Alternative Objective Function Research Articles

Optimizing Freight Vehicle Routing in Dynamic Time-Varying Networks with Carbon Dioxide Emission Trajectory Analysis

In this study, we formulate a freight vehicle path-planning model in the context of dynamic time-varying networks that aims to capture the spatial and temporal distribution characteristics inherent in the carbon dioxide emission trajectories of freight vehicles. Central to this model is the minimization of total carbon dioxide emissions from vehicle distribution, based on the comprehensive modal emission model (CMEM). Our model also employs the freight vehicle travel time discretization technique and the dynamic time-varying multi-path selection strategy. We then design an improved genetic algorithm to solve this complicated problem. Empirical results vividly illustrate the superior performance of our model over alternative objective function models. In addition, our observations highlight the central role of accurate period partitioning in time segmentation considerations. Finally, the experimental results underline that our multi-path model is able to detect the imprint of holiday-related effects on the spatial and temporal distribution of carbon dioxide emission trajectories, especially when compared to traditional single-path models.

Optimize to generalize in Gaussian processes: An alternative objective based on the Rényi divergence

We introduce an alternative closed-form objective function α-ELBO for improved parameter estimation in the Gaussian process ( G P ) based on the Rényi α-divergence. We use a decreasing temperature parameter α to iteratively deform the objective function during optimization. Ultimately, our objective function converges to the exact log-marginal likelihood function of G P . At early optimization stages, α-ELBO can be viewed as a regularizer that smoothes some unwanted critical points. At late stages, α-ELBO recovers the exact log-marginal likelihood function that guides the optimizer to solutions that best explain the observed data. Theoretically, we derive an upper bound of the Rényi divergence under the proposed objective and derive convergence rates for a class of smooth and non-smooth kernels. Case studies on a wide range of real-life engineering applications demonstrate that our proposed objective is a practical alternative that offers improved prediction performance over several state-of-the-art inference techniques.

Adversarial Training Methods for Deep Learning: A Systematic Review

Deep neural networks are exposed to the risk of adversarial attacks via the fast gradient sign method (FGSM), projected gradient descent (PGD) attacks, and other attack algorithms. Adversarial training is one of the methods used to defend against the threat of adversarial attacks. It is a training schema that utilizes an alternative objective function to provide model generalization for both adversarial data and clean data. In this systematic review, we focus particularly on adversarial training as a method of improving the defensive capacities and robustness of machine learning models. Specifically, we focus on adversarial sample accessibility through adversarial sample generation methods. The purpose of this systematic review is to survey state-of-the-art adversarial training and robust optimization methods to identify the research gaps within this field of applications. The literature search was conducted using Engineering Village (Engineering Village is an engineering literature search tool, which provides access to 14 engineering literature and patent databases), where we collected 238 related papers. The papers were filtered according to defined inclusion and exclusion criteria, and information was extracted from these papers according to a defined strategy. A total of 78 papers published between 2016 and 2021 were selected. Data were extracted and categorized using a defined strategy, and bar plots and comparison tables were used to show the data distribution. The findings of this review indicate that there are limitations to adversarial training methods and robust optimization. The most common problems are related to data generalization and overfitting.

INSURANCE VALUATION: A TWO-STEP GENERALISED REGRESSION APPROACH

AbstractCurrent approaches to fair valuation in insurance often follow a two-step approach, combining quadratic hedging with application of a risk measure on the residual liability, to obtain a cost-of-capital margin. In such approaches, the preferences represented by the regulatory risk measure are not reflected in the hedging process. We address this issue by an alternative two-step hedging procedure, based on generalised regression arguments, which leads to portfolios that are neutral with respect to a risk measure, such as Value-at-Risk or the expectile. First, a portfolio of traded assets aimed at replicating the liability is determined by local quadratic hedging. Second, the residual liability is hedged using an alternative objective function. The risk margin is then defined as the cost of the capital required to hedge the residual liability. In the case quantile regression is used in the second step, yearly solvency constraints are naturally satisfied; furthermore, the portfolio is a risk minimiser among all hedging portfolios that satisfy such constraints. We present a neural network algorithm for the valuation and hedging of insurance liabilities based on a backward iterations scheme. The algorithm is fairly general and easily applicable, as it only requires simulated paths of risk drivers.

