Exact Optimization Research Articles

Delayed resonator with multiple distributed delays – Considering and optimizing the inherent loop delay

We generalize the distributed delayed resonator (DDR) concept by incorporating the previously unutilized but inevitable feedback loop delay, thus creating a so-called multiple-delay distributed delayed resonator (MD-DDR) for complete vibration suppression. The necessary parameter tuning and control stability analysis become more involved but remain analytically solvable. Particularly, we take the operability of control parameters imposed by hardware as an explicit condition for parameter tuning and show that the loop delay (even if it is small) can lead to incomplete vibration suppression and, counter-intuitively, even no suppression if the excitation frequency exceeds a threshold value. On the other hand, such negative effects are neutralized by correcting control parameters. The loop delay is then intentionally augmented to seek enhanced performance, yielding a considerably extended operable frequency band for the desired complete vibration suppression. Furthermore, it is optimized to expedite response speed by achieving the leftmost placement of the dominant (i.e., the rightmost) characteristic root. Instead of applying a brute-force sweeping procedure as in the previous works, we analyze the dominant root locus and seek if the jump phenomenon occurs to conduct exact optimization at a low computational cost. Finally, extensive comparisons using actual experimental parameters are performed to explore various effects of the loop delay on vibration suppression and the benefits of the proposed MD-DDR in handling such issues over the conventional DDR that treats a single delay. This study fully exploits the strength of the distributed delayed control logic, moving the DDR concept closer to real applications and aiming to establish a broader design and analysis framework for the delayed resonator from a multiple-delay perspective.

Hierarchical multi-objective optimization of proton exchange membrane fuel cell with parameter uncertainty

It is important to improve the performance indexes including the net power and system efficiency for polymer electrolyte membrane fuel cell (PEMFC), especially considering the parameter uncertainty. To this end, this paper proposes a hierarchical multi-objective optimization framework including the off-line and on-line optimization. Firstly, a steadystate non-linear PEMFC system model is established as the base model. Secondly, an adaptive multi-objective particle swarm optimization (AMPSO) algorithm scheme is proposed in the off-line optimization procedure for the exact optimization of operation parameters. Meanwhile, an adaptive flight parameter strategy based on the particle dispersity (PD) information is proposed to balance the convergence and diversity of Pareto solutions. Finally, to decrease the influence caused by parameter uncertainty, the interval optimization method is proposed in the on-line optimization layer based on the results of AMPSO. The convergence condition of the proposed optimization scheme is verified by theory analysis. The proposed AMPSO is compared with different algorithms in the numerical simulation and hardware-in-loop (HIL) experiments. Meanwhile, the performance of the proposed method is tested on four representative benchmark problems. These results demonstrate that the PEMFC system with the proposed optimization scheme performs better than the base model and classical optimization algorithms in terms of the net power and system efficiency indexes, revealing the success of this hierarchical optimization approach in solving the accurate optimization and parameter uncertainty problems. By using statistical test methods, the proposed algorithm performs better hypervolume (HV) metric from the Pareto solution distribution.

Aptenodytes forsteri optimization algorithm for low-carbon logistics network under demand uncertainty.

As China's "double carbon" goal continues to advance, logistics as a key area of carbon emissions and low-carbon logistics center site selection are key links in the process. However, existing studies on logistics center location often ignore the impact of demand uncertainty, which leads to a waste of resources in the planning and construction processes. We take logistics cost and carbon emission as the objectives, and the multi-objective site selection model established based on stochastic programming theory takes demand uncertainty as a stochastic constraint. We transform the stochastic constraint model into a 0-1 mixed integer multi-objective planning model by utilizing the idea of equivalence transformation. The Aptenodytes Forsteri Optimization (AFO) algorithm is combined with the Ideal Point Method to solve the model, and the algorithm is compared with the Particle Swarm Optimization (PSO), Differential Evolutionary (DE), Tabu Search (TS), Sparrow Search (SS) algorithms, and the exact solver Linear Interactive and General Optimizer (LINGO). The examples verify the validity of the models and algorithms, with an average reduction of 6.2% and 3.6% in logistics costs and carbon emissions in the case of demand determination, and at the confidence level of 0.9 under demand uncertainty, both logistics costs and carbon emissions are decreased to varying degrees. This study provides a new research idea for the low-carbon logistics location problem under demand uncertainty, which helps to promote the transformation of the logistics industry to low-carbon and high-efficiency.

