Optimisation Problems Research Articles

Solving higher dimensional expensive black box global optimization problems using sparse directional search on surrogates

AbstractWe present a new algorithm Directional Optimization Search with Surrogate (DOSS), for optimizing problems with box constraints and a computationally expensive black-box objective function. DOSS is a radial basis function (RBF) based method that mainly focuses on higher dimensional and computationally expensive objective functions that can be multimodal. DOSS introduces three new techniques not previously used in earlier RBF algorithms, including using a combination of the coordinates knowledge level, fewer initial sampling points, and the surrogate’s gradient information. Numerical results on a test set including 14 test problems with 36, 48, and 60 dimensions show that DOSS outperforms two recently published algorithms RBFOpt and TuRBO, and earlier RBF algorithms such as DYCORS. TuRBO is a Gaussian process based optimization algorithm, which outperformed earlier state-of-the-art methods. DOSS algorithm also has a good performance on real-world optimization problems, including robot pushing and rover trajectory planning problems. Almost sure convergence for the DOSS algorithm is also proven in this paper. An implementation of DOSS is available at https://doi.org/10.5281/zenodo.13731558.

Legal remedies against amber abuse: problems of implementation and optimization

The article is devoted to the coverage of certain problems related to the use of criminal legal means against persons who commit the crimes provided for in Art. 2401 of the Criminal Code of Ukraine illegal extraction, sale, acquisition, transfer, forwarding, transportation, processing of amber, and with the improvement of such means. Emphasis is placed on the study of relevant judicial practice. The provision on the need to differentiate criminal responsibility for illegal actions with amber depending on group forms of complicity is argued. It is proved that the proposed improvement of Art. 2401 of the Criminal Code of Ukraine will be consistent with the requirements established in jurisprudence for the construction of qualified compositions of criminal offenses. The theoretical position is supported, according to which, if the relevant composition of the criminal offense does not include such features as its commission by a group of persons and an organized group, then the qualification of the offense committed by the organizer and members of the group should be carried out with a reference in the qualification formula to part 2 or part 3 st. 28 of the Criminal Code of Ukraine with the inclusion in the legal wording of the indictment of the characteristics «committed by a prior conspiracy by a group» or «committed by an organized group.» Based on the study of judicial practice materials, it has been established that the exemption of persons who commit the analyzed crime from serving a sentence is widespread (Article 75 of the Criminal Code of Ukraine), and the imperfection of the sanctions of Article 2401 of the Criminal Code of Ukraine, considerations were expressed regarding their optimization, namely the consolidation in Part 1 of Art. 2401 of the Criminal Code of Ukraine provides for a fine as the non-alternative main punishment, and in Part 2 and Part 3 of this article - alternative punishments in the form of a fine and imprisonment for a certain period. The imperfection of judicial practice related to ensuring the individualization of criminal responsibility for «amber» torts has been demonstrated - the imposition of a fine as the main type of punishment in the minimum amount and failure to take into account the role, nature and degree of participation of each of the accomplices in the commission of a criminal offense.

Experimentally-efficient data-driven rational feedforward control for multivariable systems

Feedforward control with task flexibility for MIMO systems is essential to meet the growing demands on throughput and accuracy of high-tech systems. The aim of this paper is to develop an experimentally efficient framework for data-driven tuning of rational feedforward controllers for general non-commutative MIMO systems. In the developed approach, the nonlinear terms in the non-convex optimisation problem of iterative learning control (ILC) are iteratively circumvented via approximation. This leads to a series of convex optimisation problems that can be solved offline to obtain the parameters of the rational feedforward controller. In addition, by limiting the number of offline iterations an experimentally intensive algorithm is derived, which could be beneficial in the case of severe model mismatch. A simulation study shows that the experimentally efficient approach converges fast through offline iterations and has improved convergence properties through the use of regularisation.

