Self-Configuring (1 + 1)-Evolutionary Algorithm for the Continuous p-Median Problem with Agglomerative Mutation

A hybridisation of a clustering-based technique and of a variable neighbourhood search (VNS) is designed to solve large-scale $$p$$p-median problems. The approach is based on a multi-stage methodology where learning from previous stages is taken into account when tackling the next stage. Each stage is made up of several subproblems that are solved by a fast procedure to produce good feasible solutions. Within each stage, the solutions returned are put together to make up a new promising subset of potential facilities. This augmented $$p$$p-median problem is then solved by VNS. As these problems used aggregation, a cost evaluation based on the original demand points instead of aggregation is computed for each of the `aggregation'-based solution. The one yielding the least cost is then selected and its chosen facilities included into the next stages. This multi-stage process is repeated several times until a certain criterion is met. This approach is enhanced by an efficient way to aggregate the data and a neighbourhood reduction scheme when allocating demand points to their nearest facilities. The proposed approach is tested, using various values of $$p$$p, on the largest data sets from the literature with up to 89,600 demand points with encouraging results.

Training a neural network is a difficult optimization problem because of the nonconvex objective function. Therefore, as an alternative to local search algorithms, many global search algorithms have been used to train neural networks. However, local search algorithms are more efficient with computational resources, and therefore numerous random restarts with a local algorithm may be more effective than a global algorithm at obtaining a low value of the objective function. This study examines, through Monte-Carlo simulations, the relative efficiency of a local search algorithm to 8 stochastic global algorithms: 2 simulated annealing algorithms, 1 simple random stochastic algorithm, 1 genetic algorithm and 4 evolutionary strategy algorithms. The results show that even ignoring the computational requirements of the global algorithms, there is little evidence to support the use of the global algorithms examined for training neural networks.

The maximum cut (MAX-CUT) problem is to find a bipartition of the vertices in a given graph such that the number of edges with ends in different sets reaches the largest. Though, several experimental investigations have shown that evolutionary algorithms (EAs) are efficient for this NP-complete problem, there is little theoretical work about EAs on the problem. In this paper, we theoretically investigate the performance of EAs on the MAX-CUT problem. We find that both the (1+1) EA and the (1+1) EA*, two simple EAs, efficiently achieve approximation solutions of (m/2)+(1/4)s(G) and (m/2)+(1/2)(√{8m+1}-1), where m and s(G) are respectively the number of edges and the number of odd degree vertices in the input graph. We also reveal that for a given integer k the (1+1) EA* finds a cut of size at least k in expected runtime O(nm+1/δ(4k)) and a cut of size at least (m/2)+k in expected runtime O(n(2)m+1/δ((64/3)k(2))), where δ is a constant mutation probability and n is the number of vertices in the input graph. Finally, we show that the (1+1) EA and the (1+1) EA* are better than some local search algorithms in one instance, and we also show that these two simple EAs may not be efficient in another instance.

p-Median problem is one of the most applicable problem in the areas of supply chain management and operation research. There are various versions of these problems. Continuous p-median is one of them where the facility points and the demand points lie in an ’n’ dimensional hyperspace. It has been proved that this problem is NP-complete and most of the algorithms that have been defined are mere approximations. In this paper, we present a meta-heuristic based approach that calculates the median points given a set of demand points with arbitrary demands. The algorithm is a combination of genetic algorithms, particle swarm optimization and a number of novel techniques that aims to further improve the result. The algorithm is tested on known data sets as and we show’s its performance in comparison to other known algorithms applied on the same problem.

Local search algorithms are widely adopted in solving large-scale Distributed Constraint Optimization Problems (DCOPs). However, since each agent always makes its value decision based on the values of its neighbors in local search, those algorithms usually suffer from local premature convergence. More concretely, an agent cannot make a wise decision with poor values of its neighbors since its decision space is bound up with those poor values. In this paper, we propose a Partial Decision Scheme (PDS) to relax the decision space of an agent by ignoring the value of its neighbor which has the bad impact on its local benefits. The PDS comprises two partial decision processes: trigger partial decision and recursive partial decision. The former is iteratively performed by agents who cannot enhance their local benefits unilaterally to break out of potential local optima. The latter is recursively performed by neglected agents to improve global benefits. Besides, the trigger conditions along with a self-adaptive probability are introduced to control the use of PDS. The PDS can be easily applied to any local search algorithm to overcome its local premature convergence with a small additional overhead. In our theoretical analysis, we prove the feasibility and convergence of PDS. Moreover, the experimental results also demonstrate the superiority of the use of PDS in the typical local search algorithms over state-of-the-art local search algorithms.

