Efficient anytime algorithms to solve the bi-objective Next Release Problem

TL;DR

This paper tackles the bi-objective Next Release Problem by introducing five anytime, exact ILP-based algorithms that maintain a well-spread Pareto front during search. Unlike traditional lexicographic or single-solution methods, these approaches produce both supported and non-supported efficient solutions and can yield the full Pareto front given sufficient time. Extensive experiments on standard NRP benchmarks show that the proposed anytime methods rapidly achieve high hypervolume and diverse fronts, outperforming classic exact methods in short runtimes and surpassing metaheuristics in providing guaranteed efficient solutions. The work demonstrates clear practical value for requirement engineering by enabling fast, interactive exploration of trade-offs under uncertainty and time constraints.

Abstract

The Next Release Problem consists in selecting a subset of requirements to develop in the next release of a software product. The selection should be done in a way that maximizes the satisfaction of the stakeholders while the development cost is minimized and the constraints of the requirements are fulfilled. Recent works have solved the problem using exact methods based on Integer Linear Programming. In practice, there is no need to compute all the efficient solutions of the problem; a well-spread set in the objective space is more convenient for the decision maker. The exact methods used in the past to find the complete Pareto front explore the objective space in a lexicographic order or use a weighted sum of the objectives to solve a single-objective problem, finding only supported solutions. In this work, we propose five new methods that maintain a well-spread set of solutions at any time during the search, so that the decision maker can stop the algorithm when a large enough set of solutions is found. The methods are called anytime due to this feature. They find both supported and non-supported solutions, and can complete the whole Pareto front if the time provided is long enough.

Figures (14)

• Figure 1: $z^{1}$ and $z^{2}$ form a box. The points $z^{3}$ and $z^{5}$ lies in the convex part of the box, and the point $z^{4}$ lies in the concave part of the box.
• Figure 2: For the EHybrid method, we analyze a box with two non-dominated points as opposite corners in the current iteration. The vector L is selected to look for new non-dominated points inside the box.
• Figure 3: Example of level curve for the Tchebycheff method.
• Figure 4: AnyAugmecon $(1, \lambda)$
• Figure 5: AnyAugmecon $(2, \lambda)$

Theorems & Definitions (7)

• Definition 3.1
• Definition 3.2
• Definition 3.3
• Definition 3.4
• Definition 3.5
• Definition 3.6
• Definition 4.1