Properties of Fisher information gain for Bayesian design of experiments

The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and parameters). For most common utility functions, the expected utility is rarely available in closed form and requires a computationally expensive approximation which then needs to be maximised over the space of all possible designs. This hinders practical use of the Bayesian approach to find experimental designs. However, recently, a new utility called Fisher information gain has been proposed. The resulting expected Fisher information gain reduces to the prior expectation of the trace of the Fisher information matrix. Since the Fisher information is often available in closed form, this significantly simplifies approximation and subsequent identification of optimal designs. In this paper, it is shown that for exponential family models, maximising the expected Fisher information gain is equivalent to maximising an alternative objective function over a reduced-dimension space, simplifying even further the identification of optimal designs. However, if this function does not have enough global maxima, then designs that maximise the expected Fisher information gain lead to non-identifiability.

Comparison between classical ‘P&O’ algorithm and FLC of MPPT for GPV under partial shading

<p><span lang="EN-US">When the GPV is under partial shading, several peaks appear in the characteristic P-V, namely a GMP and one or more local maximums. The classical algorithm ‘P&O’ MPPT cannot converge on the GMP for low irradiation values and is trapped by tracking down a LMP so making the algorithm ineffective making the algorithm ineffective, in this case under 200 W/m². An alternative objective function is developed to optimize the performance of the FLC by selecting the appropriate gains using PSO. In this simulation the GPV is composed of one hundred modules grouped parallel series (10x10) and subjected to partial shading. The proposed FLC provides better performance for GMP tracking for the chosen shade configuration selected.</span></p>

Simultaneous optimization approach for combined control–structural design versus the conventional sequential optimization method

Although controller devices highly improve the seismic performance of civil structures, they usually incur enormous financial costs. A variety of sequential methods for minimizing the cost function have been proposed in the literature. In most of these methods, the control system is optimally designed after the best structural configuration is provided. However, such sequential procedures are unable to yield the best overall design. This paper discusses a combined structural and control optimization approach in which the structural mass and controlled system energy are simultaneously minimized. To this end, a twofold objective function is defined by linearly combining the structural mass and linear quadratic regulator (LQR) performance index. It is shown that the optimal value of this objective function depends on the initial condition, and to circumvent this problem, an alternative objective function is introduced which allows for solving the problem of initial condition dependency. Given the complexity of the problem, a variable neighborhood search (VNS) metaheuristic method is developed. The performance of the developed method is demonstrated through case studies involving the determination of structural responses for shear-type frames. The case studies are presented for evaluating and comparing the effectiveness of the proposed simultaneous technique and the conventional sequential method. The responses of the structures are determined under an array of strong ground motions. The results of the comparative analyses revealed that the simultaneously optimized cases using the proposed methodology had superior dynamic performance compared to the sequentially optimized cases.

Multistart search for the Cyclic Cutwidth Minimization Problem

The Cyclic Cutwidth Minimization Problem (CCMP) is a Graph Layout Problem that consists of finding an embedding of the vertices of a candidate graph in a host graph, in order to minimize the maximum cut of a host edge. In this case, the host graph is restricted to be a cycle. In this paper, we identify a new lower bound for the problem, and also a property which allows search procedures to drastically reduce the neighborhood size during the search. Additionally, we propose the use of an alternative objective function for min–max optimization problems, never used before in the context of the CCMP. These strategies have been combined within a multistart search procedure for this problem. The obtained method is compared with the state of the art for the CCMP using sets of problem instances previously published. Statistical tests indicate the merit of our proposal.

Improving the accuracy of model-based quantitative nuclear magnetic resonance.

Low spectral resolution and extensive peak overlap are the common challenges that preclude quantitative analysis of nuclear magnetic resonance (NMR) data with the established peak integration method. While numerous model-based approaches overcome these obstacles and enable quantification, they intrinsically rely on rigid assumptions about functional forms for peaks, which are often insufficient to account for all unforeseen imperfections in experimental data. Indeed, even in spectra with well-separated peaks whose integration is possible, model-based methods often achieve suboptimal results, which in turn raises the question of their validity for more challenging datasets. We address this problem with a simple model adjustment procedure, which draws its inspiration directly from the peak integration approach that is almost invariant to lineshape deviations. Specifically, we assume that the number of mixture components along with their ideal spectral responses are known; we then aim to recover all useful signals left in the residual after model fitting and use it to adjust the intensity estimates of modelled peaks. We propose an alternative objective function, which we found particularly effective for correcting imperfect phasing of the data - a critical step in the processing pipeline. Application of our method to the analysis of experimental data shows the accuracy improvement of 20 %-40 % compared to the simple least-squares model fitting.