Qualitative analysis of optimisation problems with respect to non-constant Robin coefficients

Following recent interest in the qualitative analysis of some optimal control and shape optimisation problems, we provide in this article a detailed study of the optimisation of Robin boundary conditions in PDE constrained calculus of variations. Our main model consists of an elliptic PDE of the form −∆u β = f (x, u β) endowed with the Robin boundary conditions ∂ν u β +β(x)u β = 0. The optimisation variable is the function β, which is assumed to take values between 0 and 1 and to have a fixed integral. Two types of criteria are under consideration: the first one is non-energetic criteria. In other words, we aim at optimising functionals of the form J (β) =\int_{Ω or ∂Ω} j(u β). We prove that, depending on the monotonicity of the function j, the optimisers may be of bang-bang type (in other words, the optimisers write 1Γ for some measurable subset Γ of ∂Ω) or, on the contrary, that they may only take values strictly between 0 and 1. This has consequence for a related shape optimisation problem, in which one tries to find where on the boundary Neumann (∂ν u = 0) and constant Robin conditions (∂ν u + u = 0) should be placed in order to optimise criteria. The proofs for this first case rely on new fine oscillatory techniques, used in combination with optimality conditions. We then investigate the case of compliance-type functionals. For such energetic functionals, we give an in-depth analysis and even some explicit characterisation of optimal β * .

Augmented ɛ‐constraint‐based matheuristic methodology for Bi‐objective production scheduling problems

AbstractMatheuristic is an optimisation methodology that integrates mathematical approaches and heuristics to address intractable combinatorial optimisation problems, where a common framework is to insert mixed integer linear programming (MILP) models as local search functions for evolutionary algorithms. However, since a mathematical programming formulation only tries to find the solution with the best objective value, matheuristics are rarely adopted to multi‐objective scenarios asking for a set of Pareto optimal solutions, for example, vehicle routing problems and production scheduling problems. In this situation, the ɛ‐constraint, which transforms multi‐objective problems into single‐objective formulations by considering selected objectives as constraints, seems to be a promising approach. First, an augmented ɛ‐constraint‐based matheuristic methodology (ɛ‐MH) is proposed to apply the idea of ɛ‐constraint to embedded MILP models, so that Pareto fronts obtained by meta‐heuristics can be further improved by solving a set of MILP models. Afterwards, four speed‐up strategies are developed to alleviate the computational burden resulting from repeatedly solving mathematical formulations, which also imply preferable scenarios for taking advantages of the ɛ‐MH. Finally, several real‐world bi‐objective scheduling problems are discussed to present potential applications for the proposed methodology.

Ultra‐high‐dimensional multi‐level optimisation strategies for electrical machines

AbstractElectrical machine optimisation is normally a high‐dimensional non‐linear multi‐objective optimisation problem. A multi‐level optimisation (MO) strategy is currently used to improve efficiency, where sensitivity analysis is required for dividing design parameters into different groups. However, the conventional MO strategy cannot handle ultra‐high‐dimensional optimisation problems. In this paper, a sensitivity analysis method with variable weighted intervals is proposed to calculate the sensitivity coefficient in the parameter design range. Moreover, three improved multi‐level optimisation strategies based on different optimisation algorithms, sequential sensitivity strategies, and machine learning models are proposed, analysed, and compared with the conventional MO strategy. Through a case study of a synchronous reluctance machine, it can be seen that the proposed optimisation strategies can improve the optimisation results and efficiency of ultra‐high‐dimensional optimisation of electrical machines.

Using query semantic and feature transfer fusion to enhance cardinality estimating of property graph queries

With the increasing complexity and diversity of query tasks, cardinality estimation has become one of the most challenging problems in query optimization. In this study, we propose an efficient and accurate cardinality estimation method to address the cardinality estimation problem in property graph queries, particularly in response to the current research gap regarding the neglect of contextual semantic features. We first propose formal representations of the property graph query and define its cardinality estimation problem. Then, through the query featurization, we transform the query into a vector representation that can be learned by the estimation model, and enrich the feature vector representation by the context semantic information of the query. We finally propose an estimation model for property graph queries, specifically introducing a feature information transfer module to dynamically control the information flow meanwhile achieving the model’s feature fusion and inference. Experimental results on three datasets show that the estimation model can accurately and efficiently estimate the cardinality of property graph queries, the mean Q_error and RMSE are reduced by about 30% and 25% than the state-of-art estimation models. The context semantics features of queries can improve the model’s estimation accuracy, the mean Q_error result is reduced by about 20% and the RMSE result is about 5%.