MUSIC: Accelerated Convergence for Distributed Optimization With Inexact and Exact Methods.

Gradient-type distributed optimization methods have blossomed into one of the most important tools for solving a minimization learning task over a networked agent system. However, only one gradient update per iteration makes it difficult to achieve a substantive acceleration of convergence. In this article, we propose an accelerated framework named multiupdates single-combination (MUSIC) allowing each agent to perform multiple local updates and a single combination in each iteration. More importantly, we equip inexact and exact distributed optimization methods into this framework, thereby developing two new algorithms that exhibit accelerated linear convergence and high communication efficiency. Our rigorous convergence analysis reveals the sources of steady-state errors arising from inexact policies and offers effective solutions. Numerical results based on synthetic and real datasets demonstrate both our theoretical motivations and analysis, as well as performance advantages.

Edge Selections in Bilinear Dynamic Networks

We develop some basic principles for the design and robustness analysis of a continuous-time bilinear dynamical network, where an attacker can manipulate the strength of the interconnections/edges between some of the agents/nodes. We formulate the edge protection optimization problem of picking a limited number of attack-free edges and minimizing the impact of the attack over the bilinear dynamical network. In particular, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{2}$</tex-math></inline-formula> -norm of bilinear systems is known to capture robustness and performance properties analogous to its linear counterpart and provides valuable insights for identifying which edges are most sensitive to attacks. The exact optimization problem is combinatorial in the number of edges, and brute-force approaches show poor scalability. However, we show that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{2}$</tex-math></inline-formula> -norm as a cost function is supermodular and, therefore, allows for efficient greedy approximations of the optimal solution. We illustrate and compare the effectiveness of our theoretical findings via numerical simulations.

The effect of modified atmosphere packaging at an early postmortem stage on lamb meat quality during subsequent aging.

This study explores the influence of modified atmosphere packaging (MAP) on fresh lamb meat quality with respect to gas concentration, rigor state, and post-mortem aging time. A comparison was done for the quality characteristics of lamb Longissimus thoracis lumborum chops that had been packaged separately in air, 75%O2 +25%CO2 MAP or 50%O2 +50%CO2 MAP at 1, 6, and 24h post-mortem and then stored for 6, 12, 24, 72, and 144h post-mortem, and the quality of lamb chops had been evaluated at each post-mortem period separately. Chops packaged at 1 and 6h post-mortem in MAP had reduced pH decline, less purge loss, and enhanced redness at early post-mortem storage times. Lamb color stability was evidently greater in 75%O2 +25%CO2 MAP than in 50%O2 +50%CO2 MAP during the early storage period when a* and R630/R580 were taken into account. Shear force values were lowest in lambs packaged at 1h post-mortem with 75%O2 +25%CO2 MAP at 12h post-mortem and then increased until 72h post-mortem, suggesting that rigor has been delayed by such a high O2 MAP. Thus, fresh lamb quality was maintained most effectively when packaged at 1h post-mortem in 75%O2 +25%CO2 MAP for consumption at 12h post-mortem. The exact mechanisms and optimization of MAP based on Chinese retail conditions should be considered in future studies. PRACTICAL APPLICATION: In this study, three slaughter patterns in the meat industry involving boning immediately after dressing (hot-boning) and chilling for a short period (warm-boning) or overnight (cold-boning) are considered, as well as the behavior of non-immediate consumption after purchase. Modified atmosphere packaging provides an effective preservation of early post-mortem muscles with enhanced color stability, water holding capacity, and texture during refrigerated storage. This could provide new insights into how to process lamb muscles in the early post-mortem period to improve and stabilize lamb quality.

