Planning the construction of new transport routes or power lines on terrain is usually carried out manually by engineers, with no guarantee of optimality. We introduce a new approach for the computation of an optimal trajectory for the construction of new transit routes and power lines between two locations on a submanifold \(U\subset \mathbb {R}^{3}\) representing the topography of a terrain. U is

This paper presents a novel trust-region method for the optimization of multiple expensive functions. We apply this method to a biobjective optimization problem in fluid mechanics, the optimal mixing of particles in a flow in a closed container. The three-dimensional time-dependent flows are driven by Lorentz forces that are generated by an oscillating permanent magnet located underneath the rectangular

Manufacturing remains one of the most energy intensive sectors, additionally, the energy used within buildings for heating, ventilation and air conditioning (HVAC) is responsible for almost half of the UK’s energy demand. Commonly, these are analysed in isolation from one another. Use of machine learning is gaining popularity due to its ability to solve non-linear problems with large data sets and

Compressor stations are the heart of every high-pressure gas transport network. Located at intersection areas of the network, they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network. Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature

This paper aimed to optimize the extraction of antioxidants from plum seeds (Prunus domestica L.) using ultrasound-assisted extraction. The Box–Behnken design was used for the optimization of the extraction process. The four extraction parameters, such as the extraction time (10–40 min), ethanol concentration (20–100%, v/v), liquid-to-solid ratio (10–30 cm3 g−1), and extraction temperature (30–70 °C)

We propose a sample average approximation-based outer-approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs (SP) with any continuous or discrete probability distributions. Previous work has considered this approach for convex two-stage SP (Wei and Realff in Comput Chem Eng 28(3):333–346, 2004). The SAAOA algorithm does internal sampling within a nonconvex outer-approximation

Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of nonzero loadings in these combinations. In this paper we consider 8 different optimization formulations for computing a single sparse loading vector: we employ two norms

The application of mathematical optimization methods for water supply system design and operation provides the capacity to increase the energy efficiency and to lower the investment costs considerably. We present a system approach for the optimal design and operation of pumping systems in real-world high-rise buildings that is based on the usage of mixed-integer nonlinear and mixed-integer linear modeling

Individual technical components are usually well optimized. However, the design process of entire technical systems, especially in its early stages, is still dominated by human intuition and the practical experience of engineers. In this context, our vision is the widespread availability of software tools to support the human-driven design process with the help of modern mathematical methods. As a

This paper describes a new parallel global surrogate-based algorithm Global Optimization in Parallel with Surrogate (GOPS) for the minimization of continuous black-box objective functions that might have multiple local minima, are expensive to compute, and have no derivative information available. The task of picking P new evaluation points for P processors in each iteration is addressed by sampling

We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic 1d partial differential equations. In addition, a pooling-type mixing model is required at the nodes of the network to treat the mixing of different water temperatures

To provide electric power supply to consumers even in abnormal situations, the equipment used in electric distribution systems, including distribution lines, have sufficient capacity margins. Maintenance and/or replacement of these lines involving network reconfigurations are routinely performed. Since the monetary costs of equipment investments are significant, downsizing the equipment is important

We consider two mathematical problems that are connected and occur in the layer-wise production process of a workpiece using wire-arc additive manufacturing. As the first task, we consider the automatic construction of a honeycomb structure, given the boundary of a shape of interest. In doing this, we employ Lloyd’s algorithm in two different realizations. For computing the incorporated Voronoi tesselation

Mine planning optimization aims at maximizing the profit obtained from extracting valuable ore. Beyond its theoretical complexity—the open-pit mining problem with capacity constraints reduces to a knapsack problem with precedence constraints, which is NP-hard—practical instances of the problem usually involve a large to very large number of decision variables, typically of the order of millions for

In hydro predominant systems, the long-term hydrothermal scheduling problem (LTHS) is formulated as a multistage stochastic programming model. A classical optimization technique to obtain an operational policy is the stochastic dual dynamic programming (SDDP), which employs a forward step, for generating trial state variables, and a backward step to construct Benders-like cuts. To assess the quality

This paper concerns online portfolio selection problem. In this problem, no statistical assumptions are made about the future asset prices. Although existing universal portfolio strategies have been shown to achieve good performance, it is not easy, almost impossible, to determine upfront which strategy will achieve the maximum final cumulative wealth for online portfolio selection tasks. This paper

