an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search recently more research works are focused on multi objective particle swarm optimization algorithm mopso due to its ability of global and local search for solving multi objective optimization problems moops however most of existing mopsos cannot achieve satisfactory results in solution quality this paper proposes an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search mols named mols mopso to deal with such problem mols mopso combines an effective particle updating strategy with the local search of mols the effective particle updating strategy is used for global search to deal with premature convergence and diversity maintenance within the swarm the mols is periodically activated for fast local search to converge toward the pareto front the exploratory capabilities are enhanced more efficiently by keeping a desirable balance between global search and local search so as to ensure sufficient diversity and well distribution amongst the solutions of the non dominated fronts while retaining at the same time the convergence to the pareto optimal front comparing mols mopso with various state of the art multi objective optimization algorithms developed recently the comparative study shows the effectiveness of mols mopso which not only assures a better convergence to the pareto frontier but also illustrates a good diversity and distribution of solutions

methods for multi objective optimization an analysis decomposition based methods are often cited as the solution to multi objective nonconvex optimization problems with an increased number of objectives these methods employ a scalarizing function to reduce the multi objective problem into a set of single objective problems which upon solution yield a good approximation of the set of optimal solutions this set is commonly referred to as pareto front in this work we explore the implications of using decomposition based methods over pareto based methods on algorithm convergence from a probabilistic point of view namely we investigate whether there is an advantage of using a decomposition based method for example using the chebyshev scalarizing function over pareto based methods we find that under mild conditions on the objective function the chebyshev scalarizing function has an almost identical effect to pareto dominance relations when we consider the probability of finding superior solutions for algorithms that follow a balanced trajectory we propose the hypothesis that this seemingly contradicting result compared with currently available empirical evidence signals that the disparity in performance between pareto based and decomposition based methods is due to the inability of the former class of algorithms to follow a balanced trajectory we also link generalized decomposition to the results in this work and show how to obtain optimal scalarizing functions for a given problem subject to prior assumptions on the pareto front geometry

a multiobjective evolutionary algorithm for approximating the efficient set abstract in this article a new framework for evolutionary algorithms for approximating the efficient set of a multiobjective optimization moo problem with continuous variables is presented the algorithm is based on populations of variable size and exploits new elite preserving rules for selecting alternatives generated by mutation and recombination together with additional assumptions on the considered moo problem and further specifications on the algorithm theoretical results on the approximation quality such as convergence in probability and almost sure convergence are derived

group decision making with a fuzzy linguistic majority abstract the determination of solutions in group decision making is considered the point of departure is a collection of individual fuzzy preference relations a solution is derived either directly from the individual fuzzy preference relations or by constructing first a social fuzzy preference relation as opposed to conventional approaches in which a crisp threshold type majority rule is used we employ a fuzzy majority rule specified by a fuzzy linguistic quantifier e g most much more than 50 etc a calculus of linguistically quantified propositions is applied using the fuzzy majority various solution concepts are derived mainly of the type of core minimax opposition set and consensus winner

ferromagnetic transition in a simple variant of the ising model on multiplex networks abstract multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks layers here a simple variant of the ising model on multiplex networks with two layers is considered with spins located in the nodes and edges corresponding to ferromagnetic interactions between them critical temperatures for the ferromagnetic transition are evaluated for the layers in the form of random erdos renyi graphs or heterogeneous scale free networks using the mean field approximation and the replica method from the replica symmetric solution both methods require the use of different partial magnetizations associated with different layers of the multiplex network and yield qualitatively similar results if the layers are strongly heterogeneous the critical temperature differs noticeably from that for the ising model on a network being a superposition of the two layers evaluated in the mean field approximation neglecting the effect of the underlying multiplex structure on the correlations between the degrees of nodes the critical temperature evaluated from the replica symmetric solution depends sensitively on the correlations between the degrees of nodes in different layers and shows satisfactory quantitative agreement with that obtained from monte carlo simulations the critical behavior of the magnetization for the model with strongly heterogeneous layers can depend on the distributions of the degrees of nodes and is then determined by the properties of the most heterogeneous layer

aggregation of monotone reciprocal relations with application to group decision making this paper is composed of two complementary parts the first part is a formal investigation into the interplay of properties of reciprocal relations how monotonicity relates to some natural and intuitive properties including stochastic transitivity the goal is to aggregate monotone reciprocal relations on a given set of alternatives monotonicity is expressed w r t a linear order on the set of alternatives the second part is a practical protocol to both determine the best fitting linear order underlying the alternatives and construct a reciprocal relation monotone w r t it we formulate the problem as an optimization problem where the aggregated linear order is that for which the implied stochastic monotonicity conditions are closest to being satisfied by the distribution of the input monotone reciprocal relations we show that if stochastic monotonicity conditions are satisfied a monotone reciprocal relation is easily found on the basis of the possibly constructed stochastically monotone reciprocal distributional relation

