Kernel Search Research Articles

An advanced kernel search optimization for dynamic economic emission dispatch with new energy sources

Integrating renewable energy sources, such as wind and photovoltaic power generation, into the power grid is crucial for sustainable power system development and mitigating pollutant emissions. However, these sources’ inherent uncertainty and randomness pose significant challenges to grid operations. Metaheuristic algorithms offer efficient solutions to optimization problems in this context and are widely employed in practice. Kernel Search Optimization (KSO) has emerged as a prominent metaheuristic algorithm due to its parameter-free nature and applicability to power dispatch problems. Nevertheless, KSO’s limited local search capabilities necessitate enhancements for improved performance. This paper introduces an enhanced variant of KSO, termed Upgraded Kernel Search Optimization (UKSO), which incorporates differential evolution techniques, including mutation, crossover, and selection mechanisms, to bolster KSO’s search capabilities and overall performance. The efficacy and feasibility of UKSO are evaluated through comprehensive testing using the CEC2017 benchmark. Comparative analysis demonstrates that UKSO outperforms other algorithms by achieving more optimal solutions. To address power dispatch challenges in the context of renewable energy sources, a Two-Time Energy Dispatch (TTED) model is proposed, leveraging a weighted summation approach to minimize total fuel costs and pollution emissions simultaneously. The application of the Prophet model, based on Bayesian fitting, facilitates accurate prediction of wind and photovoltaic power outputs. Through experimentation across small (8 and 14 units) and large (58 units) systems, the feasibility of UKSO and TTED is validated. In complex scenarios, UKSO demonstrates a 0.69% to 3.64% reduction in pollution emissions and a 0.99% to 1.23% decrease in economic costs compared to KSO under varying weight configurations. Furthermore, UKSO achieves a renewable energy generation utilization rate exceeding 90%, emphasizing its ability to iterate efficiently through complex problems and its efficacy in addressing renewable power dispatch challenges. These results highlight the practical significance of UKSO in optimizing power systems and provide valuable insights for future research and applications in this domain.

Deck motion prediction using neural kernel network Gaussian process regression

Deck motion prediction and compensation are critical technologies for carrier-based aircraft automatic landing. Traditional deck motion prediction methods rely on precision of motion models and parameter adjustments, facing challenges in adaptability to complex sea conditions, different types of carriers, changes in flight conditions, and limitations in prediction duration, as well as reliability issues. This paper proposes a deck motion prediction method based on the neural kernel network Gaussian process regression (NKN-GPR) model. The NKN-GPR model can utilize a neural kernel network (NKN) to automatically construct the Gaussian process regression (GPR) model′s composite kernel, effectively addressing the limitations of the automated kernel search (ACKS) algorithm, which heavily depends on manual prior knowledge. Simulation data is generated using a combination of sine wave and power spectrum models, and the NKN-GPR model is compared with an autoregressive (AR) model based on least squares in a simulated validation. The simulation results demonstrate that the NKN-GPR model exhibits significant advantages in motion prediction accuracy, smoothness, and prediction duration, which confirms the effectiveness of the proposed algorithm. This study provides theoretical support for safe automatic landing of carrier-based aircraft.

Expressive mortality models through Gaussian process kernels

AbstractWe develop a flexible Gaussian process (GP) framework for learning the covariance structure of Age- and Year-specific mortality surfaces. Utilizing the additive and multiplicative structure of GP kernels, we design a genetic programming algorithm to search for the most expressive kernel for a given population. Our compositional search builds off the Age–Period–Cohort (APC) paradigm to construct a covariance prior best matching the spatio-temporal dynamics of a mortality dataset. We apply the resulting genetic algorithm (GA) on synthetic case studies to validate the ability of the GA to recover APC structure and on real-life national-level datasets from the Human Mortality Database. Our machine learning-based analysis provides novel insight into the presence/absence of Cohort effects in different populations and into the relative smoothness of mortality surfaces along the Age and Year dimensions. Our modeling work is done with the PyTorch libraries in Python and provides an in-depth investigation of employing GA to aid in compositional kernel search for GP surrogates.

