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Algorithm Design & Implementation

[Do NOT respond to this bid if you think this is can be trivially solved as a vector dot product]

Design and implement an algorithm using linear multiobjective programming that solves the following problem:

1. There are N items whose ordering is given by the ordinal weights vector (OWV). For example, if there are 4 items, the OWV [1 4 2 3] gives their ordering.

2. A regime vector (RV) is an ordered set of N numbers from the set {-1, 0, 1}. For example, [+1 -1 -1 +1] is a RV of size 4.

3. Each OWV can have multiple cardinal weights vector (CWV) corresponding to the same ordering. For example, if OWV is [1 2 3 4] then [0.40 0.35 0.20 0.05], [0.45 0.30 0.15 0.10], etc.. can be the corresponding CWV. It is to be noted that the sum of numbers in CWV must be equal to 1. Formally, CWV (cardinal weights vector) is a set of N numbers when they add up to 1 and they are ordered in the ordering specified in OWV.

4. The 'score' of a RV for the given OWV is equal to the probability that RV x CWV > 0. For example: OWV = [1 2 3 4] and RV = [+1 -1 -1 +1]. If CWV = [0.40 0.35 0.20 0.05], then RV x CWV < 0. But if CWV = [0.45 0.30 0.15 0.10], then RV x CWV > 0. For the given OWV, the probability that RV x CWV > 0 (over continuous values of CWV) gives the 'score' of RV.

Write a computer program that takes the OWV and a RV and outputs the score of that RV using linear multiobjective programming which gives accurate results and performs well. The solution should NOT be based on brute force or approximation heuristics (such as Monte carlo method).

In your bid response, please provide some description demonstrating that you understand the problem and understand how to solve it using multiobjective programming. Again, please do not propose an approximate solution.

For more background, please review the attached article. See also

[url removed, login to view]

for a relevant discussion of linear multiobjective programming

An html version of this problem (with any updates) can be found at

[url removed, login to view]

The program can be written in any programming language (C, C++, Java, Python et al.) BUT because its production version will be implemented as part of a larger JavaScript project, it canNOT be written in Matlab or otherwise rely upon sophisticated math libraries.

Delivery timeframe & compensation are negotiable

Skills: C Programming, Engineering, Java, Javascript, Python

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Project ID: #216405

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