Towards Question-based High-recall Information Retrieval

While continuous active learning algorithms have proven effective in finding most of the relevant documents in a collection, the cost for locating the last few remains high for applications such as Technology-assisted Reviews (TAR). To locate these last few but significant documents efficiently, Zou et al. [2018] have proposed a novel interactive algorithm. The algorithm is based on constructing questions about the presence or absence of entities in the missing relevant documents. The hypothesis made is that entities play a central role in documents carrying key information and that the users are able to answer questions about the presence or absence of an entity in the missing relevance documents. Based on this, a Sequential Bayesian Search-based approach that selects the optimal sequence of questions to ask was devised. In this work, we extend Zou et al. [2018] by (a) investigating the noise tolerance of the proposed algorithm; (b) proposing an alternative objective function to optimize, which accounts for user “erroneous” answers; (c) proposing a method that sequentially decides the best point to stop asking questions to the user; and (d) conducting a small user study to validate some of the assumptions made by Zou et al. [2018]. Furthermore, all experiments are extended to demonstrate the effectiveness of the proposed algorithms not only in the phase of abstract appraisal (i.e., finding the abstracts of potentially relevant documents in a collection) but also finding the documents to be included in the review (i.e., finding the subset of those relevant abstracts for which the article remains relevant). The experimental results demonstrate that the proposed algorithms can greatly improve performance, requiring reviewing fewer irrelevant documents to find the last relevant ones compared to state-of-the-art methods, even in the case of noisy answers. Further, they show that our algorithm learns to stop asking questions at the right time. Last, we conduct a small user study involving an expert reviewer. The user study validates some of the assumptions made in this work regarding the user’s willingness to answer the system questions and the extent of it, as well as the ability of the user to answer these questions.

On integer linear programming formulations of a patrol boat scheduling problem with complete coverage requirements

The Patrol Boat Scheduling Problem with Complete Coverage (PBSPCC) is concerned with finding a minimum size patrol boat fleet to provide continuous coverage at a set of maritime patrol regions, ensuring that there is at least one vessel on station in each patrol region at any given time. This requirement is complicated by the necessity for patrol vessels to be replenished on a regular basis in order to carry out patrol operations indefinitely. In this paper, we establish a number of important theoretical results for the PBSPCC. In particular, we establish a set of conditions under which an alternative objective function (minimize the total time not spent on patrol) can be used to derive a minimum size fleet. Preliminary results suggest that the new theoretical insights can be used as part of an acceleration strategy to improve the column generation runtime performance.

QUEST – A new quadratic decision model for the multi-satellite scheduling problem

Demand for earth observation satellite imagery is pervasive and increasing rapidly across multiple domains, highlighting the key problem to optimally schedule satellite image acquisition/collection, subject to ground and on-board constraints. Despite the variety of reported approaches to solving the NP-hard multi-satellite scheduling problem (m-SatSP), serious limitations still prevail, largely overlooking problem structure exploitation and/or domain knowledge. Assuming a few constraints, problem modelling—or scope—is often confined to a simple trailing satellite constellation composition perspective and tends to conveniently oversimplify footprint coverage intricacies. As a result, adequate problem task decomposition properly reflecting complex kinematic behaviour for an ad hoc satellite constellation remains elusive. Known approaches also fail to provide valuable solution optimality gap estimations to objectively qualify best computed solution and/or to control run-time execution in solving hard problem instances. In this paper, a novel approach to solving the single objective static m-SatSP is proposed. It is based on network flow optimization using mathematical programming. Unlike previous methods, QUEST (QUadratically constrainEd program Solver Technology) relies on a sound alternative approximate objective function and, the exploitation of exact problem-solving techniques. Derived from domain knowledge and problem structure considerations, QUEST generalizes problem modelling to successfully handle virtual constellation, avoiding unsuitable utilization of traditional area coverage decomposition scheme. The proposed decision model concurrently captures coverage approximation, imaging success uncertainty and quality for a variety of tasks. It also includes new and optional constraints while embracing an acceptable upper bound on collection value. A QUEST variant alternatively relying on “delayed reward” to bridge promising search regions on move selection, further shows optimality gap reduction and provides additional speedup. Computational results prove QUEST to be cost-effective and to outperform some recent baseline methods derived from best-known m-SatSP procedures. It comparatively demonstrates measurable collection and run-time gains, and provides a tight upper bound on the optimal solution of hard problems.