fuzzy sets and decision analysis abstract this survey points out recent advances in multiple attribute decision making methods dealing with fuzzy or ill defined information fuzzy maut as well as fuzzy outranking methods are reviewed aggregation procedures choice problems and treatment of interactive attributes are covered trends in research and open problems are indicated

measuring volatility based on ordered weighted average operators agricultural products prices case of use abstract agricultural products have experienced sudden changes in prices in recent years as a result of volumes of production and demand at the international level volatility is a key element in understanding the difficulties that the market may have however the traditional formula for volatility only considers historical information and does not consider decision makers knowledge and skills to improve this approach and obtain more accurate results consistent with the reality of the market the ordered weighted averaging owa operator is used these new approaches are the owa volatility induced owa volatility heavy owa volatility probabilistic owa volatility induced probabilistic owa volatility and induced heavy owa volatility in addition some particular cases are presented in which the aggregation process is only applied to one part of the formula or quasi arithmetic means are used an example of volatility calculations for corn prices in 2017 is presented

a hybrid immune multiobjective optimization algorithm in this paper we develop a hybrid immune multiobjective optimization algorithm himo based on clonal selection principle in himo a hybrid mutation operator is proposed with the combination of gaussian and polynomial mutations gp hm operator the gp hm operator adopts an adaptive switching parameter to control the mutation process which uses relative large steps in high probability for boundary individuals and less crowded individuals with the generation running the probability to perform relative large steps is reduced gradually by this means the exploratory capabilities are enhanced by keeping a desirable balance between global search and local search so as to accelerate the convergence speed to the true pareto optimal front in the global space with many local pareto optimal fronts when comparing himo with various state of the art multiobjective optimization algorithms developed recently simulation results show that himo performs better evidently

an evolutionary artificial immune system for multi objective optimization in this paper an evolutionary artificial immune system for multi objective optimization which combines the global search ability of evolutionary algorithms and immune learning of artificial immune systems is proposed a new selection strategy is developed based upon the concept of clonal selection principle to maintain the balance between exploration and exploitation in order to maintain a diverse repertoire of antibodies an information theoretic based density preservation mechanism is also presented in addition the performances of various multi objective evolutionary algorithms as well as the effectiveness of the proposed features are examined based upon seven benchmark problems characterized by different difficulties in local optimality non uniformity discontinuity non convexity high dimensionality and constraints the comparative study shows the effectiveness of the proposed algorithm which produces solution sets that are highly competitive in terms of convergence diversity and distribution investigations also demonstrate the contribution and robustness of the proposed features

balancing exploration and exploitation with adaptive variation for evolutionary multi objective optimization abstract although recent studies have shown that evolutionary algorithms are effective tools for solving multi objective optimization problems their performances are often bottlenecked by the suitability of the evolutionary operators with respect to the optimization problem at hand and their corresponding parametric settings to adapt the search dynamic of evolutionary operation in multi objective optimization this paper proposes an adaptive variation operator that exploits the chromosomal structure of binary representation and synergizes the function of crossover and mutation the overall search ability is deterministically tuned online to maintain a balance between extensive exploration and local fine tuning at different stages of the evolutionary search also the coordination between the two variation operators is achieved by means of an adaptive control that ensures an efficient exchange of information between the different chromosomal sub structures throughout the evolutionary search extensive comparative studies with several representative variation operators are performed on different benchmark problems and significant algorithmic performance improvements in terms of proximity uniformity and diversity are obtained with the incorporation of the proposed adaptive variation operator into the evolutionary multi objective optimization process

a compendium of fuzzy weak orders representations and constructions the present paper gives a state of the art overview of representation and construction results for fuzzy weak orders we do not assume that the underlying domain is finite instead we concentrate on results that hold in the most general case that the underlying domain is possibly infinite this paper presents three fundamental representation results each of which also provides a construction method i score function based representations ii inclusion based representations iii representations by decomposition into crisp linear orders and fuzzy equivalence relations which also facilitates a pseudo metric based construction

