# Tag Info

1 vote

### Enforcing Order in a Linear Programming Question

For simplicity, I will omit the $t$ index. You want to enforce $$x_1+x_2+x_3\ge d \implies x_4=0.$$ Equivalently, enforce the contrapositive $$x_4>0 \implies x_1+x_2+x_3< d.$$ Let $\epsilon$ be ...
• 32.8k

### My Professor couldn't complete the model for this optimization problem. how do i model this problem?

There are at least two approaches that can be used to model this. The more obvious one uses binary variables $x_{wsd}$ equal to 1 if and only if worker $w$ is scheduled in slot $s$ on day $d.$ Some of ...
• 39.6k

### Constrained optimization with heuristic algorithm in actual production

Besides the mentioned answer, there are many cases in which either a simple rule or an algorithm, or a heuristic can solve a practical problem in an efficient manner and still without defining any ...
• 8,960

### Constrained optimization with heuristic algorithm in actual production

For genetic algorithms, there is a variant called random key genetic algorithms (and a variant of that called biased random key genetic algorithms -- the bias part being a tweak to the evolutionary ...
• 39.6k
Accepted

### Modeling $-\ln(1 - w \cdot \sigma(x))$ as disciplined convex programming

It doesn't look particularly convex: https://www.desmos.com/calculator/v17plvovb8.
Accepted

### Is 0-1 knapsack problem still NP-Hard (1) with an equality constraint and (2) when all the weights in the constraint are equal to one?

The general case where not all weights are equal to one, is ${NP}$ hard, as the subset sum problem reduces to it with a constant objective function. If all weights $w_i$ are equal to one, the problem ...
• 6,647
Accepted

### Avoid double counting in objective function for a maintenance scheduling problem

You want to minimize $\sum_i \sum_t r_t \max_j x_{ijt}$. To linearize this objective, introduce binary decision variable $y_{it}$ to represent $\max_j x_{ijt}$, impose constraints $x_{ijt} \le y_{it}$...
• 32.8k
1 vote
Accepted

### choose constraint from IIS to build penalty function

I think that, when selecting constraints to relax (with penalties), you should look at the IIS from the perspective of the final decision maker. Which constraints do they think absolutely must be ...
• 39.6k

### Improve a heuristic to solve the MS-RCPSP

It is very hard problem and very limited number of papers can really help. Probably exact solvers using optional intervals are a way to go with a few thousands of tasks.
• 189
Accepted

### How is this function piece-wise linear?

For a linear function $g(a)$, the function $g(a)^+=\max(g(a),0)$ is piecewise linear (with two pieces). Also, finite combinations (weighted sums) of piecewise linear functions are piecewise linear. ...
• 32.8k
1 vote

### Improve a heuristic to solve the MS-RCPSP

Check this review. There are several papers referenced that could help you to find a good method to solve it. This is also a good paper to check.
One of the necessary conditions is $L_u = 0$. If you assume that $\mu(t) = 0$, it follows from $L_u = \mu_x(t) + \mu(t) = 0$ that $\mu_x(t) = 0$. Because $u(t)$ can take any value when $\mu_x(t) = 0$, ...