Fair and efficient vaccine allocation: A generalized Gini index approach

The paper proposes an optimization model for the allocation of vaccines to a heterogeneous population composed of several subpopulations with different sizes and epidemiological disease transmission parameters. As the objective, an aggregated function combining a standard utilitarian efficiency criterion with a Gini index–related penalty term is considered. Contrary to previous work, we adopt an outcome equity view: The inequity measure is not based on vaccination fractions or other input factors, but on the fractions of individuals escaping infection, as predicted by an susceptible‐infectious‐removed (SIR) model. An adjusted pro rata (APR) policy of vaccine allocation minimizing inequity in this outcome view is introduced, and a numerical procedure for its determination is presented. The concepts are developed both for the case of segregated subpopulations and for that of interactions between the subpopulations. Interestingly, in a large number of instances, the optimal solution under the aggregated objective function turns out to be identical to APR. Whether APR is locally or even globally optimal in a concrete case depends on the relation of an inequity aversion parameter to certain threshold values. While the local optimality threshold can be determined by linear programming, the determination of the global optimality threshold, as the vaccine allocation problem itself, is a problem of nonconvex optimization. We suggest an exact optimization approach for smaller instances, and propose algorithms building on particle swarm optimization for threshold determination and allocation optimization at larger instances. Extensions to alternative outcome measures such as the number of fatalities are presented as well. In addition to the investigation of randomly generated instances, two test cases from the literature are revisited in the context of the present work. Moreover, a new case study based on data from the COVID‐19 outbreak in Austria in 2020 is introduced and analyzed.

Multi-objective optimization, comparison of using different biomass fuels in hybrid energy system for electricity-distilled water production based on supercritical CO2 and humidification and dehumidfication cycles

Biomass-derived power generation presents various potential benefits compared to conventional fossil fuel-based power generation. Also, efficient integration of energy systems leads to higher sustainability and effectiveness. This paper presents a biomass-fueled energy system with two open and closed Brayton cycles in the waste heat, of which a humidification and dehumidification system is implemented. The usage of four different biomasses as the fuel of the gasifier is tested and put to comparison from the aspects of thermodynamics, economics, and environment. The Grassman diagram for each layout is presented to signpost the exact point of highest exergy destruction and irreversibility. The optimization based on machine learning techniques is conducted to pinpoint the exact optimum operational conditions. The results indicate that wood offers more sustainability compared to other biomasses, and the amount of energy efficiency, exergy efficiency, and freshwater flow rate produced for Wood biomass in the proposed system are 75.81 %, 36.98 %, and 0.4091 kg/s, respectively. Also, two optimization scenarios have been done for this study. In the initial optimal solution finding, effectivness, unit product cost, and carbon dioxide emission index are equal to 45.9 %, 12.6 $/GJ, and 0.7161 kg/kWh, correspondingly. In the latter scenario, the effectiveness, net power production, and production unit cost of products are equal to 45.9 %, 6580 kW, and 12.61 $/GJ, respectively.

A Q-learning-based multi-objective evolutionary algorithm for integrated green production and distribution scheduling problems

In recent years, integrated production and distribution scheduling (IPDS) has received growing attention from academia and industry. With increasingly global economic activities, it is vital to extend IPDS to distributed environments. Besides, the production and distribution systems are the main contributors to carbon emissions due to their high energy consumption. Driven by this, this work introduces an integrated green distributed production and distribution scheduling problem with the objectives of total tardiness and total carbon emissions minimization. To provide a clear definition, a mixed-integer mathematical programming model is created. Considering the problem's NP-hard nature, a Q-learning-based multi-objective evolutionary algorithm (Q-MEA) is designed to handle it. To evaluate the performance of Q-MEA, a comparison pool including four variants, five meta-heuristics, and an exact optimizer named CPLEX is constructed to implement numerical experiments. The results demonstrate that Q-MEA has clear advantages over its rivals in tackling our problems. Furthermore, comparing the integrated model with a separate one shows that the former can achieve an average decrease of about 13.10% in total tardiness and 21.02% in total carbon emissions.