ising model in clustered scale free networks the ising model in clustered scale free networks has been studied by monte carlo simulations these networks are characterized by a degree distribution of the form p k ensuremath sim k ensuremath ensuremath gamma for large k clustering is introduced in the networks by inserting triangles i e triads of connected nodes the transition from a ferromagnetic fm to a paramagnetic pm phase has been studied as a function of the exponent ensuremath gamma and the triangle density for ensuremath gamma g3 our results are in line with earlier simulations and a phase transition appears at a temperature t c ensuremath gamma in the thermodynamic limit system size n ensuremath rightarrow ensuremath infty for ensuremath gamma ensuremath le 3 a fm pm crossover appears at a size dependent temperature t mathrm co so the system remains in a fm state at any finite temperature in the limit n ensuremath rightarrow ensuremath infty thus for ensuremath gamma 3 t mathrm co scales as lnn whereas for ensuremath gamma l3 we find t mathrm co ensuremath sim j n z where the exponent z decreases for increasing ensuremath gamma adding motifs triangles in our case to the networks causes an increase in the transition or crossover temperature for exponent ensuremath gamma g3 or ensuremath le 3 for ensuremath gamma g3 this increase is due to changes in the mean values ensuremath langle k ensuremath rangle and ensuremath langle k 2 ensuremath rangle i e the transition is controlled by the degree distribution nearest neighbor connectivities for ensuremath gamma ensuremath le 3 however we find that clustered and unclustered networks with the same size and distribution p k have different crossover temperature i e clustering favors fm correlations thus increasing the temperature t mathrm co the effect of a degree cutoff k mathrm cut on the asymptotic behavior of t mathrm co is discussed

the pareto fitness genetic algorithm test function study evolutionary algorithms have shown some success in solving multiobjective optimization problems the methods of fitness assignment are mainly based on the information about the dominance relation between individuals we propose a pareto fitness genetic algorithm pfga in which we introduce a modified ranking procedure and a promising way of sharing a new fitness function based on the rank of the individual and its density value is designed this is considered as our main contribution the performance of our algorithm is evaluated on six multiobjective benchmarks with different pareto front features computational results quality of the approximation of the pareto optimal set and the number of fitness function evaluations proving its efficiency are reported

moss multiobjective scatter search applied to non linear multiple criteria optimization abstract this paper introduces a multiple criteria scatter search to deal with bounded constrained non linear continuous vector optimization problems of high dimension applying a multistart tabu search ts as a diversification generation method each ts works with its own starting point recency memory and aspiration threshold frequency memory is used to diversify the search and it is shared between the ts a pareto relation is applied in order to designate a subset of the best generated solutions to be reference solutions a choice function called kramer choice function is used to divide the reference solutions in two subsets the euclidean distance is used as a measure of dissimilarity in order to find diverse solutions to be combined linear combinations of the reference solutions are used as a solution combination method balls in the decision space and the objective space are used to avoid duplications different tabu sets with different tabu tenures are employed in the scatter phase to enhance the diversity of the search the performance of our approach is compared with pareto optimal frontiers and three other state of the art moeas for a suite test problems taken from the literature

a competitive and cooperative co evolutionary approach to multi objective particle swarm optimization algorithm design multi objective particle swarm optimization mopso is an optimization technique inspired by bird flocking which has been steadily gaining attention from the research community because of its high convergence speed on the other hand in the face of increasing complexity and dimensionality of today s application coupled with its tendency of premature convergence due to the high convergence speeds there is a need to improve the efficiency and effectiveness of mopso in this paper a competitive and cooperative co evolutionary approach is adapted for multi objective particle swarm optimization algorithm design which appears to have considerable potential for solving complex optimization problems by explicitly modeling the co evolution of competing and cooperating species the competitive and cooperative co evolution model helps to produce the reasonable problem decompositions by exploiting any correlation interdependency between components of the problem the proposed competitive and cooperative co evolutionary multi objective particle swarm optimization algorithm ccpso is validated through comparisons with existing state of the art multi objective algorithms using established benchmarks and metrics simulation results demonstrated that ccpso shows competitive if not better performance as compared to the other algorithms

a new hybrid differential evolution with simulated annealing and self adaptive immune operation differential evolution de has become a very powerful tool for global continuous optimization many strategies have been proposed for the generation of new solutions and every strategy has its own pros and cons so which one of them should be selected is critical for de performance besides being problem dependent in this paper different new solution generation strategies are integrated together and the individual advantages of different generation strategies are utilized to enhance the exploring ability and or to accelerate the convergence simulated annealing idea is introduced to escape from possible local optimum attraction clonal selection operation employs self adaptive gaussian hyper mutation along each dimension to focus the exploitation on the promising areas and exerts different influences on different dimensions experiments show that the proposed ideas benefit the performance of the algorithm and the proposed algorithm performs comprehensively better than other de variants in terms of convergence stability and solution accuracy

