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Deep neural networks (DNNs) have witnessed widespread adoption across various domains. However, their computational demands pose significant challenges due to the extensive inter-neuron communication within the network. Moreover, the energy consumption of DNNs is substantial, primarily driven by the vast data movement and computational requirements. To overcome these challenges, novel accelerator architectures are essential. In this study, we present a novel heuristic algorithm for neuron grouping, catering to both fully connected and partially pruned DNN models. Our algorithm aims to minimize the overall data communication cost among neuron groups while also considering computational load balance. It outperforms existing heuristic neuron grouping methods classified into three main approaches from the literature by an average improvement in communication cost ranging from 33.01% to 47.11%. By optimizing neuron grouping, our approach may be used to enhance the efficiency of DNN accelerators, enabling improved performance and reduced energy consumption.

Parallel programs may be represented as a set of interrelated sequential tasks. When multiprocessors are used to execute such programs, the parallel portion of the application can be speeded up by an appropriate allocation of processors to the tasks of the application. Given a parallel application defined by a task precedence graph, the goal of task scheduling (or processor assignment) is thus the minimization of the makespan of the application. In a heterogeneous multiprocessor system, task scheduling consists of determining which tasks will be assigned to each processor, as well as the execution order of the tasks assigned to each processor. In this work, we apply the tabu search metaheuristic to the solution of the task scheduling problem on a heterogeneous multiprocessor environment under precedence constraints. The topology of the Mean Value Analysis solution package for product form queueing networks is used as the framework for performance evaluation. We show that tabu search obtains much better results, i.e., shorter completion times, improving from 20 to 30% the makespan obtained by the most appropriate algorithm previously published in the literature.

The scheduling problem deals with the optimal assignment of a set of tasks to processing elements in a distributed system such that the total execution time is minimized. One approach for solving the scheduling problem is task clustering. This involves assigning tasks to clusters where each cluster is run on a single processor. This paper aims to show the feasibility of using Genetic Algorithms for task clustering to solve the scheduling problem. Genetic Algorithms are robust optimization and search techniques that are used in this work to solve the task-clustering problem. The proposed approach shows great promise to solve the clustering problem for a wide range of clustering instances.

Hopfield neural network (HNN) is a nonlinear computational model successfully applied in finding near-optimal solutions of several difficult combinatorial problems. In many cases, the network energy function is obtained through a learning procedure so that its minima are states falling into a proper subspace (feasible region) of the search space. However, because of the network nonlinearity, a number of undesirable local energy minima emerge from the learning procedure, significantly effecting the network performance.

In the neural model analyzed here, we combine both a penalty and a stochastic process in order to enhance the performance of a binary HNN. The penalty strategy allows us to gradually lead the search towards states representing feasible solutions, so avoiding oscillatory behaviors or asymptotically instable convergence. Presence of stochastic dynamics potentially prevents the network to fall into shallow local minima of the energy function, i.e., quite far from global optimum. Hence, for a given fixed network topology, the desired final distribution on the states can be reached by carefully modulating such process.

The model uses pseudo-Boolean functions both to express problem constraints and cost function; a combination of these two functions is then interpreted as energy of the neural network. A wide variety of NP-hard problems fall in the class of problems that can be solved by the model at hand, particularly those having a monotonic quadratic pseudo-Boolean function as constraint function. That is, functions easily derived by closed algebraic expressions representing the constraint structure and easy (polynomial time) to maximize.

We show the asymptotic convergence properties of this model characterizing its state space distribution at thermal equilibrium in terms of Markov chain and give evidence of its ability to find high quality solutions on benchmarks and randomly generated instances of two specific problems taken from the computational graph theory.

The problem of automatic scheduling hypermedia documents consists in finding the optimal starting times and durations of objects to be presented, to ensure spatial and temporal consistency of a presentation while respecting limits on shrinking and stretching the ideal duration of each object. The combinatorial nature of the minimization of the number of objects whose duration is modified makes it the most difficult objective to be tackled by optimization algorithms. We formulate this scheduling problem as a mixed integer programming problem and report some preliminary investigations. We propose an original approach to the minimization of the number of objects which are shrinked or stretched. A simple primal heuristic based on variable fixations along the solution of a sequence of linear relaxations of the mixed integer programming formulation is described. Computational experiments on realistic size problems are reported. The effectiveness of the heuristic in finding good approximate solutions within very small processing times makes of it a quite promising approach to be integrated within existing document formatters to perform compile time scheduling or even run time adjustments. We also discuss results obtained by Lagrangean relaxation and propose a dual heuristic using the modified costs, which consistently improves the solutions found by the primal heuristic.