Multi-strategy enhanced kernel search optimization and its application in economic emission dispatch problems

Abstract The kernel search optimizer (KSO) is a recent metaheuristic optimization algorithm that is based on kernel theory, eliminating the need for hyper-parameter adjustments, and demonstrating excellent global search capabilities. However, the original KSO exhibits insufficient accuracy in local search, and there is a high probability that it may fail to achieve local optimization in complex tasks. Therefore, this paper proposes a multi-strategy enhanced KSO (MSKSO) to enhance the local search ability of the KSO. The MSKSO combines several control strategies, including chaotic initialization, chaotic local search mechanisms, the high-altitude walk strategy (HWS), and the Levy flight (LF), to effectively balance exploration and exploitation. The MSKSO is compared with ten well-known algorithms on 50 benchmark test functions to validate its performance, including single-peak, multi-peak, separable variable, and non-separable variable functions. Additionally, the MSKSO is applied to two real engineering economic emission dispatch (EED) problems in power systems. Experimental results demonstrate that the performance of the MSKSO nearly optimizes that of other well-known algorithms and achieves favorable results on the EED problem. These case studies verify that the MSKSO outperforms other algorithms and can serve as an effective optimization tool.

A heuristic approach for the integrated production–transportation problem with process flexibility

We study an integrated multi-item production and distribution problem considering a network of multiple plants and clients, who are geographically dispersed, with direct shipments from the plants to the clients. In addition to the decisions on production and distribution, a decision needs to be taken on the level of process flexibility in the network, i.e., which items can be produced in which plants. There is a clear trade-off between these decisions. On the one hand, a network with total flexibility where each plant can produce all types of items allows for lower transportation costs, but requires large investments in flexibility and frequent setups. On the other hand, a network with a limited amount of flexibility where each plant produces only a few items, will increase the transportation costs, but requires a lower investment in flexibility. We model this problem as an extension of the capacitated lot-sizing problem. We limit the investment in flexibility by a budget constraint and minimize the operational costs. Varying this budget allows us to analyze different levels of flexibility. In this paper, we propose mathematical models and a hybrid solution method that combines a mixed integer programming-based approach and a kernel search heuristic. Our computational results using data sets from the literature show that the proposed hybrid method produces on average better solutions with significantly lower computational times when compared with the results produced by a state-of-the-art optimization software. Additional computational results are presented by varying key parameters and analyzing their impact on the value of flexibility. These computational experiments indicate that some of the main managerial insights which were derived in the literature for the case without transportation costs are no longer valid when we consider transportation costs.

Neural network Gaussian processes as efficient models of potential energy surfaces for polyatomic molecules

Kernel models of potential energy surfaces (PESs) for polyatomic molecules are often restricted by a specific choice of the kernel function. This can be avoided by optimizing the complexity of the kernel function. For regression problems with very expensive data, the functional form of the model kernels can be optimized in the Gaussian process (GP) setting through compositional function search guided by the Bayesian information criterion. However, the compositional kernel search is computationally demanding and relies on greedy strategies, which may yield sub-optimal kernels. An alternative strategy of increasing complexity of GP kernels treats a GP as a Bayesian neural network (NN) with a variable number of hidden layers, which yields NNGP models. Here, we present a direct comparison of GP models with composite kernels and NNGP models for applications aiming at the construction of global PES for polyatomic molecules. We show that NNGP models of PES can be trained much more efficiently and yield better generalization accuracy without relying on any specific form of the kernel function. We illustrate that NNGP models trained by distributions of energy points at low energies produce accurate predictions of PES at high energies. We also illustrate that NNGP models can extrapolate in the input variable space by building the free energy surface of the Heisenberg model trained in the paramagnetic phase and validated in the ferromagnetic phase. By construction, composite kernels yield more accurate models than kernels with a fixed functional form. Therefore, by illustrating that NNGP models outperform GP models with composite kernels, our work suggests that NNGP models should be a preferred choice of kernel models for PES.

Closed-loop inventory routing problem for perishable food with returnable transport items selection

Urged by the necessity to establish sustainable supply chains (SCs), this study focuses on exploring the closed-loop inventory routing problem (CIRP) for perishable food packed by multi-type returnable transport items (RTIs). The selling revenue of perishable food is dependent on food's remaining shelf life and the specific type of RTIs used for packaging. RTI selection decisions need to be jointly considered in the CIRP to weigh the potential benefits against associated costs. For this problem, we first develop an integer linear programme (ILP) to maximise the total profit of the holistic SC. Subsequently, we design a tailored kernel search (KS) matheuristic as an efficient solution. A real CIRP with multi-type RTIs for fresh strawberries is used to demonstrate the practicality of the ILP. For this case study, we perform extensive sensitivity analysis of the relevant parameters, extracting valuable managerial insights. Finally, experiments are conducted on 170 randomly generated instances. Computational results show that the proposed KS manages to achieve competitive solutions for instances with up to 10 retailers much more efficiently than CLPEX. For instances with up to 40 retailers, the KS algorithm significantly outperforms CPLEX in terms of solution quality, improving the obtained profit by 80.03% on average under the same computational time.