A New Hybrid Conjugate Gradient Method with Global Convergence Properties

This work introduces a novel hybrid conjugate gradient (CG) technique for tackling unconstrained optimisation problems with improved efficiency and effectiveness. The parameter is computed as a convex combination of the standard conjugate gradient techniques using and . Our proposed method has shown that when using the strong Wolfe-line-search (SWC) under specific conditions, it achieves global theoretical convergence. In addition, the new hybrid CG approach has the ability to generate a search direction that moves downward with each iteration. The quantitative findings obtained by applying the recommended technique about 30 functions with varying dimensions clearly illustrate its effectiveness and potential. This work introduces a novel hybrid conjugate gradient (CG) technique for tackling unconstrained optimisation problems with improved efficiency and effectiveness. The parameter is computed as a convex combination of the standard conjugate gradient techniques using and . Our proposed method has shown that when using the strong Wolfe-line-search (SWC) under specific conditions, it achieves global theoretical convergence. In addition, the new hybrid CG approach has the ability to generate a search direction that moves downward with each iteration. The quantitative findings obtained by applying the recommended technique about 30 functions with varying dimensions clearly illustrate its effectiveness and potential.

A Combined Quasi-Newton-Type Method Using 4th-Order Directional Derivatives for Solving Degenerate Problems of Unconstrained Optimization

Introduction. Methods of unconstrained optimization play a significant role in machine learning [1–6]. When solving practical problems in machine learning, such as tuning nonlinear regression models, the extremum point of the chosen optimality criterion is often degenerate, which significantly complicates its search. Therefore, degenerate problems are the most challenging in optimization. Known numerical methods for solving the general unconstrained optimization problem, up to the second order, have very low convergence rates when solving degenerate problems [7, 8]. This is explained by the fact that for a significant improvement in convergence rate in this case, it is necessary to use higher-order derivatives in the method than the second order [10]. The purpose of the paper is to develop an efficient quasi-Newton method for solving degenerate unconstrained optimization problems, the idea of which (unlike regularization) involves dividing the entire space into the sum of two orthogonal subspaces. This idea was introduced in [23]. The space division at each iteration of the method is based on the spectral decomposition of the matrix approximating the Hessian of the objective function using the BFGS formula [3]. Each subspace exhibits its own behavior of the objective function, and therefore, an appropriate minimization method is applied on it. Results. A combined quasi-Newton method is presented for solving degenerate unconstrained optimization problems, based on orthogonal decomposition of the Hessian approximation matrix and division of the entire space into the sum of two orthogonal subspaces. On one subspace (the kernel of the Hessian approximation matrix), a method is applied where derivatives in the direction of the 4th order are computed, while on the orthogonal complement to it, a quasi-Newtonian method is applied. A separate one-dimensional search is applied on each of these subspaces to determine the step multiplier in the respective direction. The effectiveness of the presented combined method is confirmed by numerical experiments conducted on widely accepted test functions for unconstrained optimization problems. The proposed method allows obtaining fairly accurate solutions to test tasks in case of degeneracy of the minimum point with significantly lower computational costs for gradient calculations compared to optimization procedures of well-known mathematical packages. Conclusions. The idea of dividing the entire space into the sum of two (or possibly more) orthogonal subspaces when solving complex optimization problems is quite promising in terms of applying a combination of different numerical methods on separate subspaces. In the future, it is planned to conduct theoretical research on the convergence rate of the presented combined method in solving degenerate unconstrained optimization problems. Keywords: unconstrained optimization, quasi-Newton methods, degenerate minimum point, spectral matrix decomposition, Machine Learning.