This article presents a new heuristic for generalized assignment problems with a very large number of jobs. The heuristic applies a probabilistic acceptance of a move, based on a percentile threshold, using information from recent moves. This percentile search heuristic (PSH) is compared to tabu search, simulated annealing, and threshold accepting using a rigorous computational experimentation with randomly generated problem instances of up to 50,000 jobs and 40 agents. The PSH did find the best solution among the heuristics for 45% of the instances, particularly larger size problems, versus 30% for tabu search, but required more fine-tuning of the heuristic parameters.

We propose the use of metaheuristics for the resource-capacitated multilevel lot-sizing problem with general product structures, setup costs, setup times, and lead times. Initially, we develop a heuristic which moves production in time in order to obtain feasible solutions with good quality. Strategies for the short-term memory and long-term memory of tabu search are then included to guide the search of the subordinate heuristic for new, feasible, and better solutions. Simulated annealing components are embedded into tabu search in order to improve its performance. For small problems, the solutions provided by tabu search and the hybrid metaheuristic are compared to optimal solutions and for larger problems, the quality of the solutions is evaluated against a lower bound generated by Lagrangean relaxation.

This paper considers quality of service in terms of end-to-end delay in planning backup routes for multicast communications. The problem of preplanning backup routes considering both cost minimization and end-to-end delay guarantee for multicast communications in the case a single link failure is investigated. Two delay labels, the limited label and the tolerable label, are defined to evaluate the end-to-end delay requirement. Four heuristic algorithms, including two tree-based algorithms, one subtree-based algorithm, and one link-based algorithm, are proposed to determine the delay-constrained backup routes having the minimum costs. Two procedures to determine a node selection sequence, Random and Minimum-Cost, are used in the tree-based algorithm. Experimental results show that the tree-based algorithm by the Minimum-Cost sequence yields the best performance in cost minimization with guarantee of end-to-end delay.

In this paper, we present a hybrid genetic algorithm for a version of the early/tardy scheduling problem in which no unforced idle time may be inserted in a sequence. The chromosome representation of the problem is based on random keys. The genetic algorithm is used to establish the order in which the jobs are initially scheduled, and a local search procedure is subsequently applied to detect possible improvements. The approach is tested on a set of randomly generated problems and compared with existing efficient heuristic procedures based on dispatch rules and local search. The computational results show that this new approach, although requiring slightly longer computational times, is better than the previous algorithms in terms of solution quality.

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Several dispatching rules are considered as evaluation functions, to analyze the effect of different rules on the effectiveness of the beam search algorithms.

The computational results show that using better rules improves the performance of the beam search heuristics. The detailed, filtered beam search (FBS) and recovering beam search (RBS) procedures outperform the best existing heuristic. The best results are given by the recovering and detailed variants, which provide objective function values that are quite close to the optimum. For small to medium size instances, either of these procedures can be used. For larger instances, the detailed beam search (DBS) algorithm requires excessive computation times, and the RBS procedure then becomes the heuristic of choice.

In this paper, we have proposed a hybrid permutation-coded steady-state genetic algorithm for a single machine scheduling problem with earliness and tardiness costs and no machine idle time. The steady-state genetic algorithm generates schedules, which are further improved by successive applications of an adjacent pairwise interchange procedure. We have compared our approach against the best approaches reported in the literature. Computational results show the effectiveness of our approach, since it obtained better quality solutions in shorter time.

This paper describes a tabu search approach for a multiprocessor scheduling problem, where a list of jobs has to be scheduled on identical parallel processors. Each job in the list has a release date, a due date, a processing time and a set of predecessors. The objective is to minimize the number of processors used while respecting the constraints imposed by release dates, due dates and precedences. Two versions of this problem are considered here, in the first one precedence constraints are relaxed, they are taken into account in the second one. The proposed method is used to solve High Level Synthesis problem instances. The results show the effectiveness of our approach for both versions of the problem. A comparison with an exact method is also conducted.

Tabu search (TS) has always been a very popular algorithm for graph coloring, both as a stand-alone optimizer as well as a subroutine inside population-based hybrid methods. We present two TS extensions that could allow previous TS algorithms to improve their behavior at almost no additional computational cost. First, we integrate two new evaluation functions which employ supplementary (structural or dynamic) information in addition to the conventional objective function (the number of edges with both ends of the same color). These new evaluation functions allow the search process to differentiate configurations not distinguished by the conventional evaluation function. The second extension concerns a reactive mechanism for improving the tabu list management. Theoretical arguments show that this reactive component completely eliminates the risk of getting blocked looping on plateaus. Numerical experiments show that the two proposed TS extensions can be very useful inside a stand-alone TS optimizer, as well as inside TS subroutines of state-of-the-art hybrid methods.