Heuristic algorithm for univariate stratification problem

In sampling theory, stratification corresponds to a technique used in surveys, which allows segmenting a population into homogeneous subpopulations (strata) to produce statistics with a higher level of precision. In particular, this article proposes a heuristic to solve the univariate stratification problem – widely studied in the literature. One of its versions sets the number of strata and the precision level and seeks to determine the limits that define such strata to minimize the sample size allocated to the strata. A heuristic-based on a stochastic optimization method and an exact optimization method was developed to achieve this goal. The performance of this heuristic was evaluated through computational experiments, considering its application in various populations used in other works in the literature, based on 20 scenarios that combine different numbers of strata and levels of precision. From the analysis of the obtained results, it is possible to verify that the heuristic had a performance superior to four algorithms in the literature in more than 94% of the cases, particularly concerning the known algorithm of Lavallée–Hidiroglou.

Distributed constrained optimization with periodic dynamic quantization

This paper uses the mirror descent algorithm with periodic dynamic quantization to solve constrained distributed optimization problems with limited communication channels. Due to the imperfect network environment, obtaining accurate information is impractical, and thus a communication scheme under quantization needs to be considered. A periodic dynamic quantizer with finite quantization levels is proposed in this paper to achieve exact optimization. Moreover, a time-varying control parameter in the mirror descent algorithm is designed to control the quantization error. After a comprehensive analysis, the proposed algorithm can obtain an optimal value, and the optimal convergence rate is O(1/T0.25).

An exact penalty function optimization method and its application in stress constrained topology optimization and scenario based reliability design problems

A smooth penalty function method which does not involve dual and slack implicit variables to formulate constrained optimization conditions is proposed. New active and loss functions are devised to independently and adaptively handle the violation of each constraint function. A single unconstrained minimization of the proposed penalty function produces a solution to the original optimization problem. The constrained optimization conditions depending only on the primal variable are derived and reduce to the canonical Karush-Kuhn-Tucker(KKT) conditions in a much more general framework. The derivative of the proposed loss functions with respect to constraint function can be interpreted as the Lagrange multiplier of the traditional Lagrangian function. The appearance of the first-order Hessian information is unveiled. This is in contrast to the existing works where the classical Lagrange Hessian contains only second order derivatives. Finally, some numerical examples including medium-scale stress constrained topology optimization and scenario based reliability design problems are presented to demonstrate the effectiveness of the proposed methodology.

Quickest change detection in statistically periodic processes with unknown post-change distribution

Algorithms are developed for the quickest detection of a change in statistically periodic processes. These are processes in which the statistical properties are nonstationary but repeat after a fixed time interval. It is assumed that the pre-change law is known to the decision maker but the post-change law is unknown. In this framework, three families of problems are studied: robust quickest change detection, joint quickest change detection and classification, and multi-slot quickest change detection. In the multi-slot problem, the exact slot within a period where a change may occur is unknown. Algorithms are proposed for each problem, and either exact optimality or asymptotic optimality in the low false alarm regime is proved for each of them. The developed algorithms are then used for anomaly detection in traffic data and arrhythmia detection and identification in electrocardiogram (ECG) data. The effectiveness of the algorithms is also demonstrated on simulated data.

