optimization – Weighted activity selection problem to change the start time

I have some activities with weights and I would like to select activities that do not overlap by maximizing the total weight. This is a known problem and the solution exists.

In my case, I am allowed to shift the start time of activities while the duration remains the same. This will give me some flexibility and I could increase my use.

Scenario example is something like the following where all activities are supposed to be in the interval (0-200):

(start, end, profit)
a1: 10 12 120
a2: 10 13 100
a3: 14 18 150
a4: 14 20 100
a5: 120 130 100
a6: 126 132 150

Without changing flexibility, I would choose (a1, a3, a6) and that's all. By cons I have changing flexibility left / right by at most t units for any task where t is given. In this case, I could suggest this schedule and all tasks can be selected.

t: 5

a1: 8 10 120 (shifted -2 to left)
a2: 10 13 100
a3: 14 18 150
a4: 18 23 100 (shifted +4 to right)
a5: 115 125 100 (shifted -5 to left)
a6: 126 132 150

In my problem, I have enough room for each activity in the time domain. There are overlapping groups of activities and a very large empty space where there are no activities and there is another group of overlapping activities, that is, a1, a2, a3 and a4 are cluster1 and a5 and a6 are cluster2. Each group can be expanded in time by moving some of them to the left and the right. By doing this, I can select more activities than the original activity selection problem. However, I do not know how to decide which tasks to move left or right.

Is there a workable solution to this problem?

What are off-page optimization techniques?

Hello friends,

What are off-page optimization techniques?

optimization – How to better collect and synchronize data between a mobile application and a Web REST API?

I am confronted with the following scenario:

We have a mostly offline mobile application that is used to record and store medical records of places where there is little or no connectivity. These records are recently synchronized with a given web server, which implements a REST API. The case is that it generates many requests from all the mobile agents that synchronize the data to the API endpoints, such as many POST / medical-records requests. In some cases, we make a request by registration, on others, we put them in batches and send pieces.

What interests me currently, is to know if there is a better known approach to reduce the number of requests and data transferred between the server and the mobile application in similar scenarios or the like.

Optimization of the game

Using the pooling of objects, assuming I like to create 500 cubes every three seconds, how can I improve performance? I need ideas, not code itself.

convex optimization – find a PSD matrix that checks the sum of equality matrices

$ A $, $ C $ (n, n)$ ; are ; symmetric ; PSD ; matrices,
B $ ; is ; Symmetrical PD ; matrix and $ $ H_i $ $ ; $$ (i = (1, m))
$$ represents $
m $ complex matrices

Our goal is to find the PSD X matrix allowing:

$ A sum limits_ {i = 1} ^ {m – 1} {{H_i} (B + X) {H_i} + A (X + B) + {H_m} (B + X) = C} $

Can we pose an optimization problem as a problem of machine learning?

There seems to be a growing tendency to pose issues pertaining to the theory of classical optimization as problems with machine learning.

Can you explain when one would resort to machine learning instead of optimization? Is there a trade-off between precision and speed? Also, how to choose to use ML or optimization for a given problem? Is there an advantage to choosing one over the other?

optimization – Min Spanning Tree LP with point of origin

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optimization – dynamic programming algorithm with O (n) performance that will give the optimal solution

I am currently learning the dynamic substructure and the optimal solution for parts transformation. One of my teacher's questions is to describe a global O (n) dynamic programming algorithm that will give the optimal solution and why is it O (n)? Can someone help me understand the question? Thank you!

optimization – Break down the contributions of the multiplier into contributions from the adder

I found this formula on the mathematical override but I can not find the message anymore. I was wondering where the formula came from. All I remember is that it's an optimal solution to an optimization problem.

Suppose that M = m1 * m2 * m3 * … mN

We want the numbers a1, a2, a3 …, aN so that (1.0 + a1 + a2 + a3 + … + aN) = M

Set ai = M – M / mi – Sum (M-M / mi) / N

For example, say M = 0.5 * 2.0
N = 2, sum (MM / mi) = (1.0-1.0 / 0.5) + (1.0-1.0 / 2.0) = (-1) + (0.5) = -0.5

Then a1 = 1.0 – 1.0 / 0.5 – (-0.5 / 2) = 1.0-2.0 + 0.25 = -0.75
a2 = 1.0 – 1.0 / 2.0 – (-0.5 / 2) = 1.0-0.5 + 0.25 = 0.75

So 1.0 + a1 + a2 = 1.0

In one way or another, the choices of AI minimize the difference, of something.

I was wondering if anyone had an idea of ​​what it might be to minimize. Obviously, many staffing choices would be appropriate, but this formula offers a special solution.

Social media optimization

According to you, this is the most important platform for SMO.