I've got a collection of products with varying costs and features. Each product offers a unique set of features.
I'm in need of an algorithm that, when given the specific features I desire, can recommend the most cost-effective combination of products to purchase in order to obtain all those desired features
Any suggestions on how to tackle this problem? Preferably in JavaScript?
Exploring the realm of optimization, we come across the intriguing set cover problem. When facing instances that resist brute force solutions, employing an integer program solver emerges as a surprisingly effective approach. Consider SimplexJS by Iain Dunning, a JavaScript-based solver (available at SimplexJS). While it lacks certain advanced features like presolver or cutting planes, its fundamental utility remains intact.
The abstract concept presented in the Wikipedia link leads us to a practical scenario involving products A, B, C, and D; each associated with specific feature sets and prices:
A: {1, 2, 3}, 9.99
B: {2, 4}, 7.99
C: {3, 4}, 6.99
D: {4, 5}, 8.99
Introducing binary variables xA, xB, xC, xD for individual products, where they signify purchase decision (1) or non-purchase (0). The primary goal is represented as:
minimize 9.99 xA + 7.99 xB + 6.99 xC + 8.99 xD
Each feature imposes a constraint mandating the inclusion of a product possessing that feature:
1: xA >= 1
2: xA + xB >= 1
3: xA + xC >= 1
4: xB + xC + xD >= 1
5: xD >= 1
Utilizing a suitable library simplifies the process, requiring a translation of the instance into a structured program similar to this model for solver execution.
In scenarios necessitating custom library development, familiarity with concepts like branch and bound along with the simplex method becomes imperative. Optimal resolution demands a depth-first search coupled with best-first backtracking. Crafting a tailored solution entails meticulous coding spanning several hundred lines.
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