arXiv subjects

Daniel Karapetyan

Publications and source records attributed to Daniel Karapetyan.

At least 19 recordsLinked to original sources

arXiv2025

Fully Automated Generation of Combinatorial Optimisation Systems Using Large Language Models

Over the last few decades, researchers have made considerable efforts to make decision support more accessible for small and medium enterprises by reducing the cost of designing, developing and maintaining automated decision support systems. However, due to the diversity of the underlying combinatorial optimisation problems, reusability of such systems has been limited; in most cases, expensive expertise has been required to implement bespoke software components. We explore the feasibility of fully automated generation of combinatorial optimisation systems using large language models (LLMs). An LLM will be responsible for interpreting the user-provided problem description in natural language and designing and implementing problem-specific software components. We discuss the principles of fully automated LLM-based optimisation system generation, and evaluate several proof-of-concept generators, comparing their performance on four optimisation problems.

cs.SE↗

arXiv2024

Speeding up deferred acceptance

A run of the deferred acceptance (DA) algorithm may contain proposals that are sure to be rejected. We introduce the accelerated deferred acceptance algorithm that proceeds in a similar manner to DA but with sure-to-be rejected proposals ruled out. Accelerated deferred acceptance outputs the same stable matching as DA but does so more efficiently: it terminates in weakly fewer rounds, requires weakly fewer proposals, and final pairs match no later. Computational experiments show that these efficiency savings can be strict.

econ.TH↗

arXiv2024

Bi-objective Optimization in Role Mining

Role mining is a technique used to derive a role-based authorization policy from an existing policy. Given a set of users $U$, a set of permissions $P$ and a user-permission authorization relation $\mahtit{UPA}\subseteq U\times P$, a role mining algorithm seeks to compute a set of roles $R$, a user-role authorization relation $\mathit{UA}\subseteq U\times R$ and a permission-role authorization relation $\mathit{PA}\subseteq R\times P$, such that the composition of $\mathit{UA}$ and $\mathit{PA}$ is close (in some appropriate sense) to $\mathit{UPA}$. In this paper, we first introduce the Generalized Noise Role Mining problem (GNRM) -- a generalization of the MinNoise Role Mining problem -- which we believe has considerable practical relevance. Extending work of Fomin et al., we show that GNRM is fixed parameter tractable, with parameter $r + k$, where $r$ is the number of roles in the solution and $k$ is the number of discrepancies between $\mathit{UPA}$ and the relation defined by the composition of $\mathit{UA}$ and $\mathit{PA}$. We further introduce a bi-objective optimization variant of GNRM, where we wish to minimize both $r$ and $k$ subject to upper bounds $r\le \bar{r}$ and $k\le \bar{k}$, where $\bar{r}$ and $\bar{k}$ are constants. We show that the Pareto front of this bi-objective optimization problem (BO-GNRM) can be computed in fixed-parameter tractable time with parameter $\bar{r}+\bar{k}$. We then report the results of our experimental work using the integer programming solver Gurobi to solve instances of BO-GNRM. Our key findings are that (a) we obtained strong support that Gurobi's performance is fixed-parameter tractable, (b) our results suggest that our techniques may be useful for role mining in practice, based on our experiments in the context of three well-known real-world authorization policies.

cs.CR↗

arXiv2024

Exploitation Strategies in Conditional Markov Chain Search: A case study on the three-index assignment problem

The Conditional Markov Chain Search (CMCS) is a framework for automated design of metaheuristics for discrete combinatorial optimisation problems. Given a set of algorithmic components such as hill climbers and mutations, CMCS decides in which order to apply those components. The decisions are dictated by the CMCS configuration that can be learnt offline. CMCS does not have an acceptance criterion; any moves are accepted by the framework. As a result, it is particularly good in exploration but is not as good at exploitation. In this study, we explore several extensions of the framework to improve its exploitation abilities. To perform a computational study, we applied the framework to the three-index assignment problem. The results of our experiments showed that a two-stage CMCS is indeed superior to a single-stage CMCS.

cs.AI↗

arXiv2022

Solving the Workflow Satisfiability Problem using General Purpose Solvers

The workflow satisfiability problem (WSP) is a well-studied problem in access control seeking allocation of authorised users to every step of the workflow, subject to workflow specification constraints. It was noticed that the number $k$ of steps is typically small compared to the number of users in the real-world instances of WSP; therefore $k$ is considered as the parameter in WSP parametrised complexity research. While WSP in general was shown to be W[1]-hard, WSP restricted to a special case of user-independent (UI) constraints is fixed-parameter tractable (FPT). However, restriction to the UI constraints might be impractical. To efficiently handle non-UI constraints, we introduce the notion of branching factor of a constraint. As long as the branching factors of the constraints are relatively small and the number of non-UI constraints is reasonable, WSP can be solved in FPT time. Extending the results from Karapetyan et al. (2019), we demonstrate that general-purpose solvers are capable of achieving FPT-like performance on WSP with arbitrary constraints when used with appropriate formulations. This enables one to tackle most of practical WSP instances. While important on its own, we hope that this result will also motivate researchers to look for FPT-aware formulations of other FPT problems.