Boosting Kernel Search Optimizer with Slime Mould Foraging Behavior for Combined Economic Emission Dispatch Problems

Boosting Kernel Search Optimizer with Slime Mould Foraging Behavior for Combined Economic Emission Dispatch Problems

A kernel search algorithm for virtual machine consolidation problem in cloud computing

Virtual machine consolidation refers to the process of reallocating virtual machines across a set of target servers. It can be formulated as a mixed integer linear programming problem, which is known to be NP-hard. In this paper, we propose a kernel search (KS) heuristic algorithm based on hard variable fixing to quickly obtain high-quality solutions for large-scale virtual machine consolidation problems (VMCPs). Since existing variable fixing strategies in KS algorithms may result in some VMCP instances being infeasible, our proposed KS algorithm employs a more efficient strategy to choose a set of fixed variables based on their corresponding reduced costs. Our numerical results on VMCP instances demonstrate that our proposed KS algorithm significantly outperforms mixed integer linear programming solvers in terms of CPU time. Moreover, our proposed strategy of variable fixing improves the efficiency of the KS algorithm significantly, with negligible degradation in solution quality.

A matheuristic for the electric vehicle routing problem with time windows and a realistic energy consumption model

We address an Electric Vehicle Routing Problem with Time Windows (E-VRPTW) considering several real-like factors in the energy consumption model, e.g., the payload and the vehicle speed. We model E-VRPTW as a Mixed Integer Linear Program (MILP) where the speeds of vehicles are continuous variables that can vary between a minimum and a maximum value. Moreover, the proposed MILP formulation is cloneless since it allows using more than once the same recharging station without introducing dummy copies of it. To efficiently solve large-sized instances of the problem, we design a Random Kernel Search (RKS) matheuristic approach, based on the cloneless MILP formulation, that in turn exploits another matheuristic, called Random k-Degree Search (RkDS), to generate an initial feasible solution. We compare the results produced by a MILP solver using the MILP formulation with the ones obtained by the RKS on instances up to 100 customers derived from the benchmark instances of E-VRPTW. We show that the proposed matheuristic outperforms the cloneless MILP formulation on the medium/large-sized instances and also that it is robust, being not significantly sensitive to the values of the parameters used by the RkDS to generate the initial solution and to the initial time limit for the restricted MILP models.

Electric aircraft charging network design for regional routes: A novel mathematical formulation and kernel search heuristic

The uptake of electric aircraft appears faster today than predicted. Given the prominent electric aircraft technologies, short- and medium-haul routes are the ones that will benefit first, with the promise to revolutionize regional aviation at short notice. This paper proposes an optimization model to support the strategic design of charging networks for electric aircraft as a key enabling factor to prepare for and take full advantage of aviation electrification. The model, named Electric Aircraft Charging Network for Regional Routes, defines a network of airports and flight paths to optimally trade-off the number of charging bases (and associated investment costs) with connectivity and population coverage targets typical of regional routes serving remote regions. Due to computational challenges in large problem instances, we propose a Kernel Search heuristic and illustrate how it can deliver high quality solutions for large cases in a shorter computational time than the branch-and-cut algorithms. A real-world application to Sweden then demonstrates the practical insights of the proposed approach. We find that leveraging the many currently under-utilized regional airports has connectivity and investment benefits (on average +12.1% in number of origins covered, +5.8% in population coverage, and −7.3% reduction of travel times). Furthermore, increasing the maximum aircraft range on a single charge implies significantly fewer charging bases and more feasible travel options, thus favoring network resilience and granting higher flexibility for later planning stages.

Hybrid kernel search and particle swarm optimization with Cauchy perturbation for economic emission load dispatch with valve point effect

Due to growing concerns over environmental protection, economic and environmentally responsible power dispatching has become a hot topic in the field of power system control. Multi-objective optimization minimizes fuel costs and pollution emissions without violating operational constraints. To solve this problem, the MOP is decomposed into individual objects via the weighted sum method, and Newton’s method is used to tackle equality constraints iteratively. To this end, a hybrid algorithm (HKSOPSO-CP) based on kernel search optimization (KSO) and particle swarm optimization (PSO) with Cauchy perturbation is proposed in this paper. An experiment with 23 CEC benchmark functions shows that HKSOPSO-CP offers better performance compared with various popular algorithms proposed in recent years. When employed to solve the IEEE standard economic emission dispatch (EED) problems with 6, 10, 40, and 110 units, the proposed HKSOPSO-CP algorithm produces results indicating a better trade-off between the objectives relating to fuel costs and emissions compared to other algorithms that have recently been reported on in the literature.