Logistics delivery companies typically deal with delivery problems that are strictly constrained by time while ensuring optimality of the solution to remain competitive. Often, the companies depend on intuition and experience of the planners and couriers in their daily operations. Therefore, despite the variability-characterizing daily deliveries, the number of vehicles used every day are relatively constant. This motivates us towards reducing the operational variable costs by proposing an efficient heuristic that improves on the clustering and routing phases. In this paper, a decision support system (DSS) and the corresponding clustering and routing methodology are presented, incorporating the driver’s experience, the company’s historical data and Google map’s data. The proposed heuristic performs as well as $k$-means algorithm while having other notable advantages. The superiority of the proposed approach has been illustrated through numerical examples.

In any airline’s schedule development process, aircraft rotations must be planned for individual fleet types after fleet assignment. The aircraft rotation plans must conform to stringent maintenance requirements and this problem can be formulated as a periodic routing problem on an Eulerian graph. We analyze the computational complexity of developing maintenance rotations when some overnighting aircraft may not have sufficient time on the ground to complete extended maintenance (referred to as a maintenance infeasibility). The paper also provides a theoretical analysis of heuristics for the aircraft maintenance rotation problem with maintenance infeasibilities.

The parallel implementation of image processing algorithms implies an important choice of data distribution strategy. In order to handle the specific constraints associated with images, data distribution must take into account not only the locality of the data and its geometrical regularity but also the possible irregular computation costs associated with different image elements. A widely studied field to tackle this problem is the family of methods related to rectilinear partitioning. We introduce two fully parallel heuristics that compute suboptimal partitions, with a better complexity than the best known algorithms that compute optimal partitions. In this paper, we compare our heuristics to an optimal partitioning, both in terms of execution time and accuracy of the partition. We give some theoretical bounds on the quality of these heuristics that are corroborated by results of random numerical experiments and real applications.

This paper presents a mathematical model for the test selection problem in protocol conformance testing, the goal of which is to select a suitable test set from a given test suite. The problem is described together with its mathematical formulation including two optimization problems and four different models for the coverage. The test selection problem is shown to be NP-hard. The Integer Programming transformation of the problems is also discussed. We propose greedy algorithms for the selection, which perform much better than the existing methods and can provide very good solutions as experimental results show.

The computing power of mobile devices is too limited to execute computation tasks fast. Mobile edge computing (MEC) allows mobile devices to offload tasks to near servers to reduce the completion time of the tasks (a.k.a makespan). The input data of some critical tasks should be encrypted before the offloading. Aiming at the security critical tasks in the MEC composed of multiple servers, this paper addresses to minimize the makespan by scheduling security-critical tasks. We provide the formulation of the problem which is generally an integer programming problem, and three effective composite heuristics CH1–CH3 are proposed to solve the problem. Task permutations are considered as solutions. We construct a greedy heuristic algorithm to calculate the value of the objective. These three composite heuristics consist of two phases: solution initialization and solution improvement. In the first phase, the solutions of all the proposed algorithms are generated by a task arrangement rule called Biggest data Task First (BTF), and then in the second phase, improved by three searching methods based on different neighborhoods including a insertion neighborhood, a swap neighborhood and a hybrid neighborhood, respectively. Experimental results show that CH1–CH3 outperform the well-known RoundRobin algorithm. Particularly, BTF is demonstrated to initialize highly qualified solutions, making contributions to the high effectiveness. Meanwhile, all the improvement methods are justified to be effective and the method based on the hybrid neighborhood achieves the best effectiveness.

Estimation by analogy (EBA) predicts effort for a new project by learning from the performance of former projects. This is done by aggregating effort information of similar projects from a given historical data set that contains projects, or objects in general, and attributes describing the objects. While this has been successful in general, existing research results have shown that a carefully selected subset, as well as weighting, of the attributes may improve the performance of the estimation methods.

In order to improve the estimation accuracy of our former proposed EBA method AQUA, which supports data sets that have non-quantitative and missing values, an attribute weighting method using rough set analysis is proposed in this paper. AQUA is thus extended to AQUA⁺ by incorporating the proposed attribute weighting and selection method. Better prediction accuracy was obtained by AQUA⁺ compared to AQUA for five data sets. The proposed method for attribute weighting and selection is effective in that (1) it supports data sets that have non-quantitative and missing values; (2) it supports attribute selection as well as weighting, which are not supported simultaneously by other attribute selection methods; and (3) it helps AQUA⁺ to produce better performance.

In this paper we develop a software reliability model for Artificial Intelligence (AI) programs. We show that conventional software reliability models must be modified to incorporate certain special characteristics of AI programs, such as (1) failures due to intrinsic faults, e.g., limitations due to heuristics and other basic AI techniques, (2) fuzzy correctness criterion, i.e., difficulty in accurately classifying the output of some AI programs as correct or incorrect, (3) planning-time versus execution-time tradeoffs, and (4) reliability growth due to an evolving knowledge base. We illustrate the approach by modifying the Musa-Okumoto software reliability growth model to incorporate failures due to intrinsic faults and to accept fuzzy failure data. The utility of the model is exemplified with a robot path-planning problem.