## Constraint satisfaction in a resource allocation problem optimized using evolutionary algorithms

I am working on an allocation problem where a resource $$R$$ needs to be allocated to $$n$$ users each with demand $$d_i$$. The problem has two objectives: objective 1 – maximize user utility given by $$f_1(e_i)=log(1+e_i/d_i)$$ and objective 2 – minimize $$f_2(e_i) = {e_i}^2/c_i$$ where $$e_i$$ is the allocation to the $$ith$$ user $$d_i$$ and $$c_i$$ are constants. The problem has two constraints i.e., $$e_i \le d_i$$ (allocation is ≤ demand) and $$\sum_i^{n} e_i = R$$ (sum of all allocations equals total available resource). I am using an evolutionary algorithm for this problem. But, after the evolution is complete, the algorithm leaves unallocated resource while there is still unmet user demand. I am curious if it is an expected outcome or it is due to some algorithmic or implementation flaw. I would appreciate any guidance

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## Is there an algorithm that provides the highest possible “sum of satisfaction” for a priority based distribution problem?

Let’s say we have n (e.g. 6) children and a box of candy. The box has k (e.g. 8) different flavours, and m (e.g. 4) piece of candy in each flavour. This question is specifically about the cases where k > n and n > m.

We can assume a maximum of a 1 piece of a flavour per person.

We ask them to make a list of the flavours from most liked to least liked, so we know the preferences of each child.

We of course want the “sum of satisfaction” to be the highest possible.

Is there an algorithm that is able to give the perfect distribution, or one that’s quite close?

## How can be measured the performance of CSPs(Constraint Satisfaction Problems) algorithms?

Measuring with the time complexity is the best way to measure with CSPs algorithms or not?Which way suits the best to measure CSPs algorithms?

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