Optimization of the home energy system in presence of price fluctuation and intermittent renewable energy sources in grid-connected and islanded modes

The home energy management (HEM) system is a critical tool for managing energy consumption and minimizing the related costs in a building. A smart renewable-based HEM system that participates in the demand response program is modeled in this work and its operations in both grid-connected and islanded modes are studied. This HEM receives its energy from wind turbines in islanded mode and upstream grid in grid-connected mode. This system also includes a diesel generator in the case of wind generation insufficiency. In the connected mode, electricity price is uncertain and in islanded mode, wind generation is uncertain, which are taken into account in modeling. The goal of this paper is the minimization of the electricity bill cost for the households. The studied system also contains a controllable appliance to simulate participation in the demand response program. Moreover, the electric vehicles (EVs) in this system operate in vehicle-to-home (V2H) mode which means the battery in the EV can supply some of the needed energy if needed. Also, the kernel search optimization algorithm is utilized to improve system operation in presence of some uncertainties. The impact of applying the optimization is assessed to validate this approach. The optimization is also done in the grid-connected because the price fluctuates throughout the day and proper management of power purchase from the grid can greatly reduce the cost of energy. The system behavior is studied separately in four seasons with both operation modes, and with and without the optimization. The results indicate that using the optimization has decreased the energy costs in connected mode by 13.18 % and islanded mode by 9.55 %, which proves the effectiveness of the proposed modeling and optimization algorithm.

Kernel Search for the Capacitated Vehicle Routing Problem

This paper addresses the Capacitated Vehicle Routing Problem (CVRP), which is a widely studied optimization problem due to its relevance to the field of transportation, distribution, and logistics. We present a matheuristic method for CVRP that adopts the main idea of the Kernel Search algorithm (KS) based on decomposing the original problem into sub-problems that are easier to solve. Unlike the original scheme of KS, our approach uses the Clarke–Wright savings algorithm to construct a sequence of smaller sub-problems, which are subsequently solved using mathematical programming strategies. The computational experiments performed on a set of benchmark instances showed that the proposed matheuristics achieves good results in acceptable computational time.

Exact and matheuristic methods for the parallel machine scheduling and location problem with delivery time and due date

The scheduling and location (ScheLoc) problem is a new and important research topic with a wide range of practical applications. It jointly optimizes machine locations, job assignments, and sequence decisions to yield a globally optimal solution. Current studies on the ScheLoc problem are limited, and most have focused on makespan minimization. This paper investigates a new variant of the parallel-machine ScheLoc problem with job delivery time and due date considerations. This is motivated by practical situations where jobs must be transported back to their original locations upon completion of processing, and a specific due date is associated with each job. The objective is to minimize the total weighted sum of location, transportation, and tardiness penalty costs incurred if a job is delivered after its due date. We propose three models adapted from classic ones for scheduling problems. We then develop an exact logic-based Benders decomposition method, which decomposes the problem into a master problem (MP) for determining machine locations and job assignments, and a subproblem (SP) for determining job sequences on each machine. The MP is augmented by dynamically adding optimality cuts generated by solving the SP. We also develop a matheuristic (MH) and its variant to achieve near-optimal solutions. An approximate model with predetermined job processing sequences on each machine is formulated and solved to determine the machine locations and job assignments. The obtained solutions are further improved by solving a series of single-machine scheduling problems. The variant combines a kernel search framework to make MH more efficient. Computational experiments on 720 randomly generated instances show the effectiveness and efficiency of both the exact and matheuristic methods.

Hybridizing adaptive large neighborhood search with kernel search: a new solution approach for the nurse routing problem with incompatible services and minimum demand

AbstractThe average age of the population has grown steadily in recent decades along with the number of people suffering from chronic diseases and asking for treatments. Hospital care is expensive and often unsafe, especially for older individuals. This is particularly true during pandemics as the recent SARS‐CoV‐2. Hospitalization at home has become a valuable alternative to face efficiently a huge increase in treatment requests while guaranteeing a high quality of service and lower risk to fragile patients. This new model of care requires the redefinition of health services organization and the optimization of scarce resources (e.g., available nurses). In this paper, we study a Nurse Routing Problem that tries to find a good balance between hospital costs reduction and the well‐being of patients, also considering realistic operational restrictions like maximum working times for the nurses and possible incompatibilities between services jointly provided to the same patient. We first propose a Mixed Integer Linear Programming formulation for the problem and use some valid inequalities to strengthen it. A simple branch‐and‐cut algorithm is proposed and validated to derive ground benchmarks. In addition, to efficiently solve the problem, we develop an Adaptive Large Neighborhood Search hybridized with a Kernel Search and validate its performance over a large set of different realistic working scenarios. Computational tests show how our matheuristic approach manages to find good solutions in a reasonable amount of time even in the most difficult settings. Finally, some interesting managerial insights are discussed through an economic analysis of the operating context.

