On the Effect of Connectedness for Biobjective Multiple and Long Path Problems

In intensity-modulated radiation therapy, treatment planners aim to irradiate the tumour according to a medical prescription while sparing surrounding organs at risk as much as possible. Although this problem is inherently a multi-objective optimisation (MO) problem, most of the models in the literature are single-objective ones. For this reason, a large number of single-objective algorithms have been proposed in the literature to solve such single-objective models rather than multi-objective ones. Further, a difficulty that one has to face when solving the MO version of the problem is that the algorithms take too long before converging to a set of (approximately) non-dominated points. In this paper, we propose and compare three different strategies, namely random PLS (rPLS), judgement-function-guided PLS (jPLS) and neighbour-first PLS (nPLS), to accelerate a previously proposed Pareto local search (PLS) algorithm to solve the beam angle selection problem in IMRT. A distinctive feature of these strategies when compared to the PLS algorithms in the literature is that they do not evaluate their entire neighbourhood before performing the dominance analysis. The rPLS algorithm randomly chooses the next non-dominated solution in the archive and it is used as a baseline for the other implemented algorithms. The jPLS algorithm first chooses the non-dominated solution in the archive that has the best objective function value. Finally, the nPLS algorithm first chooses the solutions that are within the neighbourhood of the current solution. All these strategies prevent us from evaluating a large set of BACs, without any major impairment in the obtained solutions’ quality. We apply our algorithms to a prostate case and compare the obtained results to those obtained by the PLS from the literature. The results show that algorithms proposed in this paper reach a similar performance than PLS and require fewer function evaluations.

Objectives Facility service districting problem(FSDP) refers to the design of facility service areas according to the facility locations and service capacities in a geographical region. The design criteria for service areas include the balance of service demand and supply, the highest service accessibility, and the spatial contiguity. The spatial contiguity is a necessity for satisfying some policies on public services, such as school districting and medical districting. However, solving the FSDP with contiguity constraints is challenging. We present a hybrid algorithm framework for solving the FSDP. Methods The algorithm is proposed based on the general local search algorithm and furtherly enhanced by multi-start, ruin-recreate, set-partitioning and other optimization strategies. The basic modules such as initial solution generation method, local search operators, solution perturbation, model building and solving, and search strategies, are provided in the framework. Using these building blocks, some exact, metaheuristic and hybrid algorithms could be implemented effectively. Five algorithms are implemented for the FSDP: Exact method by solving a mixed integer linear programming model, simulated annealing (SA) algorithm, iterative local search (ILS) algorithm, SA with set-partitioning, and ILS with set-partitioning. In addition, four instances are designed to test the algorithms. The instance size, supply-demand ratio, and geographic environment are considered in the instance design. Results There are several findings from computing experimentation: Optimal or near-optimal solutions of the instances could be obtained by CPLEX optimizer; high-quality solutions could be found by SA and ILS algorithms much more efficiently; the set-partitioning procedure is capable of improving the solution quality. Conclusions Based on the proposed algorithm framework, it is easy and flexible to design local-search based matheuristics and hybrid algorithms for the FSDP. High quality solutions could be obtained by coupling the local search with ruin-recreate perturbation and set-partitioning.

Maximum satisfiability problem is the central problem in theoretical computer science.Maximum 3-satisfiability problem(Max-(3)-Sat) is one of the most important sub problem of the maximum satisfiablity problem.Local search has been testified to be very effective for solving this problem by many times of real computation.However,there is no related results for analyzing the performance of the local search method to solve the problem.This paper approaches the local search method to solve the maximum satisfiablity problems and analyzes the performance of the method.The central issue of the paper is to discuss the local search algorithm to solve the Max-(3)-Sat.The authors show that the one-bit-flip local search algorithm can achieve the performance ratio 4/3 for solving the Max-(3)-Sat;and the algorithm of one-bit-flip local search following the conditionally all-bits-flip can achieve the performance ratio 5/4 for solving Max-(3)-Sat.And the authors design a new local search algorithm to solve the Max-(3)-Sat problem using the one-bit-flip local search following the all-bits-flip,and show the new algorithm have the performance ratio 8/7.The 8/7-approximation algorithm can be extended to solve the Max-(k)-Sat problem with performance ratio (2k+2)/(2k+1) for k4.Finally the authors give the two-bits-flip local search algorithm to solve the Max-(k)-Sat problem,and prove the algorithm can have the performance ratio 1+12k+1+k(k-1)/(n-k) for k4.Repeatedly running the local search algorithm can further improve the performance of the solution.The results of the paper demonstrate the inevitability for local search to have high performances in solving the maximum satisifiablity problems.