Based on the theoretical framework recently proposed by Bonifacius and Neitzel (Math Control Relat Fields 8(1):1–34, 2018. https://doi.org/10.3934/mcrf.2018001) we discuss the sequential quadratic programming (SQP) method for the numerical solution of an optimal control problem governed by a quasilinear parabolic partial differential equation. Following well-known techniques, convergence of the method

A global optimisation strategy based on the hybrid surrogate model method and the competitive mechanism-based multi-objective particle swarm optimisation (CMOPSO) algorithm was developed to improve the accuracy of the aerodynamic performance optimisation of a high-speed train running in open air without a crosswind. Free-form deformation was used to improve the optimisation efficiency without remodelling

Generating polyhedral outer approximations and solving mixed-integer linear relaxations remains one of the main approaches for solving convex mixed-integer nonlinear programming (MINLP) problems. There are several algorithms based on this concept, and the efficiency is greatly affected by the tightness of the outer approximation. In this paper, we present a new framework for strengthening cutting planes

In areas that require high performance components, such as the automotive, aeronautics and aerospace industries, optimization of the dynamic behavior of structures is sought through different approaches, such as the design of materials specific to the application, for instance through structural topology optimization. The bi-directional evolutionary structural optimization (BESO) method, in particular

Along with the advantages provided by the material and ease of assembly/disassembly, the ease of repair provided by minimum deformation after a collision and its sustainability highlight the preference of concrete barriers for roadside safety. However, concrete barriers, as rigid systems, are highly risky in case of a collision. Because the top priority of the application purpose is safety, it is desirable

Inverse problems are of great importance in some engineering texts and many industrial applications. Owing to this, we exhibit a method for numerically estimating two cases of the two-dimensional inverse problems in this research work. The considered inverse problem includes the time-dependent source control parameter r(t). This method is based on operational matrices of differential and integration

In this work, we consider a risk-averse ultimate pit problem where the grade of the mineral is uncertain. We derive conditions under which we can generate a set of nested pits by varying the risk level instead of using revenue factors. We propose two properties that we believe are desirable for the problem: risk nestedness, which means the pits generated for different risk aversion levels should be

A coupled topology and domain shape optimization framework is presented that is based on incorporating the shape design variables of the design domain in the Solid Isotropic Material with Penalization topology optimization method. The shape and topology design variables are incrementally updated in a sequential fashion, using a staggered numerical update scheme. Non-Uniform Rational B-Splines are employed

In this study we present an optimization problem where machine scheduling and personnel allocation decisions are solved simultaneously. The machine scheduling consists of solving a variant of the job shop problem where jobs are allocated in batches and multitasking is allowed. On the other hand, the personnel allocation problem searches for the optimal allocation of human resources to support the facility

Storage planning and utilization are among the most important considerations of practical batch process scheduling. Modeling the available storage options appropriately can be crucial in order to find practically applicable solutions with the best objective value. In general, there are two main limitations on storage: capacity and time. This paper focuses on the latter and investigates different techniques

The present paper addresses the robustness and convergence behavior of the direct limit analysis (LA) based methodology developed for the topology design of continuum structures subject to prescribed statically and plastically admissible loads. The design methodology, based on a direct method formulation of the static LA problem, has recently been proposed for continuous topology optimization and its

This paper aims to obtain a strong convergence result for a Douglas–Rachford splitting method with inertial extrapolation step for finding a zero of the sum of two set-valued maximal monotone operators without any further assumption of uniform monotonicity on any of the involved maximal monotone operators. Furthermore, our proposed method is easy to implement and the inertial factor in our proposed

One crucial advantage of additive manufacturing regarding the optimization of lattice structures is that there is a reduction in manufacturing constraints compared to classical manufacturing methods. To make full use of these advantages and to exploit the resulting potential, it is necessary that lattice structures are designed using optimization. Against this backdrop, two mixed integer programs are

We present a convection–diffusion inverse problem that aims to identify an unknown number of sources and their locations. We model the sources using a binary function, and we show that the inverse problem can be formulated as a large-scale mixed-integer nonlinear optimization problem. We show empirically that current state-of-the-art mixed-integer solvers cannot solve this problem and that applying

