A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

Where Quantum Complexity Helps Classical Complexity

Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum computing. Nonetheless, there are defined boundaries to the capabilities of quantum computing. This paper concentrates on aggregating prior research efforts dedicated to solving intricate classical computational problems through quantum computing. The objective is to systematically compile an exhaustive inventory of these solutions and categorize a collection of demanding problems that await further exploration

Decentralized algorithm of dynamic task allocation for a swarm of homogeneous robots

The current trends in the robotics field have led to the development of large-scale swarm robot systems, which are deployed for complex missions. The robots in these systems must communicate and interact with each other and with their environment for complex task processing. A major problem for this trend is the poor task planning mechanism, which includes both task decomposition and task allocation. Task allocation means to distribute and schedule a set of tasks to be accomplished by a group of robots to minimize the cost while satisfying operational constraints. Task allocation mechanism must be run by each robot, which integrates the swarm whenever it senses a change in the environment to make sure the robot is assigned to the most appropriate task, if not, the robot should reassign itself to its nearest task. The main contribution in this thesis is to maximize the overall efficiency of the system by minimizing the total time needed to accomplish the dynamic task allocation problem. The near-optimal allocation schemes are found using a novel hybrid decentralized algorithm for a dynamic task allocation in a swarm of homogeneous robots, where the number of the tasks is more than the robots present in the system. This hybrid approach is based on both the Simulated Annealing (SA) optimization technique combined with the Discrete Particle Swarm Optimization (DPSO) technique. Also, another major contribution in this thesis is the formulation of the dynamic task allocation equations for the homogeneous swarm robotics using integer linear programming and the cost function and constraints are introduced for the given problem. Then, the DPSO and SA algorithms are developed to accomplish the task in a minimal time. Simulation is implemented using only two test cases via MATLAB. Simulation results show that PSO exhibits a smaller and more stable convergence characteristics and SA technique owns a better quality solution. Then, after developing the hybrid algorithm, which combines SA with PSO, simulation instances are extended to include fifteen more test cases with different swarm dimensions to ensure the robustness and scalability of the proposed algorithm over the traditional PSO and SA optimization techniques. Based on the simulation results, the hybrid DPSO/SA approach proves to have a higher efficiency in both small and large swarm sizes than the other traditional algorithms such as Particle Swarm Optimization technique and Simulated Annealing technique. The simulation results also demonstrate that the proposed approach can dislodge a state from a local minimum and guide it to the global minimum. Thus, the contributions of the proposed hybrid DPSO/SA algorithm involve possessing both the pros of high quality solution in SA and the fast convergence time capability in PSO. Also, a parameters\u27 selection process for the hybrid algorithm is proposed as a further contribution in an attempt to enhance the algorithm efficiency because the heuristic optimization techniques are very sensitive to any parameter changes. In addition, Verification is performed to ensure the effectiveness of the proposed algorithm by comparing it with results of an exact solver in terms of computational time, number of iterations and quality of solution. The exact solver that is used in this research is the Hungarian algorithm. This comparison shows that the proposed algorithm gives a superior performance in almost all swarm sizes with both stable and small execution time. However, it also shows that the proposed hybrid algorithm\u27s cost values which is the distance traveled by the robots to perform the tasks are larger than the cost values of the Hungarian algorithm but the execution time of the hybrid algorithm is much better. Finally, one last contribution in this thesis is that the proposed algorithm is implemented and extensively tested in a real experiment using a swarm of 4 robots. The robots that are used in the real experiment called Elisa-III robots

The Use of an Exact Algorithm within a Tabu Search Maximum Clique Algorithm

Let G = (V, E) be an undirected graph with vertex set V and edge set E. A clique C of G is a subset of the vertices of V with every pair of vertices of C adjacent. A maximum clique is a clique with the maximum number of vertices. A tabu search algorithm for the maximum clique problem that uses an exact algorithm on subproblems is presented. The exact algorithm uses a graph coloring upper bound for pruning, and the best such algorithm to use in this context is considered. The final tabu search algorithm successfully finds the optimal or best known solution for all standard benchmarks considered. It is compared with a state-of-the-art algorithm that does not use exact search. It is slower to find the known optimal solution for most instances but is faster for five instances and finds a larger clique for two instances

Internet of Things in urban waste collection

Nowadays, the waste collection management has an important role in urban areas. This paper faces this issue and proposes the application of a metaheuristic for the optimization of a weekly schedule and routing of the waste collection activities in an urban area. Differently to several contributions in literature, fixed periodic routes are not imposed. The results significantly improve the performance of the company involved, both in terms of resources used and costs saving

A Hybrid Metaheuristic Algorithm for Stop Point Selection in Wireless Rechargeable Sensor Network

A wireless rechargeable sensor network (WRSN) enables charging of rechargeable sensor nodes (RSN) wirelessly through a mobile charging vehicle (MCV). Most existing works choose the MCV’s stop point (SP) at random, the cluster’s center, or the cluster head position, all without exploring the demand from RSNs. It results in a long charging delay, a low charging throughput, frequent MCV trips, and more dead nodes. To overcome these issues, this paper proposes a hybrid metaheuristic algorithm for stop point selection (HMA-SPS) that combines the techniques of the dragonfly algorithm (DA), firefly algorithm (FA), and gray wolf optimization (GWO) algorithms. Using FA and GWO techniques, DA predicts an ideal SP using the run-time metrics of RSNs, such as energy, delay, distance, and trust factors. The simulated results demonstrate faster convergence with low delay and highlight that more RSNs can be recharged with fewer MCV visits, further enhancing energy utilization, throughput, network lifetime, and trust factor

Evaluating Particle Swarm Intelligence Techniques for Solving University Examination Timetabling Problems

The purpose of this thesis is to investigate the suitability and effectiveness of the Particle Swarm Optimization (PSO) technique when applied to the University Examination Timetabling problem. We accomplished this by analyzing experimentally the performance profile-the quality of the solution as a function of the execution time-of the standard form of the PSO algorithm when brought to bear against the University Examination Timetabling problem. This study systematically investigated the impact of problem and algorithm factors in solving this particular timetabling problem and determined the algorithm\u27s performance profile under the specified test environment. Keys factors studied included problem size (i.e., number of enrollments), conflict matrix density, and swarm size. Testing used both real world and fabricated data sets of varying size and conflict densities. This research also provides insight into how well the PSO algorithm performs compared with other algorithms used to attack the same problem and data sets. Knowing the algorithm\u27s strengths and limitations is useful in determining its utility, ability, and limitations in attacking timetabling problems in general and the University Examination Timetabling problem in pal1icular. Finally, two additional contributions were made during the course of this research: a better way to fabricate examination timetabling data sets and the introduction of the PSO-No Conflicts optimization approach. Our new data set fabrication method produced data sets that were more representative of real world examination timetabling data sets and permitted us to construct data sets spanning a wide range of sizes and densities.· The newly derived PSO-No Conflicts algorithm permitted the PSO algorithm to perform searches while still satisfying constraints