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.

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.

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.

The Local Search algorithm (or Hill Climbing, or Iterative Improvement) is one of the simplest heuristics to solve the Satisfiability and Max-Satisfiability problems. Although it is not the best known Satisfiability algorithm even for the class of problems we study, the Local Search is a part of many satisfiability and max-satisfiability solvers, where it is used to find a good starting point for a more sophisticated heuristics, and to improve a candidate solution. In this paper we give an analysis of Local Search on random planted 3-CNF formulas. We show that a sharp transition of efficiency of Local Search occurs at density \(\varrho = \frac{7}{6} \ln n\). Specifically we show that if there is \(\kappa <\frac{7}{6}\) such that the clause-to-variable ratio is less than \(\kappa \ln n\) (n is the number of variables in a CNF) then Local Search whp does not find a satisfying assignment, and if there is \(\kappa >\frac{7}{6}\) such that the clause-to-variable ratio is greater than \(\kappa \ln n\) then the local search whp finds a satisfying assignment. As a byproduct we also show that for any constant \(\varrho \) there is \(\gamma \) such that Local Search applied to a random (not necessarily planted) 3-CNF with clause-to-variable ratio \(\varrho \) produces an assignment that satisfies at least \(\gamma n\) clauses less than the maximal number of satisfiable clauses.KeywordsLocal Search (LS)Satisfiable ClausesAlgorithm LSProper Local MinimumDistribution SatisfiesThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

ABSTRACTThe paper targets an optimal soil cutting operation by considering economic and productive aspects. Three realistic objectives and three problem-specific constraints are developed, and the optimization problem is solved using a hybrid evolutionary multi-objective optimization (EMO) technique. In this technique, a set of non-dominated solutions is generated by using an existing EMO technique, and then a few of them are selected for local search using the -constraint method. These selected solutions are used for starting independent local searches using fmincon solver of Matlab. Results demonstrate that the local searches have improved the non-dominated solutions a little, thereby suggesting a closeness of evolved solutions from EMO technique with true Pareto-optimal (PO) solutions. The PO solutions are further validated using experimental data from the literature. Overall, this study offers a platform to choose an appropriate solution from the set of PO solutions. Moreover, the post-optimal analysis demonstrates the commonality principle of few decision variables, which is followed by all PO solutions. The rest of the decision variables decipher important relationships that are responsible for trade-off among the PO solutions. The relationships are later used for preparing guidelines for a practitioner in selecting an appropriate solution for the optimal operation.

Optimization Solution Task is a typical and important task in many applications. Many optimization problems have been proved to be NP-hard problems, which cannot be solved by some predefined mathematic formulae. In this case, computer aided method is very helpful. While some local search algorithms are easily to fall into a local optimum solution. On contrast, the population based methods, such as Genetic Algorithms, Artificial Immune System, Autonomy Oriented Computing, are global search algorithms. However, they are not good at the local search. In this paper, an improved method is proposed by combining the local and global search ability, so as to improve the performance in terms of the convergence speed and the convergence reliability. We construct a generic form to deal with the common objective function space or the objective function with the partial derivative. In addition, we present an n-hold method in population based evolution method. The experiments indicate that our approach can effectively improve the convergence reliability, which is much concerned in some applications with the expensive executing expense.

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 .

In multiobjective genetic local search (MOGLS) algorithms, the local search is usually applied to all offsprings generated by genetic operations. This paper proposes an idea of selecting only good offsprings as initial solutions for the local search. Simulation results show that the proposed idea significantly improves the search ability of MOGLS algorithms.

In this paper, we present a fast hypervolume-based multi-objective local search algorithm, where the fitness assignment is realized by the approximating computation of hypervolume contribution. In the algorithm, we define an approximate hypervolume contribution indicator as the selection mechanism and apply this indicator to an iterated local search. We carry out a range of experiments on three-objective flow shop problem. Experimental results indicate that our algorithm is highly effective in comparison with the algorithms based on the binary indicators and the exact hypervolume contribution indicator.Keywordsmulti-objective optimizationapproximate hypervolume contributionlocal searchflow shop problem

A Variable Iterated Local Search Algorithm for Energy-Efficient No-idle Flowshop Scheduling 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.

Differential evolution with fusion of local and global search strategies