Classification is important task of data mining used to extract knowledge from huge volume of data. By nature, classification is multi-objective problem, as it required optimization of multiple objectives simultaneously like accuracy, sensitivity, squared error, precision etc. Traditionally, evolutionary algorithms were used to solve multi-objective classification problem by considering it as single-objective problem, but this approach gives single solution to problem. Therefore, multi-objective evolutionary algorithms are used to solve classification problem. In this paper, we have used Pareto approach to optimize neural network to solve classification problem. Non-dominated sorting genetic algorithm is used to simultaneously optimize accuracy and mean squared error objectives of neural network along with local search. As slow convergence to optimal solutions is major disadvantage of evolutionary algorithm. To speed up convergence to optimal solutions hybrid technique is adopted by augmenting evolutionary technique with local search algorithm. This proposed approach gives set of Pareto optimal solutions which represent different solutions for given classification problem.

A hybrid Particle Swarm Optimization – Variable Neighborhood Search algorithm for Constrained Shortest Path problems

In this research, a bi-criteria group scheduling problem is investigated in a hybrid flow shop (HFS) environment, wherein the parallel machines are unrelated. The objective of the problem is to minimize a linear combination of the total weighted completion time being mindful of the producer and the total weighted tardiness being mindful of the customers. The underlying assumption is that the jobs are released into the system in dynamic times. The machine ready times are considered to be dynamic as well. Sequence-dependent setup times are required for changing the process between groups of jobs. The runtimes of jobs are assumed to be decreasing as the workers learn how to process similar jobs. A mixed-integer linear programing model is developed for the problem. However, since the problem is non-deterministic polynomial-time hard (NP-hard), it may not be solved to optimality within a reasonable time. This research comprehensively addresses the question of what type of meta-heuristic algorithm is more appropriate for solving these problems. In particular, local search algorithms are compared to the population-based algorithms with respect to the permutation or non-permutation properties of the optimal solution. Three algorithms based on tabu search as well as three algorithms based on simulated annealing are developed to represent the local search algorithms. Two other algorithms are developed based on genetic algorithm (GA) to exemplify the population-based algorithms. The results of a comprehensive experimental design reveal that GA-based algorithms have greater potential for identifying better quality solutions in HFS scheduling problems compared to the local search algorithms.

Designing an automated agent for Human-Agent Negotiation is a challenging task. Especially in the domain that combines multi-issue bilateral negotiations and repeated negotiations. In this domain, the agents negotiate with humans over more than one item, and there are several rounds of negotiation in each game. Designing this kind of agent can be very challenging. Our agent needs to estimate the preferences of the human opponent in real-time, proposing fair offers that will be excepted by the human opponent but taking into account, not proposing offers that don’t increase the agent’s score. On the other hand, local search algorithms have proven to be effective in a variety of fields in artificial intelligence. In this paper, we present a novel approach for an automated agent for this type of negotiation by using local search algorithms, in particular: Simulated Annealing and Hill Climbing. As we analyze the results from our experiments and compare the local search algorithms, we show that local search algorithms can be more efficient in Human-Agent negotiation than traditional methods. Moreover, our agent is capable of negotiating efficiently and outperforming the human opponent.

Benchmarking and performance analysis play an important role in understanding the behaviour of iterative optimization heuristics (IOHs) such as local search algorithms, genetic and evolutionary algorithms, Bayesian optimization algorithms, etc. This task, however, involves manual setup, execution, and analysis of the experiment on an individual basis, which is laborious and can be mitigated by a generic and well-designed platform. For this purpose, we propose IOHanalyzer, a new user-friendly tool for the analysis, comparison, and visualization of performance data of IOHs. Implemented in R and C++ , IOHanalyzer is fully open source. It is available on CRAN and GitHub. IOHanalyzer provides detailed statistics about fixed-target running times and about fixed-budget performance of the benchmarked algorithms with a real-valued codomain, single-objective optimization tasks. Performance aggregation over several benchmark problems is possible, for example in the form of empirical cumulative distribution functions. Key advantages of IOHanalyzer over other performance analysis packages are its highly interactive design, which allows users to specify the performance measures, ranges, and granularity that are most useful for their experiments, and the possibility to analyze not only performance traces, but also the evolution of dynamic state parameters. IOHanalyzer can directly process performance data from the main benchmarking platforms, including the COCO platform, Nevergrad, the SOS platform, and IOHexperimenter. An R programming interface is provided for users preferring to have a finer control over the implemented functionalities.

