Multidimensional Multiple-choice Knapsack Problem Research Articles

Discrete Data Rate Adaptation for Wireless Body Area Networks

eHealth services require continuous data streaming and a stable level of quality of service. However, wireless network connections can be characterized by variable bandwidths. This requires continuous adaptation of systems, including adapting the bit rates of data streamed by sensors. Assigning appropriate rates to the data represents a main task in congestion control. Most of the current methods look for proper sensor data rates within continuous domains. We examine the case when sensors can generate data streams with several different qualities (e.g., sampling rates, sampling accuracies, etc.). For this reason, the domain of the data rate values can be restricted to the discrete values representing the data rates of the possible quality variations. This paper examines the optimization of the utility of the delivered data under resource constraints by selecting an appropriate variation of the provided data from a discrete set. We provide a formal model for delivering data streams in WBANs and recommend an optimization algorithm to solve the problem. Our recommended solutions are related to the multiple-choice multidimensional knapsack problem. By comparing the proposed algorithms, we found that the greedy method closely approximates the optimum in a short running time.

Modified Artificial Bee Colony Algorithm for Multiple-Choice Multidimensional Knapsack Problem

The multiple-choice multidimensional knapsack problem (MMKP) is a well-known NP-hard problem that has many real-time applications. However, owing to its complexity, finding computationally efficient solutions for the MMKP remains a challenging task. In this study, we propose a Modified Artificial Bee Colony algorithm (MABC) to solve the MMKP. The MABC employs surrogate relaxation, Hamming distance, and a tabu list to enhance the local search process and exploit neighborhood information. We evaluated the performance of the MABC on standard benchmark instances and compared it with several state-of-the-art algorithms, including RLS, ALMMKP, ACO, PEGF-PERC, TIKS-TIKS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and D-QPSO. The experimental results reveal that MABC produces highly competitive solutions in terms of the best solutions found, achieving approximately 2% of the optimal solutions with trivial (milliseconds) CPU time. The Kruskal-Wallis test revealed that there was no statistically significant difference in the objective function values between the MABC algorithm and other state-of-the-art algorithms (H = 0.31506, p = 0.98882). However, for CPU efficiency, the test showed a statistically significant difference (H = 84.90850, p = 0), indicating that the MABC algorithm exhibited significantly better CPU efficiency (with shorter execution times) than the other algorithms did. Along with these findings, the ease of implementation of the algorithm and the small number of control parameters make our approach highly adaptive for large-scale real-time systems.

Cost-Efficient Workflow Scheduling Algorithm for Applications With Deadline Constraint on Heterogeneous Clouds

In recent years, more and more large-scale data processing and computing workflow applications run on heterogeneous clouds. Such cloud applications with precedence-constrained tasks are usually deadline-constrained and their scheduling is an essential problem faced by cloud providers. Moreover, minimizing the workflow execution cost based on cloud billing periods is also a complex and challenging problem for clouds. In realizing this, we first model the workflow applications as I/O Data-aware Directed Acyclic Graph (DDAG), according to clouds with global storage systems. Then, we mathematically state this deadline-constrained workflow scheduling problem with the goal of minimum execution financial cost. We also prove that the time complexity of this problem is NP-hard by deducing from a multidimensional multiple-choice knapsack problem. Third, we propose a heuristic cost-efficient task scheduling strategy called CETSS, which includes workflow DDAG model building, task subdeadline initialization, greedy workflow scheduling algorithm, and task adjusting method. The greedy workflow scheduling algorithm mainly consists of dynamical task renting billing period sharing method and unscheduled task subdeadline relax technique. We perform rigorous simulations on some synthetic randomly generated applications and real-world applications, such as Epigenomics, CyberShake, and LIGO. The experimental results clearly demonstrate that our proposed heuristic CETSS outperforms the existing algorithms and can effective save the total workflow execution cost. In particular, CETSS is very suitable for large workflow applications.

Simple strategies that generate bounded solutions for the multiple‐choice multi‐dimensional knapsack problem: a guide for OR practitioners

AbstractThe multiple‐choice multi‐dimensional knapsack problem (MMKP) is an NP‐hard generalization of the classic 0–1 knapsack problem. The MMKP has a variety of important industrial and business applications. Approximate solution approaches characteristically give no guarantees on solution quality. Exact solution approaches usually generate solutions that are guaranteed to be close to the optimum but typically take excessive computation times—one to several hours have been recorded in the literature. In this article, we use both simple single‐step and multiple step strategies to demonstrate how a commercial software package (Gurobi in this case) can easily be used to generate guaranteed tightly bounded solutions for 293 MMKP instances commonly tested in the literature. These four simple strategies that require no problem‐specific algorithms are shown to perform competitively with the five best published algorithms for the MMKP. Since no problem‐specific coding is required, these simple strategies are easy for operations research practitioners to use.