A matheuristic approach for the family traveling salesman problem

In the family traveling salesman problem (FTSP), there is a set of cities which are divided into a number of clusters called families. The salesman has to find a shortest possible tour visiting a specific number of cities from each of the families without any restriction of visiting one family before starting the visit of another one. In this work, the general concept of the Partial OPtimization Metaheuristic Under Special Intensification Conditions is linked with the exact optimization by a classical solver using a mathematical programming formulation for the FTSP to develop a matheuristic. Moreover, a genetic and a simulated annealing algorithm are used as metaheuristics embedded in the approach. The method is examined on a set of benchmark instances and its performance is favorably compared with a state-of-the-art approach from literature. Moreover, a careful analysis of the specific components of the approach is undertaken to provide insights into the impact of their interplay.

Solving the incremental graph drawing problem by multiple neighborhood solution-based tabu search algorithm

With the advent of the era of big data, more and more complex networks and knowledge based systems require data visualization for analysis and presentation, where graphs have become a standard representation model. Graph drawing addresses the problems of constructing geometric representations of graphs to make them easy to analyze. In this paper we aim to reduce the edge crossing number in the context of the incremental graph drawing problem (IGDP), in which we want to preserve the layout of a graph over successive drawings to present complex networks or knowledge-based systems. Specifically, we propose a metaheuristic algorithm called multiple neighborhood solution-based tabu search (MNSB-TS) by combining a solution-based tabu strategy and a multiple neighborhood structure for solving the incremental graph drawing problem. Our MNSB-TS approach introduces four neighborhood operators to accompany the solution-based tabu strategy for determining the tabu status of each neighbor solution. Extensive computational experiments on public benchmark instances demonstrate that the proposed MNSB-TS is highly competitive in comparison with the state-of-the-art heuristics and the exact optimization solver Gurobi. Key components of the approach are analyzed to evaluate their impact on algorithm performance and learn which search mechanisms are better suited for incremental graph drawing.

Fast Vehicle Routing via Knowledge Transfer in a Reproducing Kernel Hilbert Space

Vehicle routing problems (VRPs) are essential in logistics. In the literature, many exact and heuristic optimization algorithms have been proposed to solve the VRPs. These traditional approaches, however, generally start the optimization from scratch and ignore the experiences of solving related VRPs, which may lead to unnecessary computational costs in searching repeated problems and reduce the efficiency of vehicle routing. Recently, transfer optimization (TO) has been presented to speed up vehicle routing by reusing the knowledge learned from similarly solved VRPs. However, existing TO methods build connections across VRPs in a low-dimensional Euclidean space, which has limited modeling ability in the cases of having nonlinear correlations. Keeping this in mind, this article presents a study of TO equipped with the kernel method for fast vehicle routing. In contrast to existing TO methods, in this work, the learning of connections across VRPs for knowledge transfer is conducted in a reproducing kernel Hilbert space (RKHS), which thus has greater modeling capacity in nonlinear customer relationships between VPRs. To evaluate the performance of the proposed method, comprehensive empirical studies have been conducted using well-known VRP benchmarks, against existing state-of-the-art TO methods for vehicle routing. Finally, a well-known real-world VRP application given by a routing company (Jingdong), namely, the package delivery problem (PDP), is investigated to further assess the efficacy of our proposed method.

An exact optimization method for coordinating the arrival times of urban rail lines at a common corridor

The trips of a high-frequency urban rail line are typically planned with the aim of achieving even time headways. This results in reliable services for each urban rail line, where successive trips have the same time headway. Maintaining even time headways for each service line has significant advantages for the passengers of the line, but it might result in safety issues, vehicle bunching, and increased transfer times at a common corridor served by multiple urban rail lines. This study investigates the problem of urban rail corridor coordination and develops an exact optimization method for coordinating the vehicle trips of different lines that serve stations along a joint corridor. The proposed formulation is a non-convex mathematical program which is reformulated as a mixed-integer quadratic program with a convex objective function. A branch-and-bound algorithm coupled with the Active-set method is proposed for solving the model to global optimality. Results from a toy network and a case study of the light rail service in The Hague, The Netherlands, demonstrate the improvement potential of time headways at a common corridor, while accounting for the effect on the variation of time headways at isolated segments of the individual service lines.