The assessment of the ecological impact of different powertrain concepts is of increasing relevance considering the enormous efforts necessary to limit the global warming effect due to the man-made climate change. Within this contribution, we adopt existing methods for the optimization of electric and hybrid electric powertrains using a vehicle simulation environment and derive a method to identify

The paper concerns with the two numerical methods for approximating solutions of a monotone and Lipschitz variational inequality problem in a Hilbert space. We here describe how to incorporate regularization terms in the projection method, and then establish the strong convergence of the resulting methods under certain conditions imposed on regularization parameters. The new methods work in both cases

We present a novel parameter space exploration algorithm for three classes of multiparametric problems, namely linear (mpLP), quadratic (mpQP), and mixed-integer linear (mpMILP). We construct subsets of the parameter space in the form of simplices through Delaunay triangulation to facilitate identification of the optimal partitions that describe the solution space. The presented exploration strategy

In this paper, we focus on multiobjective two-level simple recourse programming problems, in which multiple objective functions are involved in each level, shortages and excesses arising from the violation of the constraints with discrete random variables are penalized, and the sum of the objective function and the expectation of the amount of the penalties is minimized. To deal with such problems

We propose a semismooth Newton-type method for nonsmooth optimal control problems. Its particular feature is the combination of a quasi-Newton method with a semismooth Newton method. This reduces the computational costs in comparison to semismooth Newton methods while maintaining local superlinear convergence. The method applies to Hilbert space problems whose objective is the sum of a smooth function

The employment of industrial robot systems especially in the automotive industry noticeably changed the view of production plants and led to a tremendous increase in productivity. Nonetheless, rising technological complexity, the parallelization of production processes, as well as the crucial need for respecting specific safety issues pose new challenges for man and machine. Our goal is to develop

The objective of this research is to efficiently solve complicated high dimensional optimization problems by using machine learning technologies. Recently, major optimization targets have been changed to more complicated ones such as discontinuous and high dimensional optimization problems. It is necessary to solve the high-dimensional optimization problems to obtain an innovate design from topology

Particle swarm optimization (PSO) is one of the most commonly used stochastic optimization algorithms for many researchers and scientists of the last two decades, and the pattern search (PS) method is one of the most important local optimization algorithms. In this paper, we test three methods of hybridizing PSO and PS to improve the global minima and robustness. All methods let PSO run first followed

The synthesis of energy systems is a two-stage optimization problem where design decisions have to be implemented here-and-now (first stage), while for the operation of installed components, we can wait-and-see (second stage). To identify a sustainable design, we need to account for both economical and environmental criteria leading to multi-objective optimization problems. However, multi-objective

Real-time and short-term prediction of river flow is essential for efficient flood management. To obtain accurate flow predictions, a reliable rainfall-runoff model must be used. This study proposes the application of two evolutionary algorithms, particle swarm optimization (PSO) and genetic algorithm (GA), to train the artificial neural network (ANN) parameters in order to overcome the ANN drawbacks

The scheduling of drilling and hydraulic fracturing of wells in an unconventional oil field plays an important role in the profitability of the field. A key challenge arising in this problem is the requirement that neither drilling nor oil production can be done at wells within a specified neighborhood of a well being fractured. We propose a novel mixed-integer linear programming (MILP) formulation

Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables. Additionally, complex system design problems occasionally present a variable-size design space. This results in an optimization problem for which the search space varies dynamically

Most parallel surrogate-based optimization algorithms focus only on the mechanisms for generating multiple updating points in each cycle, and rather less attention has been paid to producing them through the cooperation of several algorithms. For this purpose, a surrogate-based cooperative optimization framework is here proposed. Firstly, a class of parallel surrogate-based optimization algorithms

In this paper, we present a new approach to solve multi-attribute decision making (MADM) problems considering subjective preferences and non-preferences of the decision maker in the form of triangular fuzzy preference relations and triangular fuzzy non-preference relations, respectively. Some important characteristics of these relations are used to form non-linear programming problems corresponding

It is now generally accepted that Euclidean-based metrics may not always adequately represent the subjective judgement of a human observer. As a result, many image processing methodologies have been recently extended to take advantage of alternative visual quality measures, the most prominent of which is the Structural Similarity Index Measure (SSIM). The superiority of the latter over Euclidean-based

Lion and Man problems are classical examples of pursuit and evasion games. However, the traditional analytic methods and indirect numerical methods only can handle the generalization of Lion and Man problems in games with small scales and simple scenarios. In this study, we first extend the original Lion and Man problems to a more complicated and time-varying game environment. Then we propose the simultaneous

