**4. Concluding remarks**

156 Bio-Inspired Computational Algorithms and Their Applications

The algorithm was coded using Visual C++. Its execution time was about 25 minutes for one million generations running on a Pentium-4 processor with a, 2.1 GHz clock cycle. This architecture was complemented with 256 MB of physical memory and a 74.5-GB hard disk drive. The experimental results shown in Table 3 indicate a significant improvement in the

These results represent an average saving of 6.514 million dollars, equivalent to 13.02% of the total budget. This improvement has a positive impact on the number of supported projects, as Table 4 reveals. The average number of supported projects is 12.5 % higher than

1 1406.80 1533.95 9% 2 1282.36 1496.16 16.67% 3 1279.58 1458.48 14% 4 1393.58 1566.97 12.44%

1 237 267 12.76% 2 257 285 10.89% 3 265 299 12.83% 4 246 279 13.41%

The model described in Problem definition 2 can be generalized to incorporate temporal

**Problem definition 3**. An optimal portfolio of projects with temporal dependencies can be selected by maximizing U= Σik f(μik(dik)) wik, subject to (**d**, **t**)∈ R''F , where vector **t** =(t(p1), t(p2),…) denotes the decision variables valid during the period of time when each project starts. R''F contemplates time-precedence restrictions, restrictions on the time projects can

Value of the optimized portfolio

Number of supported projects in the optimized

portfolio

Improvement

Increment

value of the optimized portfolio with respect to conventional approaches.

when conventional methods were used.

Instance Value of the portfolio funding following

Table 3. Traditional Funding versus our Approach.

Instance Number of supported projects

**3.6 Modeling temporal dependencies** 

start, and the available funds for each time interval.

restrictions.

by project evaluations

the ranking given by project evaluations

funding following the ranking given

Table 4. Traditional Funding versus our Approach (portfolio's cardinality).

Given a set of premises, it is possible to create a value model for selecting optimal portfolios from an SDM perspective. While this problem is Turing-decidable, finding its exact solution requires exponential time. However, the use of genetic algorithms for solving this problem can closely approximate the optimal portfolio selection.

Inspired by a normative approach, the set of premises presented here is based on the following assumptions.


As for the algorithmic solution to the portfolio problem, its computational complexity can increase considerably when synergic effects and temporal dependencies are considered. However strategic planning requires a high quality model. The problems defined in this scenario are so important that they justify the use of computational intensive solutions.