fuzzy rationality measures fuzzy preference relations formalize intensity of individual preferences over fixed sets of alternatives it is therefore natural to extend to fuzzy preferences the notion of rationality or consistency with this goal in mind we address in this paper the problem of giving an axiomatic basis for defining the concept of fuzzy rationality specifically we establish a collection of conditions that any fuzzy rationality measure must satisfy some examples of fuzzy rationality measures are then given and analyzed

a rational consensus model in group decision making using linguistic assessments abstract a new consensus model for the consensus reaching process in a linguistic framework is presented in heterogeneous group decision making problems called rational consensus model it is guided by some linguistic consensus and linguistic consistency meaures all the measures are calculated from a set of linguistic preference relations used to provide experts opinions this consensus model allows more rational consensus solutions to be obtained and thus more human consistency to be incorporated in decision support systems

group decision making with expertons and uncertain generalized probabilistic weighted aggregation operators abstract expertons and uncertain aggregation operators are tools for dealing with imprecise information that can be assessed with interval numbers this paper introduces the uncertain generalized probabilistic weighted averaging ugpwa operator it is an aggregation operator that unifies the probability and the weighted average in the same formulation considering the degree of importance that each concept has in the aggregation moreover it is able to assess uncertain environments that cannot be assessed with exact numbers but it is possible to use interval numbers thus we can analyze imprecise information considering the minimum and the maximum result that may occur further extensions to this approach are presented including the quasi arithmetic uncertain probabilistic weighted averaging operator and the uncertain generalized probabilistic weighted moving average we analyze the applicability of this new approach in a group decision making problem by using the theory of expertons in strategic management

resource allocation model and double sphere crowding distance for evolutionary multi objective optimization abstract convergence speed and diversity of nondominated solutions are two important performance indicators for multi objective evolutionary algorithms moeas in this paper we propose a resource allocation ra model based on game theory to accelerate the convergence speed of moeas and a novel double sphere crowding distance dscd measure to improve the diversity of nondominated solutions the mechanism of ra model is that the individuals in each group cooperate with each other to get maximum benefits for their group and then individuals in the same group compete for private interests the dscd measure uses hyper spheres consisting of nearest neighbors to estimate the crowding degree experimental results on convergence speed and diversity of nondominated solutions for benchmark problems and a real world problem show the efficiency of these two proposed techniques

evolving better population distribution and exploration in evolutionary multi objective optimization the aim of multi objective evolutionary optimization is to minimize the distance between the solution set and the true pareto front to distribute the solutions evenly and to maximize the spread of solution set this paper addresses these issues by presenting two features that enhance the optimization ability of multi objective evolutionary algorithms the first feature is a variant of the mutation operator that adapts the mutation rate along the evolution process to maintain a balance between the introduction of diversity and local fine tuning in addition this adaptive mutation operator adopts a new approach to strike a compromise between the preservation and disruption of genetic information the second feature is an enhanced exploration strategy that encourages the exploration towards less populated areas and hence achieves better discovery of gaps in the generated front the strategy also preserves non dominated solutions in the evolving population to achieve a good convergence for the optimization comparative studies of some well known diversity operators mutation operators and multi objective evolutionary algorithms are performed on different benchmark problems which illustrate the effectiveness and efficiency of the proposed features

theory of expertons and fuzzy logic abstract since 1965 when l a zadeh presented the concept of fuzzy sets various types of extensions have been proposed the treatment of subjectivity knowledge and uncertain data from one or several experts is now an important field in computer science in this paper a general concept the experton is described it is especially adapted for the case where several experts and or users are concerned the properties of expertons give also a monoid and a distributive lattice with the norms min and max then every process used with fuzzy sets stays available for expertons with a constraint of monotonicity expertons are based on probabilistic sets when intervals of probabilities are considered

a multiobjective immune algorithm based on a multiple affinity model abstract this paper presents a new multiobjective immune algorithm based on a multiple affinity model inspired by immune system mam moia the multiple affinity model builds the relationship model among main entities and concepts in multiobjective problems mops and multiobjective evolutionary algorithms moeas including feasible solution variable space objective space pareto optimal set ranking and crowding distance in the model immune operators including clonal proliferation hypermutation and immune suppression are designed to proliferate superior antibodies and suppress the inferiors mam moia is compared with nsga ii spea2 and nnia in solving the zdt and dtlz standard test problems the experimental study based on three performance metrics including coverage of two sets convergence and spacing proves that mam moia is effective for solving mops

