Finding Optimal Solutions Research Articles

SMT-Based Contention-Free Task Mapping and Scheduling on 2D/3D SMART NoC with Mixed Dimension-Order Routing

SMART NoCs achieve ultra-low latency by enabling single-cycle multiple-hop transmission via bypass channels. However, contention along bypass channels can seriously degrade the performance of SMART NoCs by breaking the bypass paths. Therefore, contention-free task mapping and scheduling are essential for optimal system performance. In this article, we propose an SMT (Satisfiability Modulo Theories)-based framework to find optimal contention-free task mappings with minimum application schedule lengths on 2D/3D SMART NoCs with mixed dimension-order routing. On top of SMT’s fast reasoning capability for conditional constraints, we develop efficient search-space reduction techniques to achieve practical scalability. Experiments demonstrate that our SMT framework achieves 10× higher scalability than ILP (Integer Linear Programming) with 931.1× (ranges from 2.2× to 1532.1×) and 1237.1× (ranges from 4× to 4373.8×) faster average runtimes for finding optimum solutions on 2D and 3D SMART NoCs and our 2D and 3D extensions of the SMT framework with mixed dimension-order routing also maintain the improved scalability with the extended and diversified routing paths, resulting in reduced application schedule lengths throughout various application benchmarks.

DECISION-MAKING MECHANISMS REGARDING THE ESTABLISHMENT OF THE FINANCING SOURCES OF THE INVESTMENT PROGRAMS IN PUBLIC UTILITY SERVICES

This paper is an empirical study that addresses a topical issue in terms of decision-making methods for setting up sources of funding for investment programs in public utilities in Romania. In order to ensure a high level of security and accessibility, equal treatment, promotion of universal access and users’ rights, public utilities are subject to specific public service obligations. Considering that in the utilities services there is still a process of implementation of the European requirements regarding the satisfaction of the quantitative and qualitative requirements of the users; consumer protection and quality of life, environmental conservation in accordance with specific regulations in force, sustainable development, protection and capitalization of the public and private domain of territorial administrative units, it is necessary to introduce modern management methods to achieve these desired. The deepening of the notions, of the particularities in the field, creates the premises for finding optimal and viable solutions regarding the improvement of the legal framework of functioning and operation in the public utilities services, so that the decisional and financial mechanisms are the optimal ones in the concrete socio-economic conditions. Considering the public and permanent functioning of the public utility services, the approached topic is of a real interest for any entity in the field concerned with the efficient, economic and effective management of the public utility system. In this regard, the establishment of the maintenance, replacement, development fund for all entities in the field of public utility services (and not only for those receiving external funds) is a real opportunity, highlighted and supported by existing investment programs in the field of water, sewerage, wastewater treatment and rainwater collection.

Проектування системи автоматизованого генерування віршованих творів

Features of designing a system of automated generation of poetic works, which opens up new opportunities for artistic speech and show business, especially the preparation of poems and songs have been considered. Quite often lyrics without special content become successful due to the lack of complex plots, as well as due to the unobtrusiveness and ease of perception by listeners. Well-known literature sources and available software products that can generate poetic works by combining different methods and algorithms are analyzed. It has been established that none of them is able to ensure the content and uniqueness of the poetic work at the same time, especially in the Ukrainian language. The existing approaches to the generation of poetic works are analysed, among which the relevant is a method based on templates, generation and testing, evolutionary algorithms and the method based on specific cases. Peculiarities of generating poetical works, first of all rhyming rules, types of strophes, poetic rhythms and sizes have been investigated. An approach to automated generation of poetic works using evolutionary algorithms and a method based on specific cases have been developed. Their combination resembles a sequence of actions for creative personalities when creating poems or writing lyrics. Peculiarities of neural network organization for automated generation of poetic works have been considered. It is proposed to perform neural network training using the method of inverse propagation and using a genetic algorithm. The principle of operation of algorithms for finding optimal solutions which contain such consecutive stages as initialization, evaluation of solutions, population selection, evolution of solutions, is analysed. Their interaction and various opportunities for neural network learning have been investigated in detail. An algorithm has been developed according to which the software application will analyse the poetic works offered by the user and generate new variants of it on the basis received from the neural network of logically connected words or lines of the verse in the poem. The user can edit both the components of the poem and the generated poetic works, and thus can train the neural network. The specification of requirements to the software application has been developed, the basic requirements to the user interface are defined, and also potential classes of users who will use it are established. Keywords: computational linguistics; Artificial Intelligence; neural network; genetic algorithm; optimal solution.