Adaptive large-neighbourhood search for optimisation in answer-set programming

Answer-set programming (ASP) is a prominent approach to declarative problem solving that is increasingly used to tackle challenging optimisation problems. We present an approach to leverage ASP optimisation by using large-neighbourhood search (LNS), which is a meta-heuristic where parts of a solution are iteratively destroyed and reconstructed in an attempt to improve an overall objective. In our LNS framework, neighbourhoods can be specified either declaratively as part of the ASP encoding or automatically generated by code. Furthermore, our framework is self-adaptive, i.e., it also incorporates portfolios for the LNS operators along with selection strategies to adjust search parameters on the fly. The implementation of our framework, the system ALASPO, currently supports the ASP solver clingo, as well as its extensions clingo-dl and clingcon that allow for difference and full integer constraints, respectively. It utilises multi-shot solving to efficiently realise the LNS loop and in this way avoids program regrounding. We describe our LNS framework for ASP as well as its implementation, discuss methodological aspects, and demonstrate the effectiveness of the adaptive LNS approach for ASP on different optimisation benchmarks, some of which are notoriously difficult, as well as real-world applications for shift planning, configuration of railway-safety systems, parallel machine scheduling, and test laboratory scheduling.

An adaptive multi-objective optimization method for structure-connection-performance design of commercial vehicle cab

A variable screening-approximate model-adaptive multi-optimization algorithm integrated method is proposed to solve the high-dimensional nonlinear problems for lightweight optimization of cabs. Firstly, a full-parametric body-in-white model of the cab is established using implicit parameterization technology, and the simulation analysis of the bending and torsional stiffness, natural modal characteristics, and passive safety are established. Then, considering the structure and connection process parameters, the design variables are screened based on a gray relational analysis-TOPSIS (GRA-TOPSIS). Finally, integrated multi-objective optimization of cab structure-connection-performance is carried out by an adaptive RBF neural network optimization method, and the optimal solution is determined by the GRA-TOPSIS method. Compared with the initial model, the mass of cab is reduced by 3.28% after optimization design. It provides guidance for the lightweight design of body.

Vertex-based graph neural network classification model considering structural topological features for structural optimization

Traditional surrogate models always face the challenge of low accuracy when dealing with high-dimensional problems in structural optimization, this study aims to overcome this problem and proposes a vertex-based graph neural network (GNN) classification model. In contrast to conventional machine learning models that treat design variables as independent inputs, the proposed model develops a vertex-based graph representation to transform structural topological features and critical physical information into the graph data. According to a message passing mechanism based on the graph convolutional, it can extract the correlations among design variables and enhance its capability in handling high-dimensional structural optimization problems. Three truss examples, including a 10-bar with 10 variables, a 600-bar with 25 variables, and a 942-bar with 59 variables, are utilized to investigate the performance of the proposed surrogate model. The results demonstrate that the GNN-based surrogate model outperforms traditional machine learning approaches, particularly in the two high-dimensional problems, showcasing its superior ability to capture complex variable correlations and handle high-dimensional structural optimization tasks. Moreover, the proposed method significantly reduces the computational expenses by over 60% compared to conventional metaheuristic algorithms, while yielding optimal designs with comparable quality. These results demonstrate the efficiency and effectiveness of the GNN-based surrogate model in tackling complex, high-dimensional structural optimization problems.

Enhancing Active Disturbance Rejection Control for a Vehicle Active Stabiliser Bar with an Improved Chicken Flock Optimisation Algorithm

An active stabiliser bar significantly enhances the anti-roll capabilities of vehicles. The control strategy is a crucial factor in enabling the active stabiliser bar to function effectively. This paper investigates an active disturbance rejection control (ADRC) strategy. Given the numerous parameters of the ADRC and their significant mutual influence, optimising these parameters is challenging. To address this, an improved chicken flock optimisation algorithm is proposed to optimise the ADRC parameters and enhance its performance. First, a three-degree-of-freedom dynamic model of the vehicle is established, and an active disturbance rejection control-based optimisation model utilising a chicken flock optimisation algorithm is constructed. To tackle the issues of getting stuck in local optima and low precision when dealing with complex problems in the traditional chicken flock optimisation (CFO) algorithm, several strategies, including improved Lévy flight, have been adopted. Subsequently, the twelve parameters of the ADRC are optimised using the improved chicken flock optimisation algorithm. Comprehensive testing on multiple benchmark functions demonstrates that the improved chicken flock optimisation (ICFO) algorithm is distinctly superior to other advanced algorithms in terms of solution quality and robustness. Simulation results show that the ICFO-ADRC controller is significantly superior. In four different complex road condition tests, the ICFO-ADRC controller shows an average performance improvement of 8% compared to the fuzzy PI-PD controller, an average improvement of 82% compared to the non-optimised ADRC controller, and an average improvement of 18% compared to the CFO-ADRC controller. Our findings confirm that this paper was able to provide new solutions for vehicle stability control whilst opening up new possibilities for the application of metaheuristic algorithms.