A critique of the objective function utilized in calculating the Thrifty Food Plan.

The Thrifty Food Plan (TFP) is the basis of benefit allocations within the USDA’s Supplemental Nutrition Assistance Program (SNAP), which administers nearly $70 billion in benefits to over 42 million people annually. To produce the allocation of food within the TFP, the USDA uses a mathematical optimization model that solves for the daily apportionment across various food groups. The model is constrained by nutritional and consumption requirements to produce an “optimal” allocation. Despite the importance of the TFP, the computational solution developed by the USDA has received insufficient attention, with only a handful of articles written on the TFP optimization model. Here, we run three alternative objective functions that are simpler than the one used by USDA. Our first alternative objective function minimizes the sum of squared errors between the consumed market basket of goods and an allocated market basket of goods, the second alternative objective function minimizes the sum of the absolute value of the difference between the consumed market basket of goods and an allocated market basket of goods, and the third alternative objective function minimizes the weighted absolute deviation of allocations and actual consumption expressed as a proportion of observed consumption. A clear theoretical advantage of either of our methods is that they eliminate the need to arbitrarily set allocated consumption to nonzero values, as is the case for the logarithmic objective function used by USDA. In an operational sense, we find that our model formulations produce an allocation that fits actual consumption better than the objective function employed by the USDA.

Enhanced intelligent proportional-integral-like fuzzy knowledge–based controller using chaos-enhanced accelerated particle swarm optimization algorithm for transient calibration of air–fuel ratio control system

The self-adaptive and highly robust proportional-integral-like fuzzy knowledge–based controller has been developed to regulate air–fuel ratio for gasoline direct injection engines, in order to improve the transient response behaviour and reduce the effort to be spent on calibration of parameter settings. However, even though the proportional-integral-like fuzzy knowledge–based controller can automatically correct the initially calibrated proportional and integral parameters, a more appropriate selection of controller parameter settings will lead to better transient performance. Thus, this article proposes an enhanced intelligent proportional-integral-like fuzzy knowledge–based controller using chaos-enhanced accelerated particle swarm optimization algorithm to automatically define the most optimal parameter settings. An alternative time-domain objective function is applied for the transient calibration programme without the need for prior selection of the search-domain. The real-time transient performance of the enhanced controller is investigated on the air–fuel ratio control system of a gasoline direct injection engine. The experimental results show that the enhanced proportional-integral-like fuzzy knowledge–based controller based on chaos-enhanced accelerated particle swarm optimization is able to damp out the oscillations with less settling time (up to 75% reduction) and less integral of absolute error (up to 64.07% reduction) compared with the conventional self-adaptive proportional-integral-like fuzzy knowledge–based controller. Repeatability tests indicate that the chaos-enhanced accelerated particle swarm optimization algorithm–based proportional-integral-like fuzzy knowledge–based controller is also able to reduce the mean value of objective function by up to 10.61% reduction and the standard deviation of the objective function by up to 28.29% reduction, compared with the conventional accelerated particle swarm optimization algorithm–based proportional-integral-like fuzzy knowledge–based controller.

Multi-Period Mean CVAR Asset Allocation: Is it Advantageous to be Time Consistent?

We formulate the multi-period, time consistent mean-CVAR (Conditional Value at Risk) asset allocation problem in a form amenable to numerical computation. Our numerical algorithm can impose realistic constraints such as: no shorting, no-leverage, and discrete rebalancing. We focus on long term (i.e. 30 year) strategies, which would be typical of an investor in a Defined Contribution (DC) pension plan. A comparison with pre-commitment mean-CVAR strategies shows that adding the time consistent constraint compares unfavourably with the pure pre-commitment strategy. Since the pre-commitment strategy computed at time zero is identical to a time consistent strategy based on an alternative objective function, the pre-commitment mean-CVAR strategy is implementable in this case. Hence it would seem that there is little to be gained from enforcing time consistency.