Techno-economic optimization of a district heat condenser in a small cogeneration plant with a novel greedy cuckoo search

The goal of the study was to develop an optimization methodology combining a cost model, a 2-D heat transfer model, and load variation, executable in a feasible time in a personal computer. The objective function to maximize is the annual net cash flow. For this purpose, the cogeneration plant performance is determined at different load points as a function of the condenser performance using IPSEpro process simulation software. This data is then used to implement the calculation process to obtain the objective function value. Due to the computationally heavy heat transfer model, and each objective function evaluation requiring multiple runs, one per load point, improving optimizer performance was given particular attention. A novel hybridization of cuckoo search and a greedy differential evolution strategy was created for this; the new algorithm is shown to perform better than either of its parent algorithms or other benchmarks, finding optimal solution reliably, and within approximately half the number of function evaluations as required by the parent algorithms.

A modeler's guide to handle complexity in energy systems optimization

• Holistic review of complexity management methods in energy systems optimization. • Data availability drives model sizes and therefore the model complexity. • Systematic temporal down-sampling or aggregation are widespread and easily accessible while spatial aggregation has only a small community. • Decomposition methods still need to be customized to the model wherefore exploitation of parallel compute infrastructure requires high efforts. • Level of details in system modeling drives non-convexity and is often avoided. Determining environmentally- and economically-optimal energy systems designs and operations is complex. In particular, the integration of weather-dependent renewable energy technologies into energy system optimization models presents new challenges to computational tractability that cannot only be solved by advancements in computational resources. In consequence, energy system modelers must tackle the complexity of their models by applying various methods to manipulate the underlying data and model structure, with the ultimate goal of finding optimal solutions. As which complexity reduction method is suitable for which research question is often unclear, herein we review different approaches for handling complexity. We first analyze the determinants of complexity and note that many drivers of complexity could be avoided a priori with a tailored model design. Second, we conduct a review of systematic complexity reduction methods for energy system optimization models, which can range from simple linearization performed by modelers to sophisticated multi-level approaches combining aggregation and decomposition methods. Based on this overview, we develop a guide for energy system modelers who encounter computational limitations.

A Hybrid Bat Algorithm for Solving the Three-Stage Distributed Assembly Permutation Flowshop Scheduling Problem

In this paper, a hybrid bat optimization algorithm based on variable neighbourhood structure and two learning strategies is proposed to solve a three-stage distributed assembly permutation flowshop scheduling problem to minimize the makespan. The algorithm is firstly designed to increase the population diversity by classifying the populations, which solves the difficult trade-off between convergence and diversity of the bat algorithm. Secondly, a selection mechanism is used to update the bat’s velocity and location, solving the difficulty of the algorithm to trade-off exploration and mining capacity. Finally, the Gaussian learning strategy and elite learning strategy assist the whole population to jump out of the local optimal frontier. The simulation results demonstrate that the algorithm proposed in this paper can well solve the DAPFSP. In addition, compared with other metaheuristic algorithms, IHBA has better performance and gives full play to its advantage of finding optimal solutions.

Methodology Of Application Of The Simplex Method In The Optimal Development Of Industrial Enterprises

Methods of solving mathematical models of industrial enterprises using the simplex method, which is one of the most important methods of constructing mathematical models, are shown in finding optimal solutions to economic problems.

Energy-efficient dispatch of multiple-chiller systems using hybrid exchange market and genetic algorithm

The inefficient dispatch of multiple-chiller systems results in drastic energy consumption, which should be investigated by optimal allocating of cooling loads between chillers in a building. Due to the nonlinearity of the dispatching problem, heuristic algorithms are more prevalent in this field. In this paper, a hybrid exchange market and genetic algorithm (EMGA) is established to solve the optimal chiller loading (OCL) problem. The decision variables of the problem are the partial load ratio (PLR) of chillers determining the power consumption of each chiller unit, and the objective of the OCL problem is to minimize the total power consumption of the multiple-chiller system. The effectiveness of the proposed algorithm is verified by a fair comparison of the results with similar attributes in three identical cases. It is shown that the proposed EMGA outperforms comparable algorithms in terms of convergence speed and finding optimal solutions. Moreover, the problem is modeled as mixed-integer non-linear programming (MINLP) in the general algebraic modeling system (GAMS) to solve mathematically using different solvers. It was shown that the mathematical approaches adopted by GAMS have a high probability of trapping in local optima when the decision variables are increasing, whiles the optimum solutions by the proposed EMGA are superior.