A Memetic Algorithm with a Novel Repair Heuristic for the Multiple-Choice Multidimensional Knapsack Problem

We propose a memetic algorithm for the multiple-choice multidimensional knapsack problem (MMKP). In this study, we focus on finding good solutions for the MMKP instances, for which feasible solutions rarely exist. To find good feasible solutions, we introduce a novel repair heuristic based on the tendency function and a genetic search for the function approximation. Even when the density of feasible solutions over the entire solution space is very low, the proposed repair heuristic could successfully change infeasible solutions into feasible ones. Based on the proposed repair heuristic and effective local search, we designed a memetic algorithm that performs well on problem instances with a low density of feasible solutions. By performing experiments, we could show the superiority of our method compared with previous genetic algorithms.

A two-phase kernel search variant for the multidimensional multiple-choice knapsack problem

The Multidimensional Multiple-choice Knapsack Problem (MMKP) is a complex combinatorial optimization problem for which finding high quality feasible solutions is very challenging. Recently, several heuristic approaches and a few exact algorithms have been proposed for its solution. These methods have been able to provide new best-known values for benchmark instances although many of them still remain unclosed to optimality. In this paper, we provide a new variant of the heuristic framework Kernel Search and apply it to the MMKP. The proposed variant keeps the method’s main idea of solving a sequence of restricted mixed-integer subproblems but innovates by partitioning the solution process into two different phases with complementary goals. The first phase strives for feasibility and collects important information to dynamically adapt subproblems’ dimension and solution time in the second phase that is focused on getting high quality solutions. This makes the global approach more scalable and efficient.Computational results on different sets of benchmark instances demonstrate that our method is extremely effective outperforming all state-of-the-art heuristics for the MMKP. The method compares extremely well also with respect to exact approaches running for five hours. The proposed algorithm is able to improve the best-known value of 185 out of 276 open benchmark instances and gets 8 out of 17 optimal solutions for the closed ones. The average deviation from optimality is always negligible.

Comparing Various Genetic Algorithm Approaches for Multiple-choice Multi-dimensional Knapsack Problem (mm-KP)

Comparing Various Genetic Algorithm Approaches for Multiple-choice Multi-dimensional Knapsack Problem (mm-KP)

A Core-Based Exact Algorithm for the Multidimensional Multiple Choice Knapsack Problem

In the multidimensional multiple choice knapsack problem (MMKP), items with nonnegative profits are partitioned into groups. Each item consumes a predefined nonnegative amount of a set of resources...

Joint optimization of building-envelope and heating-system retrofits at territory scale to enhance decision-aiding

Reduction of energy consumption in the building sector has been identified as a major instrument to tackle global climate change and improve sustainability. In this paper, we propose a methodology to address a retrofit planning problem at a community level, with a building resolution. The resulting tool helps local decision-makers identify pertinent actions to improve the environmental behavior of their territories. Two building retrofit levers are considered, namely envelope insulation and heating systems replacement. Retrofit planning is treated here as a single-objective optimization problem aimed at reducing the total costs of retrofit actions by minimizing their net present value. A multidimensional multiple-choice knapsack problem formulation is proposed through the adoption of adequate decision variables. It suitably balances the complexity induced by the large number of potential retrofit action combinations and the number of variables in the problem and permits a linear formulation. An optimization of virtual building stocks is performed to highlight the developed model’s capacity to tackle large problems (5,000 buildings) in a few minutes. Finally, three analyses finally are led on a real case-study territory, featuring both appropriate retrofit solutions and building stock information. Long-term evaluation of retrofit strategies over the short-term results in an additional 10% reduction of energy consumption and greenhouse gases emissions and encourages thermal insulation. When targeting a 40% reduction in energy demand, retrofit costs ranging from 20 to 800€/m2 are observed. Finally, the developed method was used to draw a CO2 abatement cost curve at territory level. A 70% reduction of emissions can be achieved with costs under 50 €/tCO2e.

