably mean that OOD is not appropiate. OOD is just a tool , its not god itself. It should be used to solve large scale problems , and not problems such one you presented.
So to give you an actual answer (as someone mentioned above) : use regular expression , Every solution beyond that is just an overkill.
If you insist using an OOD solution.... Well , since all formats you presented are orthogonal to each other , I dont see any need to create a class for every possible combination. I would create a class for each format and pass my input through each , in that case the complexity will grow linearly.
We would like to have user defined formulas in our c++ program.
e.g. The value v = x + ( y - (z - 2)) / 2. Later in the program the user would define x,y and z -> the program should return the result of the calculation. Somewhen later the formula may get changed, so the next time the program should parse the formula and add the new values. Any ideas / hints how to do something like this ? So far I just came to the solution to write a parser to calculate these formulas - maybe any ideas about that ?
If it will be used frequently and if it will be extended in the future, I would almost recommend adding either Python or Lua into your code. Lua is a very lightweight scripting language which you can hook into and provide new functions, operators etc. If you want to do more robust and complicated things, use Python instead.
You can represent your formula as a tree of operations and sub-expressions. You may want to define types or constants for Operation types and Variables.
You can then easily enough write a method that recurses through the tree, applying the appropriate operations to whatever values you pass in.
Building your own parser for this should be a straight-forward operation:
) convert the equation from infix to postfix notation (a typical compsci assignment) (I'd use a stack)
) wait to get the values you want
) pop the stack of infix items, dropping the value for the variable in where needed
) display results
Using Spirit (for example) to parse (and the 'semantic actions' it provides to construct an expression tree that you can then manipulate, e.g., evaluate) seems like quite a simple solution. You can find a grammar for arithmetic expressions there for example, if needed... (it's quite simple to come up with your own).
Note: Spirit is very simple to learn, and quite adapted for such tasks.
There's generally two ways of doing it, with three possible implementations:
as you've touched on yourself, a library to evaluate formulas
compiling the formula into code
The second option here is usually done either by compiling something that can be loaded in as a kind of plugin, or it can be compiled into a separate program that is then invoked and produces the necessary output.
For C++ I would guess that a library for evaluation would probably exist somewhere so that's where I would start.
If you want to write your own, search for "formal automata" and/or "finite state machine grammar"
In general what you will do is parse the string, pushing characters on a stack as you go. Then start popping the characters off and perform tasks based on what is popped. It's easier to code if you force equations to reverse-polish notation.
To make your life easier, I think getting this kind of input is best done through a GUI where users are restricted in what they can type in.
If you plan on doing it from the command line (that is the impression I get from your post), then you should probably define a strict set of allowable inputs (e.g. only single letter variables, no whitespace, and only certain mathematical symbols: ()+-*/ etc.).
Then, you will need to:
Read in the input char array
Parse it in order to build up a list of variables and actions
Carry out those actions - in BOMDAS order
With ANTLR you can create a parser/compiler that will interpret the user input, then execute the calculations using the Visitor pattern. A good example is here, but it is in C#. You should be able to adapt it quickly to your needs and remain using C++ as your development platform.