A new dynamic shape adjustment and placement algorithm for 3D yard allocation problem with time dimension

This paper studies a yard allocation problem at a container terminal, namely the 3D yard allocation problem with time dimension (3DYAPT), that determines the container storage locations in a given storage block to satisfy requirements from batches of arrived containers. The objective is to minimize the two-dimensional area of the storage block occupied for temporarily storing the containers within a given planning horizon (time dimension). The 3DYAPT is challenging and proved to be strongly NP-hard since it requires dynamically adjusting the shape of the allocated area when placing containers from the same request. We formulate the 3DYAPT as an integer linear programming model and develop a simulated annealing-based dynamic shape adjustment and placement algorithm (SA-DSAP). The simulated annealing-based algorithm comprises a novel dynamic programming procedure with several speed-up techniques that sequentially computes the storage space solution given a particular sequence of requests. Extensive computational experiments are conducted, showing that SA-DSAP is capable of finding optimal solutions very efficiently for nearly all small instances. For large instances, we also find that SA-DSAP produces significantly better heuristic solutions than the existing algorithm from the literature.

The overlap gap property: A topological barrier to optimizing over random structures

The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures, finding optimal solutions by means of fast algorithms is not known and often is believed not to be possible. At the same time, the formal hardness of these problems in the form of the complexity-theoretic NP-hardness is lacking. A new approach for algorithmic intractability in random structures is described in this article, which is based on the topological disconnectivity property of the set of pairwise distances of near-optimal solutions, called the Overlap Gap Property. The article demonstrates how this property 1) emerges in most models known to exhibit an apparent algorithmic hardness; 2) is consistent with the hardness/tractability phase transition for many models analyzed to the day; and, importantly, 3) allows to mathematically rigorously rule out a large class of algorithms as potential contenders, specifically the algorithms that exhibit the input stability (insensitivity).

Strategic Environmental Assessment in the Application of Preventive Protection for Wind Farm Noise—Case Study: Maestrale Ring Wind Farm

Determining the spatial position of wind turbines is the initial and most important phase in the development of a wind farm project. In this sensitive phase, all potential problems that may arise in the later stages of project development should be prevented by means of spatial and urban planning instruments. This makes it possible to achieve maximum use of the potential of wind in a particular space and, thus, fulfil the technical and economic requirements of the project while respecting the goals of environmental protection in that same area, through preventive protection. Therefore, it is essential, even at the earliest planning and development stage of a wind farm project, for the requirements that are important for optimal spatial solutions to be balanced. In this process, strategic environmental assessment (SEA) is a support to the planning process and an invaluable instrument for finding optimal spatial solutions for the possible key spatial impacts of wind power with regard to noise, shadow flicker, ornithofauna and chiropterofauna. The weakness of SEA can be seen in its predominant application of expert qualitative methods that bring with them subjectivity, since they depend on expert knowledge and skills. This paper presents the aspect of noise impact assessment and its inclusion in the SEA for the Maestrale Ring wind farm in Serbia. The results of the research indicate how it is possible to achieve the principle of objectivity in the process of multicriteria expert evaluation by including the results of a partial impact assessment of the noise from wind farms, using results obtained from software modeling of the spatial dispersion of wind turbine noise in the SoundPlan 8.1 software package in the SEA process. These quantitative results predicting the noise level were used in a semi-quantitative method of multicriteria evaluation in the SEA through the definition of criteria to determine the ranking of impacts, which is elaborated in the paper. The results also show the significant of the contribution of applying a methodological approach based on a combination of qualitative and quantitative evaluation methods in SEA. These methods positively affect the application of the principle of preventive protection through the optimal selection of the number and position of wind turbines on one hand and the objectivity of drawing conclusions based on which strategic decisions are made in the final phase of the SEA process, on the other.