Distinguishing the energy and non-energy actions in balancing energy markets

In the European context, balancing energy markets are established to optimise transmission system operator balancing actions closer to real-time. These actions aim to match total generation and consumption subject to a suite of security constraints (e.g., reserve requirements). However, there is no clear border between those actions that are taken due to the reserve requirements (non-energy actions) and those that are primarily taken to supply the demand mismatches (energy actions). To recognise the effect of non-energy actions, existing methods require comparing the results of counterfactual optimisation problems in which the non-energy-action-related constraints were deliberately omitted. This paper proposes a one-off solution enabling TSOs to distinguish energy actions from non-energy ones in the balancing market scheduling problem. By decomposition of the dual variables and clustering the constraints as proposed in this paper, there is no need to solve repetitive counterfactual optimisation problems. Case studies show that in addition to the non-energy actions caused by non-energy-based balancing requirements, the proposed method is able to recognise the energy actions that should be taken due to the non-energy root causes. This feature enables TSOs to efficiently retrace the effect of non-energy actions on the energy-based dispatch instructions issued according to the balancing market schedule.

Facilitating Circular Transition in the Construction Industry: Optimizing a Prefabricated Construction Site Layout Using a Novel BIM-Integrated SLP-GA Model

Prefabricated construction is being developed as one of the pathways toward circularity in the construction industry. However, compared to traditional cast-in-place construction methods, the design of prefabricated construction site layouts presents unique challenges, such as managing the space for prefabricated components and lifting equipment, and coordinating the precise timing between off-site fabrication and on-site assembly. Existing research has primarily focused on traditional cast-in-place construction, leaving room for improvement in optimisation models for prefabricated site layouts. This study develops a BIM-based System Layout Planning-Genetic Algorithm (SLP-GA) model specifically tailored for prefabricated construction site optimisation. The proposed model improves the accuracy and visualisation of layout planning through BIM technology, enabling dynamic adjustments and real-time data integration. It also incorporates genetic algorithms to address complex multi-objective optimisation problems, avoiding local optima and overcoming the limitations of traditional SLP methods that rely on subjective judgements. Unlike previous studies that do not consider secondary handling, the optimisation objectives of this study focus on minimising material handling costs associated with secondary handling and maximising comprehensive relationships, including efficiency, safety and space utilisation. The application of this model in a case study shows a reduction in logistics costs of 8.58% and an improvement in comprehensive relationships of 11.61%, indicating significant improvements. This research advances optimisation methods for prefabricated construction site layouts, enriches optimisation objectives by considering secondary handling, and provides practical guidance for improving the efficiency and effectiveness of prefabricated construction projects.

Improving decomposition-based MOEAs for combinatorial optimisation by intensifying corner weights

In the real world, a class of common problems such as supply chain management, project scheduling, portfolio optimisation and facility location design are multi-objective combinatorial optimisation problems (MOCOPs), where there are multiple objectives and the set of feasible solutions is discrete. In MOCOPs, corner solutions are solutions in which at least one objective reaches the optimal value. Corner solutions are important as they are likely to be preferred by the decision maker and are able to help improve algorithm performance. In this paper, we first reveal that in decomposition-based MOEAs, improving the corner weights (as opposed to improving the middle weights) significantly enhances the generation of corner solutions, thereby enhancing the overall performance of algorithms. Based on this, we propose a method to enhance the search for corner solutions in MOCOPs. We act on a class of popular MOEAs, decomposition-based MOEAs, and in their evolutionary mechanism we intensify the weights in the corner areas. To verify the proposed method, we conduct experiments by incorporating the method into three decomposition-based MOEAs, MOEA/D, MOEA/D-DRA-UT and MOEA/D-LdEA (the latter two were designed specifically for enhancing the search of corner solutions). The experimental results demonstrate that the proposed method can improve the spread of solution sets found, without compromising the quality of internal solutions.

