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# Questions tagged [optimization]

general questions about selecting a best element from some set of available alternatives.

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### computing the minimal NFA for a DFA

Many years ago I heard that computing the minimal NFA (nondeterministic finite automaton) from a DFA (deterministic) was an open question, as opposed to the vice versa direction which has been known ...
881 views

### What classes of mathematical programs can be solved exactly or approximately, in polynomial time?

I am rather confused by the continuous optimization literature and TCS literature about which types of (continuous) mathematical programs (MPs) can be solved efficiently, and which cannot. The ...
789 views

### Generating interesting combinatorial optimization problems

I'm teaching a course on meta-heuristics and need to generate interesting instances of classic combinatorial problems for the term project. Let's focus on TSP. We are tackling graphs of dimension $200$...
212 views

### Iteratively minimizing the function

Consider the problem $$\min_{x\in X, y \in Y} f(x,y)$$ Can I solve the problem by iteratively solving the following two sub problems? x_{k+1} = \arg\...
201 views

### minimal finite automata given in-words and out-words

this seems an interesting FSM optimization problem; have not seen it studied, wondering if it has been and/ or looking for other insight. given: two finite sets of words $S_{in}$ and $S_{out}$. ...
899 views

### Optimization problems with good characterization, but no polynomial-time algorithm

Consider optimization problems of the following form. Let $f(x)$ be a polynomial-time computable function that maps a string $x$ into a rational number. The optimization problem is this: what is the ...
2k views

### Finding the two shortest paths while minimizing the number of nearby/common edges

The shortest path problem between 2 arbitrary nodes is one that has been covered extensively and the solution is well-known. Consider the edge costs to be arbitrary. Consider the following variant: ...
89 views

### Showing hardness of maximizing stochastic objective function over graph

Consider a graph $G = (V, E)$ with $n$ vertices and $m$ edges. Each vertex $v_i$ can take positive value $a_i$ with probability $p_i$ and value $0$ with probability $1-p_i$. The challenge is to ...
655 views

### To what extent is it possible to use genetic algorithms to make wind mill turbine blades more efficient?

I recently watched this video on youtube. It featured someone explaining how he used genetic algorithms to improve the efficiency of wind mill turbines by finding the optimal shape for the blades. ...
2k views

### A simple approximation algorithm for the TSP

Consider the following extremely simple approximation algorithm for the TSP. Input: A complete weighted graph $G=(V,E).$ Take any three vertices $a,b,c\in V$ and let $H:=(a,b,c,a).$ While there ...
581 views

311 views

### Modifying Edmonds' Blossom Algorithm

Given a connected road network on an Island without one-way streets, where should I para-shoot in and what route should I take to deliver mail to all houses on the island (being picked up again by ...
2k views

### Why does the Fibonacci sequence produce a worst-case Huffman encoding?

I noticed this in my Algorithms class, but just now got around to asking.
474 views