Exact optimization and decomposition approaches for shelf space allocation

Shelf space is one of the scarcest resources, and its effective management to maximize profits has become essential to gain a competitive advantage for retailers. We consider the shelf space allocation problem with additional features (e.g., integer facings, rectangular arrangement restrictions) motivated by literature and our interactions with a local bookstore. We determine optimal number of facings of all products in two aspects (width and height of a rectangular arrangement space for each product), and allocate them as contiguous rectangles to maximize profit. We first develop a mixed-integer linear mathematical programming model (MIP) for our problem and propose a solution method based on logic-based Benders decomposition (LBBD). Next, we construct an exact 2-stage algorithm (IP1/IP2), inspired by LBBD, which can handle larger and real-world size instances. To compare performances of our methods, we generate 100 test instances inspired by real-world applications and benchmarks from the literature. We observe that IP1/IP2 finds optimal solutions for real-world instances efficiently and can increase the local bookstore’s profit up to 16.56%. IP1/IP2 can provide optimal solutions for instances with 100 products in minutes and optimally solve up to 250 products (assigned to 8 rows x 160 columns) within a time limit of 1800 s. This exact 2-stage IP1/IP2 solution approach can be effective in solving similar problems such as display problem of webpage design, allocation of product families in grocery stores, and flyer advertising.

Comparing Mixed-Integer Programming and Constraint Programming Models for the Hybrid Flow Shop Scheduling Problem with Dedicated Machines

The paper considers a two-stage hybrid flow shop scheduling problem with dedicated machines and release dates. Each job must be first processed on the single machine of stage 1, and then, the job is processed on one of the two dedicated machines of stage 2, depending on its type. Moreover, the jobs are available for processing at their respective release dates. Our goal is to obtain a schedule that minimizes the makespan. This problem is strongly NP-hard. In this paper, two mathematical models are developed for the problem: a mixed-integer programming model and a constraint programming model. The performance of these two models is compared on different problem configurations. And the results show that the constraint programming outperforms the mixed-integer programming in finding optimal solutions for large problem sizes (450 jobs) with very reasonable computing times.

Optimal Life Extension Management of Offshore Wind Farms Based on the Modern Portfolio Theory

The present study aims to develop a risk-based approach to finding optimal solutions for life extension management for offshore wind farms based on Markowitz’s modern portfolio theory, adapted from finance. The developed risk-based approach assumes that the offshore wind turbines (OWT) can be considered as cash-producing tangible assets providing a positive return from the initial investment (capital) with a given risk attaining the targeted (expected) return. In this regard, the present study performs a techno-economic life extension analysis within the scope of the multi-objective optimisation problem. The first objective is to maximise the return from the overall wind assets and the second objective is to minimise the risk associated with obtaining the return. In formulating the multi-dimensional optimisation problem, the life extension assessment considers the results of a detailed structural integrity analysis, a free-cash-flow analysis, the probability of project failure, and local and global economic constraints. Further, the risk is identified as the variance from the expected mean of return on investment. The risk–return diagram is utilised to classify the OWTs of different classes using an unsupervised machine learning algorithm. The optimal portfolios for the various required rates of return are recommended for different stages of life extension.

Finding Bounded Suboptimal Multi-Agent Path Planning Solutions Using Increasing Cost Tree Search (Extended Abstract)

The Increasing Cost Tree Search (ICTS) algorithm is used to produce optimal solutions to the multi-agent path finding problem (MAPF). In this problem, multiple agents are trying to reach their goals without conflicting with each other, while minimizing the total cost of the paths. ICTS has been shown to be very effective in finding optimal solutions. In this paper we consider the problem of finding solutions with bounded suboptimality by changing the order in which ICTS searches its increasing cost tree. With a variety of strategies, we are unable to consistently and significantly reduce the cost of ICTS. Further experimentation suggests why significantly more work is needed to modify ICTS to find suboptimal solutions.

A* Variants for Optimal Multi-Agent Pathfinding

Several variants of A* have been recently proposed for find-ing optimal solutions for the multi-agent pathfinding (MAPF)problem. We describe the application of the new enhancedpartial-expansion technique to MAPF, show how patterndatabases can be applied on top of this technique and com-pare the different A* variants experimentally.

