Nadarajen Veerapen

An Integer Linear Programming approach to the single and bi-objective Next Release Problem

ContextThe Next Release Problem involves determining the set of requirements to implement in the next release of a software project. When the problem was first formulated in 2001, Integer Linear Programming, an exact method, was found to be impractical because of large execution times. Since then, the problem has mainly been addressed by employing metaheuristic techniques. ObjectiveIn this paper, we investigate if the single-objective and bi-objective Next Release Problem can be solved exactly and how to better approximate the results when exact resolution is costly. MethodsWe revisit Integer Linear Programming for the single-objective version of the problem. In addition, we integrate it within the Epsilon-constraint method to address the bi-objective problem. We also investigate how the Pareto front of the bi-objective problem can be approximated through an anytime deterministic Integer Linear Programming-based algorithm when results are required within strict runtime constraints. Comparisons are carried out against NSGA-II. Experiments are performed on a combination of synthetic and real-world datasets. FindingsWe show that a modern Integer Linear Programming solver is now a viable method for this problem. Large single objective instances and small bi-objective instances can be solved exactly very quickly. On large bi-objective instances, execution times can be significant when calculating the complete Pareto front. However, good approximations can be found effectively. ConclusionThis study suggests that (1) approximation algorithms can be discarded in favor of the exact method for the single-objective instances and small bi-objective instances, (2) the Integer Linear Programming-based approximate algorithm outperforms the NSGA-II genetic approach on large bi-objective instances, and (3) the run times for both methods are low enough to be used in real-world situations.

Deconstructing the Big Valley Search Space Hypothesis

The big valley hypothesis suggests that, in combinatorial optimisation, local optima of good quality are clustered and surround the global optimum. We show here that the idea of a single valley does not always hold. Instead the big valley seems to de-construct into several valleys, also called ‘funnels’ in theoretical chemistry. We use the local optima networks model and propose an effective procedure for extracting the network data. We conduct a detailed study on four selected TSP instances of moderate size and observe that the big valley decomposes into a number of sub-valleys of different sizes and fitness distributions. Sometimes the global optimum is located in the largest valley, which suggests an easy to search landscape, but this is not generally the case. The global optimum might be located in a small valley, which offers a clear and visual explanation of the increased search difficulty in these cases. Our study opens up new possibilities for analysing and visualising combinatorial landscapes as complex networks.

Object-Oriented Genetic Improvement for Improved Energy Consumption in Google Guava

In this work we use metaheuristic search to improve Google’s Guava library, finding a semantically equivalent version of com.google.common.collect.ImmutableMultimap with reduced energy consumption. Semantics-preserving transformations are found in the source code, using the principle of subtype polymorphism. We introduce a new tool, Opacitor, to deterministically measure the energy consumption, and find that a statistically significant reduction to Guava’s energy consumption is possible. We corroborate these results using Jalen, and evaluate the performance of the metaheuristic search compared to an exhaustive search—finding that the same result is achieved while requiring almost 200 times fewer fitness evaluations. Finally, we compare the metaheuristic search to an independent exhaustive search at each variation point, finding that the metaheuristic has superior performance.

Visualising the Search Landscape of the Triangle Program

High order mutation analysis of a software engineering benchmark, including schema and local optima networks, suggests program improvements may not be as hard to find as is often assumed. (1) Bit-wise genetic building blocks are not deceptive and can lead to all global optima. (2) There are many neutral networks, plateaux and local optima, nevertheless in most cases near the human written C source code there are hill climbing routes including neutral moves to solutions.

Mapping the global structure of TSP fitness landscapes

The global structure of combinatorial landscapes is not fully understood, yet it is known to impact the performance of heuristic search methods. We use a so-called local optima network model to characterise and visualise the global structure of travelling salesperson fitness landscapes of different classes, including random and structured real-world instances of realistic size. Our study brings rigour to the characterisation of so-called funnels, and proposes an intensive and effective sampling procedure for extracting the networks. We propose enhanced visualisation techniques, including 3D plots and the incorporation of colour, sizes and widths, to reflect relevant aspects of the search process. This brings an almost tangible new perspective to the landscape and funnel metaphors. Our results reveal a much richer global structure than the suggestion of a ‘big-valley’ structure. Most landscapes of the tested instances have multiple valleys or funnels; and the number, disposition and interaction of these funnels seem to relate to search difficulty on the studied landscapes. We also find that the structured TSP instances feature high levels of neutrality, an observation not previously reported in the literature. We then propose ways of analysing and visualising these neutral landscapes.

Understanding Phase Transitions with Local Optima Networks: Number Partitioning as a Case Study

Phase transitions play an important role in understanding search difficulty in combinatorial optimisation. However, previous attempts have not revealed a clear link between fitness landscape properties and the phase transition. We explore whether the global landscape structure of the number partitioning problem changes with the phase transition. Using the local optima network model, we analyse a number of instances before, during, and after the phase transition. We compute relevant network and neutrality metrics; and importantly, identify and visualise the funnel structure with an approach (monotonic sequences) inspired by theoretical chemistry. While most metrics remain oblivious to the phase transition, our results reveal that the funnel structure clearly changes. Easy instances feature a single or a small number of dominant funnels leading to global optima; hard instances have a large number of suboptimal funnels attracting the search. Our study brings new insights and tools to the study of phase transitions in combinatorial optimisation.

Tunnelling Crossover Networks for the Asymmetric TSP

Local optima networks are a compact representation of fitness landscapes that can be used for analysis and visualisation. This paper provides the first analysis of the Asymmetric Travelling Salesman Problem using local optima networks. These are generated by sampling the search space by recording the progress of an existing evolutionary algorithm based on the Generalised Asymmetric Partition Crossover. They are compared to networks sampled through the Chained Lin-Kernighan heuristic across 25 instances. Structural differences and similarities are identified, as well as examples where crossover smooths the landscape.

Modelling genetic improvement landscapes with local optima networks

Local optima networks are a compact representation of the global structure of a search space. They can be used for analysis and visualisation. This paper provides one of the first analyses of program search spaces using local optima networks. These are generated by sampling the search space by recording the progress of an Iterated Local Search algorithm. Source code mutations in comparison and Boolean operators are considered. The search spaces of two small benchmark programs, the triangle and TCAS programs, are analysed and visualised. Results show a high level of neutrality i.e. connected test-equivalent mutants. It is also generally relatively easy to find a path from a random mutant to a mutant that passes all test cases.

Using Local Search with adaptive operator selection to solve the Progressive Party Problem

This paper investigates the use of adaptive operator selection in the context of Local Search to solve a constraint satisfaction problem, namely the Progressive Party Problem. Operators are selected according to a utility value which is computed, for each operator, from the solution quality and from the distance of the candidate solution to recently visited solutions in the search trajectory. We show that using several non-problem-specific operators gives comparable successful resolution rates to an algorithm customized for the problem, albeit with slower run times.

How Perturbation Strength Shapes the Global Structure of TSP Fitness Landscapes

Local optima networks are a valuable tool used to analyse and visualise the global structure of combinatorial search spaces; in particular, the existence and distribution of multiple funnels in the landscape. We extract and analyse the networks induced by Chained-LK, a powerful iterated local search for the TSP, on a large set of randomly generated (Uniform and Clustered) instances. Results indicate that increasing the perturbation strength employed by Chained-LK modifies the landscape’s global structure, with the effect being markedly different for the two classes of instances. Our quantitative analysis shows that several funnel metrics have stronger correlations with Chained-LK success rate than the number of local optima, indicating that global structure clearly impacts search performance.