Iterated local search and simulated annealing algorithms for the inventory routing problem

AbstractThis paper addresses the inventory routing problem (IRP), which consists in defining the customer visit schedule, the delivery quantities, and the vehicle routing plan to meet the demands of a set of customers over a given time horizon. We consider the variant with a single item, a single supplier, multiple vehicles, and a finite multiperiod planning horizon, minimizing the sum of inventory and travel costs. In addition, we address an alternative objective function that minimizes the logistic ratio, defined as the total travel cost divided by the total quantity delivered to customers. This second objective function, while more realistic in some logistics settings, poses a challenge for integer programming models and exact methods because of its nonlinearity. To our knowledge, no heuristic method has been proposed to address this objective in the IRP variant addressed in this paper. To solve this problem with each of these objective functions, we propose effective metaheuristic algorithms based on iterated local search and simulated annealing. Computational experiments show that these algorithms provide reasonably high‐quality solutions in relatively short running times for both objective functions when compared to other methods for well‐known instances from the literature. Moreover, the algorithms produce new best solutions for some of these instances.

Incorporating demand dynamics in multi-period capacitated fast-charging location planning for electric vehicles

We develop a multi-period capacitated flow refueling location problem for electric vehicles (EVs) as the EV market responds to the charging infrastructure. The optimization model will help us determine the optimal location of level 3 chargers as well as the number of charging modules at each station over multiple time periods. Our model can also be applied to fast-filling gaseous alternative fuel vehicles under similar assumptions. We define a number of demand dynamics, including flow demand growth as a function of charging opportunities on path as well as natural demand growth independent of charging infrastructure. We also present an alternative objective function of maximizing electric vehicle demand in addition to maximizing flow coverage. A case study based on a road network around Washington, D.C., New York City, and Boston is presented to provide numerical experiments related to demand dynamics, showing the potential problems in multi-period planning.

Order picking along a crane-supplied pick face: The SKU switching problem

This paper treats an order picking system where a crane continuously relocates stock keeping units (SKUs) in a high-bay rack subdivided into the bottommost picking level and the upper reserve area. The capacity of the pick face is not large enough to store all SKUs, so that the crane has to ensure that all SKUs demanded by a current picking order are timely provided and picker idle time is avoided. We aim at a processing sequence of picking orders and a SKU switching plan, i.e., an instruction when to exchange which SKUs in the picking level, such that an unobstructed order picking is enabled. Our problem is closely related to the tool switching problem of flexible manufacturing. Here, each job requires a subset of tools to be loaded into the tool magazine (with limited capacity) of a single flexible machine. We, however, show that an alternative objective function, i.e., minimizing the maximum number of switches between any successive job pair, is better suited in the warehouse context and even better results can be obtained by a multi-objective approach. Elementary complexity proofs as well as suited solution procedures are provided and we also address managerial aspects, such as the sizing of the pick face.

Improving scenario discovery for handling heterogeneous uncertainties and multinomial classified outcomes

Scenario discovery is a novel model-based approach to scenario development in the presence of deep uncertainty. Scenario discovery frequently relies on the Patient Rule Induction Method (PRIM). PRIM identifies regions in the model input space that are highly predictive of producing model outcomes that are of interest. To identify these, PRIM uses a lenient hill climbing optimization procedure. PRIM struggles when confronted with cases where the uncertain factors are a mix of data types, and can be used only for binary classifications. We compare two more lenient objective functions which both address the first problem, and an alternative objective function using Gini impurity which addresses the second problem. We assess the efficacy of the modification using previously published cases. Both modifications are effective. The more lenient objective functions produce better descriptions of the data, while the Gini impurity objective function allows PRIM to be used when handling multinomial classified data.

Broadband Energy Harvesting From Vibrations Using Magnetic Transduction

In this paper, an adaptive electromagnetic energy harvester is proposed and analyzed. It is composed of an oscillating mass equipped with an electromagnetic transducer, whose pins are connected to a resonant resistive–inductive–capacitive electric circuit in order to increase its effective bandwidth. Closed-form expressions for the optimal circuit parameters are presented, which maximize the power harvested by the device under harmonic excitation. The harvesting efficiency, defined as the ratio between the harvested power and the power absorbed by the oscillating device, is also reported. It is used as an alternative objective function for the optimization of the harvester circuit parameters.