A novel ameliorated Harris hawk optimizer for solving complex engineering optimization problems

This article presents a metaheuristic algorithm namely Ameliorated Harris Hawk Optimizer (AHHO) to solve multiconstrained optimization problems. AHHO mimics the hunting behavior of Harris Hawks and is modified to draw a synergy between exploration and exploitation by conducting neighborhood search of already visited iterations utilizing random exploratory forage and local random forage. The oppositional based learning has been incorporated to generate adequate diversity among solutions. The proposed algorithm is substantiated on a set of 23 standard benchmark functions to test its characteristics in finding optimal solutions. The algorithm is mathematically modeled in the current work to obtain solution for voltage constrained reactive power dispatch (VCRPD) problem for IEEE 57 and 118 bus systems. The proposed method of VCRPD is implemented first with shunt capacitors as var sources and then replacing them with static var compensator (SVC) for improved performance. The optimal placement of SVC is determined by fast voltage stability index method. The proposed AHHO algorithm reduces the transmission losses by 9.42% with shunt capacitors in IEEE 57 bus and 10.344% in IEEE 118 bus system. Similarly, transmission loss with SVC compensated system is reduced by 12.86% in IEEE 57 bus and 14.74% in IEEE 118 bus system. Results reveal the proposed technique has the potent to solve real world optimization problems and is competitive with recent methods reported in state-of- art literature.

Optimal task scheduling for partially heterogeneous systems

Task scheduling with communication delays is a strongly NP-hard problem. Previous attempts at finding optimal solutions to this problem have used branch-and-bound state–space search, with promising results. However, the scheduling model used assumes a target system with fully homogeneous processors, which is unrealistic for many real world systems for which task scheduling might be performed. This paper presents an extension to the Allocation-Ordering (AO) state–space model for task scheduling which allows a system with related heterogeneous processors to be modeled, and optimal schedules on such a system to be found. Of particular note, the distinct allocation phase allows this model to efficiently adapt to partially heterogeneous systems, in which subsets of the processors are identical to each other, which significantly helps to reduce the search space. An extensive experimental evaluation shows that the introduction of heterogeneity certainly increases the difficulty of the problem. However, many problem instances solvable using homogeneous processors remain solvable with a heterogeneous target system, made possible by the significant benefit of this model in considering partial heterogeneity.

Combinatorial optimization by weight annealing in memristive hopfield networks

The increasing utility of specialized circuits and growing applications of optimization call for the development of efficient hardware accelerator for solving optimization problems. Hopfield neural network is a promising approach for solving combinatorial optimization problems due to the recent demonstrations of efficient mixed-signal implementation based on emerging non-volatile memory devices. Such mixed-signal accelerators also enable very efficient implementation of various annealing techniques, which are essential for finding optimal solutions. Here we propose a “weight annealing” approach, whose main idea is to ease convergence to the global minima by keeping the network close to its ground state. This is achieved by initially setting all synaptic weights to zero, thus ensuring a quick transition of the Hopfield network to its trivial global minima state and then gradually introducing weights during the annealing process. The extensive numerical simulations show that our approach leads to a better, on average, solutions for several representative combinatorial problems compared to prior Hopfield neural network solvers with chaotic or stochastic annealing. As a proof of concept, a 13-node graph partitioning problem and a 7-node maximum-weight independent set problem are solved experimentally using mixed-signal circuits based on, correspondingly, a 20 × 20 analog-grade TiO2 memristive crossbar and a 12 × 10 eFlash memory array.

Solving Clique Partitioning Problems: A Comparison of Models and Commercial Solvers

Finding good solutions to clique partitioning problems remains a computational challenge. With rare exceptions, finding optimal solutions for all but small instances is not practically possible. However, choosing the most appropriate modeling structure can have a huge impact on what is practical to obtain from exact solvers within a reasonable amount of run time. Commercial solvers have improved tremendously in recent years and the combination of the right solver and the right model can significantly increase our ability to compute acceptable solutions to modest-sized problems with solvers like CPLEX, GUROBI and XPRESS. In this paper, we explore and compare the use of three commercial solvers on modest sized test problems for clique partitioning. For each problem instance, a conventional linear model from the literature and a relatively new quadratic model are compared. Extensive computational experience indicates that the quadratic model outperforms the classic linear model as problem size grows.