Energy-Aware Design of Stochastic Applications With Statistical Deadline and Reliability Guarantees

Energy efficiency, reliability, and real-time are three key requirements of mission-critical embedded systems. Existing approaches over emphasize the worst case design of real-time embedded systems, which will lead to serious waste of resources. In this paper, we aim at the energy-efficient design of soft real-time and reliable applications on uniprocessor embedded systems. We consider soft real-time tasks with stochastic execution durations regarding certain distributions. Thereby, we provide real-time guarantee with probability consideration. We utilize dynamic voltage and frequency scaling (DVFS) for saving energy, and also take into account the impact of DVFS on reliability. Our objective is to minimize the expected energy consumption of the system subject to statistical reliability and deadline constraints. The design optimization problem is a typical multidimensional multiple-choice knapsack problem, which is NP-hard. We first propose a dynamic programming-based optimal algorithm to solve the problem. To reduce the time complexity, we then develop a ( $1+{\beta }$ )-approximation algorithm based on a binary search approach, where ${\beta }$ is the approximating factor. The approximation algorithm can obtain the near-optimal solution with at most ( $1{+\beta }$ ) times of optimal energy cost under given real-time and reliability constraints and has fully polynomial time complexity. Extensive experiments and a real-life synthetic application are conducted to evaluate the performance of the proposed techniques. Compared with existing approaches, the approximation approach can save much energy with low time overhead while guaranteeing the statistical deadline and reliability constraints.

The robust multiple-choice multidimensional knapsack problem

The multiple-choice multidimensional knapsack problem (MMKP) assumes n sets composed of mutually exclusive items. The goal is to select exactly one item per set, maximizing the overall utility, without violating a family of knapsack constraints. Motivated by recent applications of the MMKP to complex system reliability and quality of service management problems, we propose a robust version. More specifically, we relinquish the assumption that the problem parameters are deterministically known by limiting their values to a pre-specified uncertainty set. Depending on the structure of the variance−covariance matrix used to model the uncertainty, we identify four different cases, leading to robust formulations characterized by second order cone programs. We show how each of these programs is transformed into an equivalent linear program, implying that the use of a robust formulation for the MMKP comes with no extra computational complexity. Finally, using a novel matheuristic designed for the MMKP, we shed lights on the trade-off between the “price of robustness,” i.e., how much worse the objective function value of a robust solution is, compared with the deterministic one, and the “reliability,” i.e., the probability that a robust solution will lead to a feasible scenario for an arbitrary realization of the uncertain parameters.

Optimal selective maintenance decisions for large serial k-out-of-n: G systems under imperfect maintenance

The selective maintenance problem (SMP) arises in many large multicomponent systems which are operated for consecutive missions interspersed with finite breaks during which only a selected set of component repairs or replacements can be carried out due to limited time, budget, or resources. The problem is to decide which components and degree of repairs should be performed in order to guarantee a pre-specified performance level during the subsequent mission. Current SMP formulations in the literature are nonlinear, deal mainly with basic or series-parallel systems and mostly use heuristic methods to obtain solutions.This paper introduces the first SMP model for serial k-out-of-n systems. Two nonlinear formulations are developed, which can be used to solve the problem for small to moderate size k-out-of-n systems. For large k-out-of-n systems or complex reliability structures, we develop a new two-phase approach which transforms the problem into a multidimensional multiple-choice knapsack problem (MMKP). The new approach is shown to be efficient through multiple sets of numerical experiments.

Utility-based Configuration of Learning Factories Using a Multidimensional, Multiple-choice Knapsack Problem

The paper presents a structural approach to configure the technical system of a learning factory by considering learning targets and maximizing the utility. Local scope conditions and intended competencies are used to operationalize requirements. The composition of the module-based technical system can be optimized by maximizing its overall utility. Therefore, an exact and efficient optimization algorithm is developed solving a multidimensional multiple-choice knapsack problem combined with a two-dimensional bin packing problem. Restrictions are the available budget and the useable area of the learning factory. As a result, the configured technical system enables optimal target orientation of the learning factory. This procedure is finally applied on the Process Learning Factory CiP.

An iterative pseudo-gap enumeration approach for the Multidimensional Multiple-choice Knapsack Problem

The Multidimensional Multiple-choice Knapsack Problem (MMKP) is an important NP-hard combinatorial optimization problem with many applications. We propose a new iterative pseudo-gap enumeration approach to solving MMKPs. The core of our algorithm is a family of additional cuts derived from the reduced costs constraint of the nonbasic variables by reference to a pseudo-gap. We then introduce a strategy to enumerate the pseudo-gap values. Joint with CPLEX, we evaluate our approach on two sets of benchmark instances and compare our results with the best solutions reported by other heuristics in the literature. It discovers 10 new better lower bounds on 37 well-known benchmark instances with a time limit of 1 hour for each instance. We further give direct comparison between our algorithm and one state-of-the-art “reduce and solve” approach on the same machine with the same CPLEX, experimental results show that our algorithm is very competitive, outperforming “reduce and solve” on 18 cases out of 37.

