Requirements prioritisation is a key decision making activity of the software development process, which relies on the capability of di erent decision-makers to identify the optimal candidate rankings of the requirements, in order to be able to perform a strategic choice among them. In this paper, we formulate such multi-decision-maker requirements prioritisation as a multi-objective optimisation problem, and outline a solution that takes advantage of metaheuristic algorithms. The proposed solution allows di erent decision-makers to specify their rankings according to a set of prioritisation criteria, it then synthesises them into a set of Pareto optimal global rankings. The ultimate choice of the prioritisation of the requirements would be made upon a focused analysis of the trade-o s amongst the solutions on the Pareto frontier.
Requirements prioritisation is an important decision-making activity in the
software development process that comes into the scene when the needs and desires
of customers must meet the delivery capacity of the development team [
Practitioners mostly carry out the requirements prioritisation activity with
traditional approaches, such as focus groups. Several approaches have also been
proposed to guide practitioners perform requirements prioritisation in a
structured way [
We observed examples of this situation in two small-medium companies in
the context of the SUPERSEDE 3 project, a project focusing on feedback-driven
adaptation and evolution of software systems. The rst company is SEnerCon, a
German company working in the domain of energy e ciency management,
providing online applications in support of household energy saving. SEnerCon
reports that when major innovation of their products need to be planned, di erent
actors are relevant in prioritising the candidate requirements that might include
the new ones that have been identi ed along the funding opportunities [
The second company is Delta, an Italian company working in serious gaming
for professional training. As part of an industrial project, called PRESTO [
In such situations, each actor involved in the prioritisation process has his/her own view regarding the priorities of the requirements, depending on their expertise and goals. Furthermore, these views of the various actors are typically of con icting nature. For instance, developers may tend to give higher priorities to requirements that could be implemented with less e ort, while experts from management may give higher priorities to requirements that would bring higher customer satisfaction (even if they incur higher development e ort). Hence, the problem then becomes how to reconcile these individual views on the priorities into a nal prioritisation of the requirements. We refer to the human actors involved in such a process, by providing their own preferences regarding the prioritisation of the requirements, as decision-makers (DMs); and we refer to the problem as a Multi-decision-maker Requirements Prioritisation problem.
In this paper, we formulate the Multi-decision-maker Requirements Prioritisation problem as a multi-objective optimisation problem, and propose an approach that uses Evolutionary Algorithms (EA) to nd optimal solutions to it. Given a set of rankings for the candidate requirements, which are made by different experts along multiple criteria, the proposed method allows to synthesise global requirements prioritisations located on a Pareto optimal frontier, thus 3 www.supersede.eu supporting the decision-maker by providing him/her with a view on alternative optimal requirements prioritisations.
The main contributions of this paper include: (i ) a generic formulation of the Multi-decision-maker Requirements Prioritisation problem; (ii ) an approach based on multi-objective optimisation for nding optimal solutions to this problem.
The rest of this paper is organised as follows: in Section 2, the formulation of the problem is given. The proposed approach for Multi-decision-maker Requirements Prioritisation is outlined in Section 3. The related works are discussed in 4. Finally, conclusions are presented in Section 5. 2
In a generic requirements prioritisation process, multiple decision-makers involved in a software project express independently their own priority list. Each decision-maker has a relative weight with respect to the other decision-makers, depending on aspects such as his/her role, expertise and so on. Moreover, any number of evaluation criteria, each with its own weight with respect to the expected nal decision, can be used to perform the prioritisation. These criteria could represent positive (values) or negative (costs) evaluations about a given prioritisation of requirements, what is important here is that decision-makers are not obliged to summarise their positive (or negative) considerations along one single criterion. Furthermore, the requirements to be prioritised have their own characteristics, which must be taken into consideration when deciding on the nal ranking, such as dependencies among requirements.
The Multi-decision-maker Requirements Prioritisation problem consists of nding the best ranking that takes into account all the individual rankings of the various decision-makers. Reaching consensus regarding the nal ranking of the requirements out of the individual rankings, given by the decision-makers, involves: (i) identifying the alternative global rankings that can be drawn from the decision-makers' opinions; and (ii) selecting the nal ranking, through a decision process that takes into account additional contextual and strategic information. While the nal decision remains a strategic action, the Multi-decision-maker Requirements Prioritisation problem concerns supporting the identi cation of the optimal rankings.