Design principles for NASICON super-ionic conductors

Na Super Ionic Conductor (NASICON) materials are an important class of solid-state electrolytes owing to their high ionic conductivity and superior chemical and electrochemical stability. In this paper, we combine first-principles calculations, experimental synthesis and testing, and natural language-driven text-mined historical data on NASICON ionic conductivity to achieve clear insights into how chemical composition influences the Na-ion conductivity. These insights, together with a high-throughput first-principles analysis of the compositional space over which NASICONs are expected to be stable, lead to the successful synthesis and electrochemical investigation of several new NASICONs solid-state conductors. Among these, a high ionic conductivity of 1.2 mS cm−1 could be achieved at 25 °C. We find that the ionic conductivity increases with average metal size up to a certain value and that the substitution of PO4 polyanions by SiO4 also enhances the ionic conductivity. While optimal ionic conductivity is found near a Na content of 3 per formula unit, the exact optimum depends on other compositional variables. Surprisingly, the Na content enhances the ionic conductivity mostly through its effect on the activation barrier, rather than through the carrier concentration. These deconvoluted design criteria may provide guidelines for the design of optimized NASICON conductors.

An innovative two-stage algorithm to optimize Firewall rule ordering

Packet classification activity performed by a FireWall (FW) introduces high latency in network communications due to the computation time required to check whether any packet matches one of the FW rules. Such a classification process is done by sequentially checking the list of rules until a match is found or the end of the list is reached. Given the complexity of FW rules in some environments, this latency could become relevant. This problem is addressed by ordering the list of FW rules to minimize the classification latency, where the rules with higher activation frequencies are placed accordingly starting from the top of the list. This is not always feasible because dependency constraints between rules could exist: swapping the positions of dependent rules results in a loss of the integrity of the implemented security policy. For this reason, the FW rule ordering problem belongs to the realm of constrained combinatorial optimization.This paper proposes a two-stage algorithm to address this problem. The first stage performs an innovative topological sorting algorithm aimed at finding an optimal ordering for the constrained rules, taking into account the fact that rule activation frequencies are influenced by inter-packet arrival time, which typically obeys Zipf's law. The second stage employs a genetic algorithm to find the optimal ordering of all rules within the list. The proposed approach is evaluated using different filtering lists of different complexity provided by ClassBench. A comparison with other state-of-the-art algorithms addressing the same problem is performed. Furthermore, the performance analysis is extended employing an exact optimization method. The results obtained show the effectiveness of the proposed algorithm in minimizing packet classification latency, while a short reordering time is required.

Mixed-integer programming models for irregular strip packing based on vertical slices and feasibility cuts

The irregular strip-packing problem, also known as nesting or marker making, is defined as the automatic computation of a non-overlapping placement of a set of non-convex polygons onto a rectangular strip of fixed width and unbounded length, such that the strip length is minimized. Nesting methods based on heuristics are a mature technology, and currently, the only practical solution to this problem. However, recent performance gains of the Mixed-Integer Programming (MIP) solvers, together with the known limitations of the heuristics methods, have encouraged the exploration of exact optimization models for nesting during the last decade. Despite the research effort, there is room to improve the efficiency of the current family of exact MIP models for nesting. In order to bridge this gap, this work introduces a new family of continuous MIP models based on a novel formulation of the NoFit-Polygon Covering Model (NFP-CM), called NFP-CM based on Vertical Slices (NFP-CM-VS). Our new family of MIP models is based on a new convex decomposition of the feasible space of relative placements between pieces into vertical slices, together with a new family of valid inequalities, symmetry breakings, and variable eliminations derived from the former convex decomposition. Our experiments show that our new NFP-CM-VS models outperform the current state-of-the-art MIP models. Ten instances are solved up to optimality within one hour for the first time, including one with 27 pieces. Finally, we provide a detailed reproducibility protocol and dataset as supplementary material to allow the exact replication of our models, experiments, and results.