cs.AI↗

arXiv2021

Valued Authorization Policy Existence Problem: Theory and Experiments

Recent work has shown that many problems of satisfiability and resiliency in workflows may be viewed as special cases of the authorization policy existence problem (APEP), which returns an authorization policy if one exists and 'No' otherwise. However, in many practical settings it would be more useful to obtain a 'least bad' policy than just a 'No', where 'least bad' is characterized by some numerical value indicating the extent to which the policy violates the base authorization relation and constraints. Accordingly, we introduce the Valued APEP, which returns an authorization policy of minimum weight, where the (non-negative) weight is determined by the constraints violated by the returned solution. We then establish a number of results concerning the parameterized complexity of Valued APEP. We prove that the problem is fixed-parameter tractable (FPT) if the set of constraints satisfies two restrictions, but is intractable if only one of these restrictions holds. (Most constraints known to be of practical use satisfy both restrictions.) We also introduce a new type of resiliency for workflow satisfiability problem, show how it can be addressed using Valued APEP and use this to build a set of benchmark instances for Valued APEP. Following a set of computational experiments with two mixed integer programming (MIP) formulations, we demonstrate that the Valued APEP formulation based on the user profile concept has FPT-like running time and usually significantly outperforms a naive formulation.

cs.DS↗

arXiv2021

Enhancing Security via Deliberate Unpredictability of Solutions in Optimisation

The main aim of decision support systems is to find solutions that satisfy user requirements. Often, this leads to predictability of those solutions, in the sense that having the input data and the model, an adversary or enemy can predict to a great extent the solution produced by your decision support system. Such predictability can be undesirable, for example, in military or security timetabling, or applications that require anonymity. In this paper, we discuss the notion of solution predictability and introduce potential mechanisms to intentionally avoid it.

cs.DM↗

arXiv2019

Conditional Markov Chain Search for the Generalised Travelling Salesman Problem for Warehouse Order Picking

The Generalised Travelling Salesman Problem (GTSP) is a well-known problem that, among other applications, arises in warehouse order picking, where each stock is distributed between several locations -- a typical approach in large modern warehouses. However, the instances commonly used in the literature have a completely different structure, and the methods are designed with those instances in mind. In this paper, we give a new pseudo-random instance generator that reflects the warehouse order picking and publish new benchmark testbeds. We also use the Conditional Markov Chain Search framework to automatically generate new GTSP metaheuristics trained specifically for warehouse order picking. Finally, we report the computational results of our metaheuristics to enable further competition between solvers.

cs.AI↗

arXiv2019

Hyperparameter Optimisation with Early Termination of Poor Performers

It is typical for a machine learning system to have numerous hyperparameters that affect its learning rate and prediction quality. Finding a good combination of the hyperparameters is, however, a challenging job. This is mainly because evaluation of each combination is extremely expensive computationally; indeed, training a machine learning system on real data with just a single combination of hyperparameters usually takes hours or even days. In this paper, we address this challenge by trying to predict the performance of the machine learning system with a given combination of hyperparameters without completing the expensive learning process. Instead, we terminate the training process at an early stage, collect the model performance data and use it to predict which of the combinations of hyperparameters is most promising. Our preliminary experiments show that such a prediction improves the performance of the commonly used random search approach.

cs.LG↗

arXiv2019

Pattern-Based Approach to the Workflow Satisfiability Problem with User-Independent Constraints

The fixed parameter tractable (FPT) approach is a powerful tool in tackling computationally hard problems. In this paper, we link FPT results to classic artificial intelligence (AI) techniques to show how they complement each other. Specifically, we consider the workflow satisfiability problem (WSP) which asks whether there exists an assignment of authorised users to the steps in a workflow specification, subject to certain constraints on the assignment. It was shown by Cohen et al. (JAIR 2014) that WSP restricted to the class of user-independent constraints (UI), covering many practical cases, admits FPT algorithms, i.e. can be solved in time exponential only in the number of steps $k$ and polynomial in the number of users $n$. Since usually $k << n$ in WSP, such FPT algorithms are of great practical interest. We present a new interpretation of the FPT nature of the WSP with UI constraints giving a decomposition of the problem into two levels. Exploiting this two-level split, we develop a new FPT algorithm that is by many orders of magnitude faster than the previous state-of-the-art WSP algorithm and also has only polynomial-space complexity. We also introduce new pseudo-Boolean (PB) and Constraint Satisfaction (CSP) formulations of the WSP with UI constraints which efficiently exploit this new decomposition of the problem and raise the novel issue of how to use general-purpose solvers to tackle FPT problems in a fashion that meets FPT efficiency expectations. In our computational study, we investigate, for the first time, the phase transition (PT) properties of the WSP, under a model for generation of random instances. We show how PT studies can be extended, in a novel fashion, to support empirical evaluation of scaling of FPT algorithms.