Optimal selection of touristic packages based on user preferences during sports mega-events

Sport mega-events, such as the Soccer World Cup or Olympic Games, attract many visitors from all over the world. Most of these visitors are also interested in, besides attending the sports events, visiting the host nation and the neighboring countries. In this paper, we focus on the upcoming FIFA World Cup Qatar 2022. As per the schedule of the tournament, a national team can play 7 matches at most. Therefore, a supporter will have six short breaks (of three to five days) between consecutive matches in addition to two longer ones, immediately before and after the tournament, during which they can plan some touristic trips. We study the problem faced by a touristic trip provider who wants to offer a set of touristic packages, chosen among a very large set of options, devoted to World-Cup related tourists. The number of packages offered must be limited due to organizational reasons and the necessity to guarantee a high participation in each trip. In this study, a set of user profiles is considered. It represents different categories of tourists, characterized by different preferences and budgets. Each user is supposed to pick the packages that maximize their satisfaction, considering their budget and time restraints. The goal of the company is to choose the set of packages to be offered that would maximize the average users satisfaction. To address this NP-Hard combinatorial optimization problem we provide a mathematical formulation and a matheuristic, named Consensus-Based Kernel Search (CKS), wherein an alternative rule is used to create the initial Kernel and partition variables in buckets. Computational results evidence the excellent performance of CKS and prove that the newly introduced algorithm systematically outperforms the classical Kernel Search.

The Heterogeneous Flexible Periodic Vehicle Routing Problem: Mathematical formulations and solution algorithms

The aim of this paper is to introduce the Flexible Periodic Vehicle Routing Problem with Heterogeneous Fleet, a variant of the Periodic Vehicle Routing Problem. Flexibility is introduced in service schedules and delivered quantities, heterogeneity comes from different vehicles capacities and speeds. Three Mixed-Integer Linear Programming formulations and a matheuristic, based on Kernel Search, are proposed. Computational tests are made to evaluate the performance of the three formulations and to assess the quality of the solutions provided by the matheuristic.

AutoNAS: Automatic Neural Architecture Search for Hyperspectral Unmixing

Owing to the powerful and automatic representation capabilities, deep learning (DL) techniques have made significant breakthroughs and progress in hyperspectral unmixing (HU). Among the DL approaches, autoencoders (AEs) have become a widely-used and promising network architecture. However, these AE-based methods heavily rely on manual design and may not be a good fit for specific datasets. To unmix hyperspectral images more intelligently, we propose an automatic neural architecture search model for HU, AutoNAS for short, to determine the optimal network architecture by considering channel configurations and convolution kernels simultaneously. In AutoNAS, the self-supervised training mechanism based on hyperspectral images is first designed for generating the training samples of the supernet. Then, the affine parameter sharing strategy is adopted by applying different affine transformations on the supernet weights in the training phase, which enables finding the optimal channel configuration. Furthermore, on the basis of the obtained channel configuration, the evolutionary algorithm with additional computational constraints is introduced into networks to achieve flexible convolution kernel search by evaluating unmixing results of different architectures in the supernet. Extensive experiments conducted on four hyperspectral datasets demonstrate the effectiveness and superiority of the proposed AutoNAS in comparison with several state-of-the-art unmixing algorithms.

Boosted kernel search: Framework, analysis and case studies on the economic emission dispatch problem

In recent years, a variety of meta-heuristic nature-inspired algorithms have been proposed to solve complex optimization problems. However, these algorithms suffer from the shortcoming that multiple hyperparameters need to be set carefully. Therefore, to solve the problem, the kernel search optimization (KSO) algorithm inspired by the kernel method has been proposed. KSO can simplify the optimization process by transforming the optimization process of nonlinear function into the linear optimization process. Despite its advantage, the original KSO requires a large amount of computation, and has no powerful exploitation search, resulting in its inability to obtain more accurate results. In the present study, a local search of the hill-climbing algorithm is adopted, and the calculation of the kernel parameter is simplified to improve the original KSO. In an experiment using 50 benchmark functions, the new algorithm outperformed KSO and some well-known algorithms in accuracy and running time. Moreover, when applied in the real-world economic emission dispatch problem, the improved algorithm achieved a better performance than other algorithms compared. An online repository will support this research at https://aliasgharheidari.com.