A hybrid particle swarm optimization and hill climbing algorithm for task scheduling in the cloud environments

In this paper, a greedy heuristic and two local search algorithms, 1-opt local search and k-opt local search, are proposed for the unconstrained binary quadratic programming problem (BQP). These heuristics are well suited for the incorporation into meta-heuristics such as evolutionary algorithms. Their performance is compared for 115 problem instances. All methods are capable of producing high quality solutions in short time. In particular, the greedy heuristic is able to find near optimum solutions a few percent below the best-known solutions, and the local search procedures are sufficient to find the best-known solutions of all problem instances with n ≤ 100. The k-opt local searches even find the best-known solutions for all problems of size n ≤ 250 and for 11 out of 15 instances of size n e 500 in all runs. For larger problems (n e 500, 1000, 2500), the heuristics appear to be capable of finding near optimum solutions quickly. Therefore, the proposed heuristics—especially the k-opt local search—offer a great potential for the incorporation in more sophisticated meta-heuristics.

We apply the transitionless driving on the local adiabatic quantum search algorithm to speed up the adiabatic process. By studying quantum dynamics of the adiabatic search algorithm with the equivalent two-level system, we derive the transitionless driving Hamiltonian for the local adiabatic quantum search algorithm. We found that when adding a transitionless quantum driving term HD(t) on the local adiabatic quantum search algorithm, the success rate is 1 exactly with arbitrary evolution time by solving the time-dependent Schr¨odinger equation in eigen-picture. Moreover, we show the reason for the drastic decrease of the evolution time is that the driving Hamiltonian increases the lowest eigenvalues to a maximum of .

Cloud manufacturing as an emerging service-oriented manufacturing paradigm integrates and manages geographically distributed manufacturing resources such that complex and highly customized manufacturing tasks can be performed cooperatively. The service composition and optimal selection (SCOS) problem, in which manufacturing cloud services are optimally selected for performing subtasks, is one of the key issues for implementing a cloud manufacturing system. In this paper, we propose a new mixed-integer programming model for solving the SCOS problem with sequential composition structure. Unlike the majority of previous research on the problem, in the proposed model, the transportation between distributed resources and its effects on quality of services are considered. Although a wide variety of metaheuristics have been tailored for solving the SCOS problem, no consistent and comprehensive conclusion has been reached so far on the superiority of a specific algorithm. Therefore, for the first time, solution space landscape of the problem was analyzed through several statistical criteria which demonstrated that the landscape is rugged and local optima are clustered in a small region of the search space. Therefore, to find good solutions, a metaheuristic algorithm needs to perform both proper exploitation and exploration of the search space. According to the landscape analysis, the basic imperialist competitive algorithm (ICA) was hybridized with a local search (LS) algorithm resulting in the hybrid ICA (HICA). To examine the performance of the proposed HICA, an example of online motorcycle production in the USA as well as four randomly generated large-scale instances, were solved through the LS, ICA, and HICA. Computational results showed that transportation consideration is indispensable for obtaining more realistic solutions in cloud manufacturing. The results also revealed that the HICA outperformed the LS and basic ICA in terms of the value of cost objective function, the stability of solutions and convergence speed. Hence, not only statistically but also analytically, it was proved that algorithms incorporating both exploitation and exploration are able to solve the SCOS problem more efficiently.

Given n demand points in the plane, the p-center problem is to find p supply points (anywhere in the plane) so as to minimize the maximum distance from a demand point to its respective nearest supply point. The p-median problem is to minimize the sum of distances from demand points to their respective nearest supply points. We prove that the p-center and the p-median problems relative to both the Euclidean and the rectilinear metrics are NP-hard. In fact, we prove that it is NP-hard even to approximate the p-center problems sufficiently closely. The reductions are from 3-satisfiability.