In summary, given: { a set of n decision-makers who providing their prioritisations; { a set of m requirements to be prioritised (not necessarily independent); { a set of dependencies where (Ri ! Rj ) implies that requirement Ri depends on requirement Rj ; { a set of k criteria along which the prioritisation is to be performed; { weights corresponding to each criterion; { weights corresponding to each decision-maker for each criterion; { the prioritisations of each decision-maker with respect to each criterion; the Multi-decision-maker Requirements Prioritisation problem consists of nding the nal prioritisation (ranking) of requirements with the minimum possible distance from the individual prioritisations (rankings) of all decision-makers, while respecting the constraints imposed by the dependencies. Distance represents a quanti cation of the dissimilarity between rankings. 3
The problem formulation presented in the previous section evidences the
inherent multi-objective nature of the problem. In fact, the optimal solution to
the problem involves trade-o s in di erent directions, in particular among the
prioritisation criteria and among the preferences of the various decision-makers
involved. Our proposed approach is based on the notion of minimising the
dissimilarity among the preferences of the various decision-makers involved in the
process. Given the preferences of each decision-maker with respect to each
criterion, we try to nd the prioritisation that is at the least possible level of
dissimilarity from all the prioritisations of all decision-makers | the middle
ground. In general, given a set of m requirements, there are m! possible
prioritisation of these requirements. Hence, our approach employs multi-objective
optimisation to explore this space of m! candidate solutions with the objective of
nding those with the minimum levels of dissimilarity from those of the
decisionmakers. Considering the potentially large number of alternatives, our proposed
approach is based on Evolutionary Algorithms (EAs) [
EAs are a class of metaheuristic search algorithms inspired by the process
of natural evolution in which a population of candidate solutions (individuals )
interact with each other and evolve through generations following the principle
of survival of the ttest [
The right side of Figure 1 depicts a simpli ed overview of the main aspects of a typical EA, which starts by creating an initial population of individuals. It then evaluates each individual in the population by means of a tness function and assigns it a tness value. The EA then proceeds by selecting ` tter' individuals (parents ) from the current population and subjects them to the process of reproduction or crossover resulting in o spring. The o spring could further be subjected to a process of mutation with the aim of introducing diversity into the population. The EA then selects, from the combined pool of parents and o spring, the individuals that form the new population in the next generation (survivors). This process continues to iterate until some stopping condition is reached, in which case the EA terminates. Requirements R1, R2, R3, …, Rm
Evolutionary Algorithm
Input Dependencies R1 → R2 …
R4 → R3 Prioritisations by DMs [DM1][C1] R4 R2 R1 … ... [DM1][Ck] R2 R4 R3 ... … [DMn][C1] R2 R3 R1 … ... [DMn][Ck] R3 R4 R2 ...
DM Weights [DM1][C1] w1 [DM1][C2] w2 … [DMn][Ck] wz
Criteria + Weights [C1] cw1 [C2] cw2 … [Ck] cwk
Start Initialise Evaluate
Selection Reproduction
Mutation
Stop
S1= R2 R3 R1 ...
...
Sn= R3 R2 R4 ... dist(S1) = d1
... dist(Sn) = dn Select solutions with small distances
Given the formulation of the multi-decision-maker requirements prioritisation problem outlined in Section 2, an instance of an EA could be applied to search within the space of all possible prioritisations, with the ultimate goal of nding one or more prioritisation(s) with minimal dissimilarity from all of the given rankings. To this end, we need to appropriately de ne the corresponding EA operations in such a way that we are able to nd optimal solutions to our problem. Speci cally, we need to de ne (1) the encoding and initialisation of individuals, (2) the tness function for evaluating individuals with respect to the problem, and (3) the selection, crossover, and mutation operators that allow the EA to evolve the individuals through generations.
Solution encoding and initialisation: Given m requirements to be prioritised, candidate solutions (individuals) are prioritisations (rankings) of these requirements. Hence, we encode an individual as: (r1; r2; : : : ; rm) where ri represents the rank of requirement i. For example, if m = 5, an individual could be: (1,3,2,5,4). In this individual, the rank of requirement 1 is 1, the rank of requirement 2 is 3, the rank of requirement 3 is 2, etc.
Fitness function: The goal of the tness function is to objectively measure how good ( t) an individual is with respect to the problem being solved. For our problem, a good individual is one that has the lowest level of dissimilarity (disagreement) among the prioritisations of the decision-makers. Hence, we rst quantify the level of dissimilarity between two rankings by means of a distance (b) Swap Mutation (a) Two Point Crossover function. Given two individuals I1 and I2 representing two rankings of m requirements, the distance between them could be computed in a number of ways. For instance, we can de ne a distance metric based on the (average) di erences between the ranks of the requirements:
m d(I1; I2) = X jI1[i] I2[i]j i=1 (1)
Similarly, other rank similarity metrics, such as Kendall's
be used to de ne a distance function:
statistic [
KendallTau(I1; I2) (2) Based on the distance functions given in Equations 1 and 2, we de ne tness functions for computing the tness of an individual I in the EA. Speci cally, we consider a multi-objective perspective in which we compute the distance of I with respect to more than one objective. For our problem formulation, we de ne a tness function considering the distance of I from each criterion.
The EA searches for individual(s) with the minimum values for the tness functions, i.e., solutions that represent minimal dissimilarity among the rankings of the various decision-makers.
EA operators: Here we describe the two most important operators, crossover and mutation, that enable the EA to evolve individuals through generations. Two point crossover in each individual's (parent ) encoding, two points are randomly picked, and parts of the individual's encoding are exchanged. Figure 2a illustrates this crossover operation. In case the crossover operator results in invalid individuals (e.g., duplicated ranks), the individual will either be corrected in a subsequent phase, or the operation will be cancelled and performed again choosing di erent points of crossover.
Swap mutation two points are randomly picked in the individual's encoding, and the values indicated by the selected points (indices) are swapped. Figure 2b illustrates this mutation operation.
Algorithm: Given the problem formulation, the encoding of individuals, and
the operators de ned above, our approach employs a multi-objective EA (e.g.,
NSGA-II [
In summary, the approach will search for optimal prioritisations that minimise dissimilarity (disagreement) among the various DMs involved in process, nding the middle ground. 4
Requirements prioritisation is an area of requirements engineering which has
received a signi cant amount of attention both from the research community
and industry [
We presented a multi-objective formulation of the multi-decision-maker requirements prioritisation problem, and outlined a solution based on Evolutionary Algorithms. The proposed approach is based on the notion of nding Pareto optimal prioritisations that exhibit the minimum levels of disagreement among the various decision-makers involved in the process. The ultimate decision-maker selects one of the optimal solutions based on additional interests (e.g., strategic) not necessarily included in the prioritisation criteria. The work is currently ongoing and we are working towards an empirical evaluation of the proposed approach on real world case studies derived from the industry.
Acknowledgement. This work is a result of the SUPERSEDE project, funded by the H2020 EU Framework Programme under agreement number 644018.