cs.AI↗

arXiv2018

Algorithm Configuration: Learning policies for the quick termination of poor performers

One way to speed up the algorithm configuration task is to use short runs instead of long runs as much as possible, but without discarding the configurations that eventually do well on the long runs. We consider the problem of selecting the top performing configurations of the Conditional Markov Chain Search (CMCS), a general algorithm schema that includes, for examples, VNS. We investigate how the structure of performance on short tests links with those on long tests, showing that significant differences arise between test domains. We propose a "performance envelope" method to exploit the links; that learns when runs should be terminated, but that automatically adapts to the domain.

cs.AI↗

arXiv2017

Conditional Markov Chain Search for the Simple Plant Location Problem improves upper bounds on twelve Körkel-Ghosh instances

We address a family of hard benchmark instances for the Simple Plant Location Problem (also known as the Uncapacitated Facility Location Problem). The recent attempt by Fischetti et al. to tackle the Körkel-Ghosh instances resulted in seven new optimal solutions and 22 improved upper bounds. We use automated generation of heuristics to obtain a new algorithm for the Simple Plant Location Problem. In our experiments, our new algorithm matched all the previous best known and optimal solutions, and further improved 12 upper bounds, all within shorter time budgets compared to the previous efforts. Our algorithm design process is split into two phases: (i) development of algorithmic components such as local search procedures and mutation operators, and (ii) composition of a metaheuristic from the available components. Phase (i) requires human expertise and often can be completed by implementing several simple domain-specific routines known from the literature. Phase (ii) is entirely automated by employing the Conditional Markov Chain Search (CMCS) framework. In CMCS, a metaheuristic is flexibly defined by a set of parameters, called configuration. Then the process of composition of a metaheuristic from the algorithmic components is reduced to an optimisation problem seeking the best performing CMCS configuration. We discuss the problem of comparing configurations, and propose a new efficient technique to select the best performing configuration from a large set. To employ this method, we restrict the original CMCS to a simple deterministic case that leaves us with a finite and manageable number of meaningful configurations.

cs.DS↗

arXiv2017

Efficient Adaptive Implementation of the Serial Schedule Generation Scheme using Preprocessing and Bloom Filters

The majority of scheduling metaheuristics use indirect representation of solutions as a way to efficiently explore the search space. Thus, a crucial part of such metaheuristics is a "schedule generation scheme" -- procedure translating the indirect solution representation into a schedule. Schedule generation scheme is used every time a new candidate solution needs to be evaluated. Being relatively slow, it eats up most of the running time of the metaheuristic and, thus, its speed plays significant role in performance of the metaheuristic. Despite its importance, little attention has been paid in the literature to efficient implementation of schedule generation schemes. We give detailed description of serial schedule generation scheme, including new improvements, and propose a new approach for speeding it up, by using Bloom filters. The results are further strengthened by automated control of parameters. Finally, we employ online algorithm selection to dynamically choose which of the two implementations to use. This hybrid approach significantly outperforms conventional implementation on a wide range of instances.

cs.DS↗

arXiv2016

The Bi-Objective Workflow Satisfiability Problem and Workflow Resiliency

A computerized workflow management system may enforce a security policy, specified in terms of authorized actions and constraints, thereby restricting which users can perform particular steps in a workflow. The existence of a security policy may mean it is impossible to find a valid plan (an assignment of steps to authorized users such that all constraints are satisfied). Work in the literature focuses on the workflow satisfiability problem, a \emph{decision} problem that outputs a valid plan if the instance is satisfiable (and a negative result otherwise). In this paper, we introduce the \textsc{Bi-Objective Workflow Satisfiability Problem} (\BOWSP), which enables us to solve \emph{optimization} problems related to workflows and security policies. In particular, we are able to compute a "least bad" plan when some components of the security policy may be violated. In general, \BOWSP is intractable from both the classical and parameterized complexity point of view. We prove there exists an fixed-parameter tractable (FPT) algorithm to compute a Pareto front for \BOWSP if we restrict our attention to user-independent constraints. We also present a second algorithm to compute a Pareto front which uses mixed integer programming (MIP). We compare the performance of both our algorithms on synthetic instances, and show that the FPT algorithm outperforms the MIP-based one by several orders of magnitude on most of the instances. Finally, we study the important question of workflow resiliency and prove new results establishing that known decision problems are fixed-parameter tractable when restricted to user-independent constraints. We then propose a new way of modeling the availability of users and demonstrate that many questions related to resiliency in the context of this new model may be reduced to instances of \BOWSP.