An improved binary search algorithm for the Multiple-Choice Knapsack Problem

The Multiple-Choice Knapsack Problem is defined as a 0-1 Knapsack Problem with additional disjoint multiple-choice constraints. Gens and Levner presented for this problem an approximate binary search algorithm with a worst case ratio of 5. We present an improved approximate binary search algorithm with a ratio of 3 + (1/2)t and a running time O(n(t + log m)), where n is the number of items, m the number of classes, and t a positive integer. We then extend our algorithm to make it also applicable to the Multiple-Choice Multidimensional Knapsack Problem with dimension d.

Improving solver performance through redundancy

It is well known that hierarchies of mathematical programming formulations with different numbers of variables and constraints have a considerable impact regarding the quality of solutions obtained once these formulations are fed to a commercial solver. In addition, even if dimensions are kept the same, changes in formulations may largely influence solvability and quality of results. This becomes evident especially if redundant constraints are used. We propose a related framework for information collection based on these constraints. We exemplify by means of a well-known combinatorial optimization problem from the knapsack problem family, i.e., the multidimensional multiple-choice knapsack problem (MMKP). This incorporates a relationship of the MMKP to some generalized set partitioning problems. Moreover, we investigate an application in maritime shipping and logistics by means of the dynamic berth allocation problem (DBAP), where optimal solutions are reached from the root node within the solver.

An empirical study of population-based metaheuristics for the multiple-choice multidimensional knapsack problem

In this paper, we study the performance of five population-based metaheuristics to solve a large 393 number of comprehensive problem instances from the literature for the important NP-Hard multiple choice multidimensional knapsack problem MMKP. The five metaheuristics are: teaching-learning-based optimisation TLBO, artificial bee colony ABC, genetic algorithm GA, criss-cross optimisation algorithm COA, and binary bat algorithm BBA. All five of these metaheuristics are similar in that they transform a population of solutions in an effort to improve the solutions in the population and they are all implemented in a straightforward manner. Statistically over all 393 problem instances, we show that COA, GA, and TLBO give similar results which are better than other published solution approaches for the MMKP. However, if we incorporate a simple neighbourhood search into each of these five metaheuristics, in addition to improved solution quality, there is now no statistically significant difference among the results for these five metaheuristics.

An empirical study of population-based metaheuristics for the multiple-choice multidimensional knapsack problem

An empirical study of population-based metaheuristics for the multiple-choice multidimensional knapsack problem

네트워크 코딩을 쓰는 언더레이 인지 무선 네트워크에서의 주파수 할당과 경로 선택 기법

In this paper, we propose frequency allocation and path selection scheme in underlay cognitive radio (CR) networks using network coding. In the proposed scheme, we choose the path with consideration of network coding and interference temperature in underlay CR networks and propose an optimization problem to maximize the system throughput of secondary users (SUs). Then, we represent the proposed optimization problem as the multi-dimensional multiple-choice knapsack problem and give the theoretical upper bound for the system throughput of SUs by using linear programming. Finally, we compute the system throughput of SUs by using brute-force search (BFS) and link quality first (LQF) scheme in underlay CR networks. Simulation results show that the system throughput of SUs with BFS is higher than that with LQF in underlay CR networks with and without application of network coding, respectively.

A set partitioning reformulation for the multiple-choice multidimensional knapsack problem

The Multiple-choice Multidimensional Knapsack Problem (MMKP) is a well-known -hard combinatorial optimization problem that has received a lot of attention from the research community as it can be easily translated to several real-world problems arising in areas such as allocating resources, reliability engineering, cognitive radio networks, cloud computing, etc. In this regard, an exact model that is able to provide high-quality feasible solutions for solving it or being partially included in algorithmic schemes is desirable. The MMKP basically consists of finding a subset of objects that maximizes the total profit while observing some capacity restrictions. In this article a reformulation of the MMKP as a set partitioning problem is proposed to allow for new insights into modelling the MMKP. The computational experimentation provides new insights into the problem itself and shows that the new model is able to improve on the best of the known results for some of the most common benchmark instances.