Good question! Basically you give this calculate_optimal_portfolio method a set of assets, an objective, and a set of constraints. It then calculates the 'best' weights of those assets while meeting all the constraints. What does 'best' mean? There are currently two objectives - TargetWeights and MaximizeAlpha. The best weights when using the TargetWeights objective is the set of weights closest to the weights one inputs with the objective. The best weights when using the MaximizeAlpha objective is the set of weights which maximizes the total alpha using the individual alphas inputed with the objective. Using these methods can greatly reduce the code and complexity in ones logic. This is especially true if one wants to balance a lot of stocks based upon sector, long/short exposure, etc. Look at the documentation for a pretty good overview (https://www.quantopian.com/docs/user-guide/tools/optimize).

I personally feel the calculate_optimal_portfolio is under-appreciated. One can think of this method as the optimization and calculation portion of the order_optimal_portfolio method. It basically does everything the order method does EXCEPT the actual ordering. Instead of returning a series of orders it returns a series of weights.

The order_optimal_portfolio method doesn't work in the research environment. To do notebook analysis using optimize one must use the calculate_optimal_portfoliomethod. In the IDE, the returned series of weights is in the same format which the order_optimal_portfoliomethod expects. So, one can do something like this

    weights = opt.calculate_optimal_portfolio(objective=my_objective,   constraints=my_constraints)  
    algo.order_optimal_portfolio(objective=opt.TargetWeights(weights),  constraints=[] )

Why would one want to calculate the weights simply to feed them into the order_optimal_portfolio method? In a word, visibility. I find it helpful to sometimes record the net leverage which the ordering method is targeting or possibly the total target positions. Like this

    record(leverage=weights.abs().sum())  
    record(stocks=weights.where(weights!=0).size)

Additionally, one could do some final tweaking to the weights before passing it to the order_optimal_portfolio method. Maybe ensure leverage is 1.

    weights = opt.calculate_optimal_portfolio(objective=my_objective,   constraints=my_constraints)  
    weights = weights / weights.abs().sum()  
    algo.order_optimal_portfolio(objective=opt.TargetWeights(weights),  constraints=[] )

Hope that helps?

sir sounds quite confusing for me if u could explain with trading example it would be great of you sir .suppose for example, I am building a long-short equity strategy simply buying the stocks wich are top 10 gainers in the past month and shorting the stocks which are in top 10 losers and say order amount will be 5000$ this amount will be divided equally for long and short stocks and to place my order I have used order_optimal _portfolio so now can u tell what will order optimal portfolio will do how will it decide in which quantity to buy wich share as it as to place total order of 2500$ for long stock and 2500$ for short stocks ?

sir on what criterion the optimization of weight is done is it giving more weight to stocks wich have shown higher return I mean what is the decision making done on like for efficient frontier we select the portfolio weights which has given the maximum returns for a specific risk according to that we weight the stocks but in order optimal portfolio I am still not getting on what basis is it is selecting weights?