cs.CR↗

arXiv2016

Markov Chain methods for the bipartite Boolean quadratic programming problem

We study the Bipartite Boolean Quadratic Programming Problem (BBQP) which is an extension of the well known Boolean Quadratic Programming Problem (BQP). Applications of the BBQP include mining discrete patterns from binary data, approximating matrices by rank-one binary matrices, computing the cut-norm of a matrix, and solving optimisation problems such as maximum weight biclique, bipartite maximum weight cut, maximum weight induced sub-graph of a bipartite graph, etc. For the BBQP, we first present several algorithmic components, specifically, hill climbers and mutations, and then show how to combine them in a high-performance metaheuristic. Instead of hand-tuning a standard metaheuristic to test the efficiency of the hybrid of the components, we chose to use an automated generation of a multi-component metaheuristic to save human time, and also improve objectivity in the analysis and comparisons of components. For this we designed a new metaheuristic schema which we call Conditional Markov Chain Search (CMCS). We show that CMCS is flexible enough to model several standard metaheuristics; this flexibility is controlled by multiple numeric parameters, and so is convenient for automated generation. We study the configurations revealed by our approach and show that the best of them outperforms the previous state-of-the-art BBQP algorithm by several orders of magnitude. In our experiments we use benchmark instances introduced in the preliminary version of this paper and described here, which have already become the de facto standard in the BBQP literature.

cs.DS↗

arXiv2016

Combining Monte-Carlo and Hyper-heuristic methods for the Multi-mode Resource-constrained Multi-project Scheduling Problem

Multi-mode resource and precedence-constrained project scheduling is a well-known challenging real-world optimisation problem. An important variant of the problem requires scheduling of activities for multiple projects considering availability of local and global resources while respecting a range of constraints. A critical aspect of the benchmarks addressed in this paper is that the primary objective is to minimise the sum of the project completion times, with the usual makespan minimisation as a secondary objective. We observe that this leads to an expected different overall structure of good solutions and discuss the effects this has on the algorithm design. This paper presents a carefully designed hybrid of Monte-Carlo tree search, novel neighbourhood moves, memetic algorithms, and hyper-heuristic methods. The implementation is also engineered to increase the speed with which iterations are performed, and to exploit the computing power of multicore machines. Empirical evaluation shows that the resulting information-sharing multi-component algorithm significantly outperforms other solvers on a set of "hidden" instances, i.e. instances not available at the algorithm design phase.

cs.DS↗

arXiv2015

Pattern Backtracking Algorithm for the Workflow Satisfiability Problem

The workflow satisfiability problem (WSP) asks whether there exists an assignment of authorised users to the steps in a workflow specification, subject to certain constraints on the assignment. (Such an assignment is called valid.) The problem is NP-hard even when restricted to the large class of user-independent constraints. Since the number of steps $k$ is relatively small in practice, it is natural to consider a parametrisation of the WSP by $k$. We propose a new fixed-parameter algorithm to solve the WSP with user-independent constraints. The assignments in our method are partitioned into equivalence classes such that the number of classes is exponential in $k$ only. We show that one can decide, in polynomial time, whether there is a valid assignment in an equivalence class. By exploiting this property, our algorithm reduces the search space to the space of equivalence classes, which it browses within a backtracking framework, hence emerging as an efficient yet relatively simple-to-implement or generalise solution method. We empirically evaluate our algorithm against the state-of-the-art methods and show that it clearly wins the competition on the whole range of our test problems and significantly extends the domain of practically solvable instances of the WSP.

cs.DS↗

arXiv2015

Satellite downlink scheduling problem: A case study

The synthetic aperture radar (SAR) technology enables satellites to efficiently acquire high quality images of the Earth surface. This generates significant communication traffic from the satellite to the ground stations, and, thus, image downlinking often becomes the bottleneck in the efficiency of the whole system. In this paper we address the downlink scheduling problem for Canada's Earth observing SAR satellite, RADARSAT-2. Being an applied problem, downlink scheduling is characterised with a number of constraints that make it difficult not only to optimise the schedule but even to produce a feasible solution. We propose a fast schedule generation procedure that abstracts the problem specific constraints and provides a simple interface to optimisation algorithms. By comparing empirically several standard meta-heuristics applied to the problem, we select the most suitable one and show that it is clearly superior to the approach currently in use.

math.OC↗