In this paper, an interior point method (IPM) based on a new kernel function for solving linearly constrained convex optimization problems is presented. So, firstly a survey on several trigonometric kernel functions defined in literature is done and some properties of them are studied. Then some common characteristics of these functions which help us to define a new trigonometric kernel function are

In this paper, we combine the subgradient extragradient method and the hybrid method with inertial extrapolation step to introduce two strongly convergent methods for solving variational inequalities for which the underlying cost function is a pseudo-monotone operator in real Hilbert spaces. The first proposed method involves step-sizes bounded by the inverse of the Lipschitz constant of the cost function

Bayesian Optimization using Gaussian Processes is a popular approach to deal with optimization involving expensive black-box functions. However, because of the assumption on the stationarity of the covariance function defined in classic Gaussian Processes, this method may not be adapted for non-stationary functions involved in the optimization problem. To overcome this issue, Deep Gaussian Processes

We consider the problem of devising optimal price-offers (bids) for an energy producer participating in a multi-period day-ahead electricity market which exhibits non-convexities due to the discrete nature of the generation units’ commitments and quantities. The problem definition assumes perfect knowledge of the market’s technical characteristics, as well as of the bidding offers of the remaining

As indicated in the recent studies about primal-dual interior-point methods (IPMs) based on kernel functions, a kernel function not only serves to determine the search direction and measure the distance of the current iteration point to the \(\mu \)-center, but also affects the iteration complexity and the practical computational efficiency of the algorithm. In this paper, we propose a new IPM for

In order to increase the driving range of battery electric vehicles, while maintaining a high level of thermal comfort inside the passenger cabin, it is necessary to design an energy management system which optimally synthesizes multiple control actions of heating, ventilation and air-conditioning (HVAC) system. To gain an insight into optimal control actions and set a control benchmark, the paper

In this paper, a new class of kernel functions is introduced. We show that most existing kernel functions belong to this class. All functions in the new class are eligible in the sense of Bai et al. (SIAM J Optim 15(1):101–128, 2004), and hence the analysis of the resulting interior-point methods can follow the scheme proposed in Bai et al. (2004). We introduce five new kernel functions and by using

We define a regularized variant of the dual dynamic programming algorithm called DDP-REG to solve nonlinear dynamic programming equations. We extend the algorithm to solve nonlinear stochastic dynamic programming equations. The corresponding algorithm, called SDDP-REG, can be seen as an extension of a regularization of the stochastic dual dynamic programming (SDDP) algorithm recently introduced which

The testing and verification of a complex hardware or software system, such as modern integrated circuits found in everything from smartphones to servers, can be a difficult process. One of the most difficult and time-consuming tasks a verification team faces is reaching coverage closure, or hitting all events in the coverage space. Coverage-directed-generation (CDG), or the automatic generation of

In this work, a design optimisation strategy is presented for expensive and uncertain single- and multi-objective problems. Computationally expensive design fitness evaluations prohibit the application of standard optimisation techniques and the direct calculation of risk measures. Therefore, a surrogate-assisted optimisation framework is presented. The computational budget limits the number of high-fidelity

Given an infeasible, unbounded, or pathological convex optimization problem, a natural question to ask is: what is the smallest change we can make to the problem’s parameters such that the problem becomes solvable? In this paper, we address this question by posing it as an optimization problem involving the minimization of a convex regularization function of the parameters, subject to the constraint

Energy management can play a significant role in energy savings and temperature control of buildings, which consume a major share of energy resources worldwide. Model predictive control (MPC) has become a popular technique for energy management, arguably for its ability to cope with complex dynamics and system constraints. The MPC algorithms found in the literature are mostly centralized, with a single

The advantages of multidisciplinary design are well understood, but not yet fully adopted by the industry where methods should be both fast and reliable. For such problems, minimum computational cost while providing global optimality and extensive design information at an early conceptual stage is desired. However, such a complex problem consisting of various objectives and interacting disciplines

When solving for optimal strategies, a financial engineer needs to take into consideration of preferences heterogeneities, which involve not only present bias, but also future-focused preferences. We provide a reusable tool (i.e. algorithm) for explicitly solving optimal strategy in the presence of preferences variation over time, decision-makers and goods. In this framework, a new discount function