Optimal innovation-based attacks against remote state estimation with side information and historical data

This work investigates the attack strategy design problem of the false data injection attack against the cyber-physical system. Distinct from the relevant results which utilise the current intercepted data or additionally consider side information, a more universal attack model is proposed which combines historical data and side information with the current intercepted data to synergistically deteriorate the system estimation performance. In order to quantify the impact resulting from the proposed attack strategy, the optimisation objective is characterised by deriving the error covariance matrix under the attacks, which becomes more intricate since the proposed attack model introduces more decision variables and coupled terms. Take the stealthiness which is characterised by Kullback-Leibler divergence as the constraints, the problem investigated in this work is equivalently transformed into the constrained multi-variable non-convex optimisation problems, which are not able to be solved directly by the methods in the relevant results. By utilising the Lagrange multiplier method, the structural characteristic of the optimal mean and the optimal covariance which only related to the Lagrange multiplier are derived, such that the optimal distribution of the modified innovation is able to be obtained by a simple search procedure. Following that, the design of the optimal attack strategy is completed by using semi-definite programming to derive the optimal attack matrices. Finally, the simulation examples are given such that the validity of the results is verified.

Cost Optimisation Tool for Multicommodity Network Flow Problem in Telecommunications

In this paper, we consider the problem of minimising the cost of data transmission as a function of the capacity of telecommunication links. To solve this problem, we first formulated a mathematical model, and then we designed and developed a software that enables the optimisation of the given or randomly generated telecommunications network. Declarative programming is a good choice for optimisation problems because it is enough to specify only the relations that must be satisfied, without giving any effective procedure for finding the values for the decision variables. To test the application, we developed a software that randomly generates a telecommunications network that meets the given requirements. This enables us to test the application on an arbitrary number of different telecommunication networks with different numbers of nodes and links, and analyse the impact of changing network parameters on the flow and results of the optimisation. As telecommunications networks operate in conditions of uncertainty, the subject of special analysis was the potential failure of some of the network links. The paper presents and thoroughly analyses the optimisation results for several selected networks, as well as summary results for a number of telecommunications networks.

A Study on the Integration of Big Data With Information Retrieval Technology in the Construction of Translation Talent Pools

This paper conducts a corresponding study on the construction of a translation talent pool internally through the context of information retrieval technology. It first discusses the current state of development of information retrieval technology in various countries in the present era and the current social development of information retrieval technology. A model of the system is constructed by basing it on information retrieval technology. The system model of information retrieval technology combined with the optimisation problems associated with translation talent pools is also investigated, incorporating a factorisation algorithm. The results of the study show that the system model of big data combined with information retrieval technology has good application in concrete practical applications after modelling and performing internal upgrading.

An improved prairie dog optimization algorithm integrating multiple strategies and its application

Aiming at the problems in prairie dog optimization (PDO), such as uneven population distribution at initialization, slow convergence, imbalance between global exploration and local exploitation, and the tendency to get trapped in the local optimum, this study proposes an Improved prairie dog optimisation algorithm integrating multiple strategies (IMSPDO). Firstly, the population is initialized using spatial pyramid matching (SPM) chaotic mapping combined with improved random opposition-based learning (IROL) to solve the problems of uneven distribution and poor diversity of the population. Secondly, the prey escapes energy formula mentioned in the harris hawks optimization (HHO) is introduced to achieve the smooth transition between the exploration phase and the exploitation phase, balancing the algorithm’s global exploration capability and local exploitation capability. Additionally, the idea of the particle swarm optimization (PSO) is applied to enhance the global optimization capability of the algorithm. Finally, the ideas of simulated annealing (SA), polynomial mutation and Cauchy mutation are also introduced to improve the ability that individuals to jump out of the local optimum. The performance of the improved algorithm is verified on a set of 21 classical benchmark functions and 8 CEC2020 test functions. The proposed IMSPDO is also evaluated against original PDO, and six other commonly used algorithms. The result of the Wilcoxon rank-sum test shows that there is a significant difference between the selected algorithms and IMSPDO. Furthermore, 3 engineering examples are used to further test the superiority of IMSPDO in dealing with real-world problems.