continuous generalized owa operator and its application to decision making in this paper we present a new class of operators called the continuous generalized ordered weighted averaging c gowa operators which extends the continuous ordered weighted averaging operator to adapt to uncertain and complex situations in decision making we use differentiated aggregation method and produce special forms of c gowa operator in addition we apply the c gowa operator to the aggregation of multiple interval arguments and obtain a wide range of aggregation operators we especially discuss the controlling parameter and the selection of basic unit interval monotonic function introduced in the information aggregation to make it more feasible we further generalize the previous approaches by using choquet integral and quasi arithmetic means obtaining the combined continuous generalized choquet integral aggregation operator and the combined continuous quasi arithmetic choquet integral aggregation operator we also present some further extension by using hierarchical aggregation rules obtaining the ordered hierarchies of the combined c gowa operator meanwhile some desirable properties of these operators are investigated finally we give a numerical example to illustrate the application of these operators to group decision making with interval arguments

on training rbf neural networks using input output fuzzy clustering and particle swarm optimization this paper elaborates on the use of particle swarm optimization in training gaussian type radial basis function neural networks under the umbrella of input output fuzzy clustering the problem being investigated concerns the selection of basis function centers that contribute most in network s performance given that the clustering process in the input space is guided by the clustering in the output space to accomplish this task we quantify the effect of the input space fuzzy partition upon network s square error in terms of an objective function that describes the ability of the partition to accurately reconstruct the input training samples we then theoretically prove that the minimization of the above function acts to minimize an upper bound of the network s square error therefore the resulting solution corresponds to a minimal square error while at the same time it maintains the structure of the input data due to the peculiarity of the aforementioned objective function we treat it as the fitness function used by the particle swarm optimizer the proposed methodology encompasses three design steps the first step implements an independent fuzzy clustering in the output space to obtain a set of cluster centers in the second step unlike other approaches the above centers are directly involved in the estimation of the membership degrees in the input output space in the third step these membership degrees are used by the particle swarm optimizer in order to obtain optimal values for the centers to summarize the novelty of our contribution lies in a the way we handle the information flow from output to input space and b the way we handle the effect of the input space partition upon network s performance the experiments indicate that the fitness function decreases as the number of hidden node increases finally a comparison between the proposed method and other sophisticated approaches shows its statistically significant superiority

building consensus in group decision making with an allocation of information granularity abstract consensus is defined as a cooperative process in which a group of decision makers develops and agrees to support a decision in the best interest of the whole it is a questioning process more than an affirming process in which the group members usually modify their choices until a high level of agreement within the group is achieved given the importance of forming an accepted decision by the entire group the consensus problem has attained a great attention as it is a major goal in group decision making in this study we propose the concept of the information granularity being regarded as an important and useful asset supporting the goal to reach consensus in group decision making by using fuzzy preference relations to represent the opinions of the decision makers we develop a concept of a granular fuzzy preference relation where each pairwise comparison is formed as a certain information granule say an interval fuzzy set rough set and alike instead of a single numeric value as being more abstract the granular format of the preference model offers the required flexibility to increase the level of agreement within the group using the fact that we select the most suitable numeric representative of the fuzzy preference relation

a novel elitist multiobjective optimization algorithm multiobjective extremal optimization abstract recently a general purpose local search heuristic method called extremal optimization eo has been successfully applied to some np hard combinatorial optimization problems this paper presents an investigation on eo with its application in numerical multiobjective optimization and proposes a new novel elitist 1 multiobjective algorithm called multiobjective extremal optimization moeo in order to extend eo to solve the multiobjective optimization problems the pareto dominance strategy is introduced to the fitness assignment of the proposed approach we also present a new hybrid mutation operator that enhances the exploratory capabilities of our algorithm the proposed approach is validated using five popular benchmark functions the simulation results indicate that the proposed approach is highly competitive with the state of the art multiobjective evolutionary algorithms thus moeo can be considered a good alternative to solve numerical multiobjective optimization problems

tweaking synchronization by connectivity modifications acknowledgments the authors wish to thank the nesin foundation for an amazing working group activity in nesin math village and we wish to thank tiago pereira for fruitful discussions p s and j k acknowledge gratefully the support of bmbf condynet fk 03sf0472a t p acknowledges fapesp no 2012 22160 7 and no 2015 02486 3 and irtg 1740 d e acknowledge support by the leibniz association wgl under grant no saw 2013 izw 2542