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This paper introduces a problem that can be seen as a combination of the traveling salesman problem with profits and the traveling repairman problem with profits, coined as the multi‐objective traveling salesman–repairman problem with profits (Mo‐TSRPP). The objective of the Mo‐TSRPP is to simultaneously optimize three objectives: the total cost, total latency, and total profit. Indirectly, the number of nodes visited is also considered although not as an objective itself since it is determined by the size of every efficient solution in the Pareto front. The Mo‐TSRPP emerges as a real‐world problem in which a freelancer, which repairs appliances, wants to plan the daily route. Moreover, the daily plan does not require to visit all customers. To solve the problem, first, a greedy randomized adaptive procedure is designed to generate a set of high‐quality nondominated solutions and then, a variable neighborhood descent algorithm is applied for further improving the initial set. This procedure allows us to attain a good approximation of the Pareto front. To prove the performance of the proposal a comparison is done against three well‐known evolutionary algorithms: NSGA‐II, SPEA‐2, and MOEA/D. Finally, a realistic problem is shown and solved to illustrate the potential of the algorithm. [ABSTRACT FROM AUTHOR]

This research proposes a mathematical model for the vehicle routing problem (VRP), which involves pickup and delivery of cargos to different depots. Vehicle capacity and energy consumption that varies with load are both contributing factors. The mathematical model seeks to simultaneously reduce costs and waiting time for customers. Multi-objective particle swarm optimisation (MPSO) and Non-dominated Sorting Genetic Algorithm-II (NSGA-II) are proposed as methods to solve the model. This is implemented and solved in the GAMS software for moderate-sized problems, and the results are compared to those obtained by two different algorithms in order to validate the model and algorithms. Then, the results are compared with those obtained by NSGA-II algorithm based on comparative metrics. [ABSTRACT FROM AUTHOR]

At present, designing an RNA sequence that folds into a specific secondary structure is a problem that is not fully solved, due to its exponentially increasing complexity. To address this matter, many computational methods have been developed, but none of them has been able to completely and in an affordable time solve Eterna100, a widely recognized benchmark used to test the performance of RNA inverse folding algorithms. In previous publications we presented the m2dRNAs tool, a Multiobjective Evolutionary Algorithm, and its extension eM2dRNAs, which added a recursive decomposition of the target structure, thus simplifying the problem. At that time they successfully improved the ability to solve the RNA inverse folding problem, but were still unable to complete the Eterna100 benchmark. Here we introduce ES+eM2dRNAs, an improvement of eM2dRNAs that optimizes the decomposition process, as a drawback in its nature was identified.A comparative study of this new tool against its predecessors and other RNA design methods was performed using the two current versions of the Eterna100 benchmark. ES+eM2dRNAs was shown to be the best in all performance indicators considered (number of structures solved, success rate, and total run time). Moreover, it is able to solve two Eterna100 structures for which none of the compared methods had ever found a solution.

Meituan pioneered an on-demand food delivery service in China, which allows consumers to place food orders online for fast delivery. Leveraging its minute-level delivery network and boasting more than five million active couriers, Meituan delivers more than 60 million orders daily, ranking it as the world's largest in terms of order volume and courier count. It has transformed itself into one of China's most critical delivery infrastructure providers. To meet its service commitment to customers and improve the working experience of its couriers, Meituan must continuously optimize its order assignment decisions. Thus, it developed a real-time intelligent dispatch system, including a set of algorithms based on operations research and machine learning techniques, to precisely model the assignment problem in a dynamic and uncertain environment, and solved this NP-hard problem in seconds generating a high-quality solution. Since implementing this dispatch system in 2019, Meituan has realized a decrease of 20.96% in average order delivery time and 23.77% in average courier traveling distance per order. In addition, the system contributes to cost reductions of about $0.23 billion annually. Moreover, the dispatch system enabled other new digital economy business formats, such as Meituan Instashopping and Meituan Grocery, to thrive. [ABSTRACT FROM AUTHOR]

In this paper, a modified Pascoletti–Serafini scalarization approach, called MOP_MPS, is proposed to generate approximations of a Pareto front of bounded multi-objective optimization problems (MOPs). The objective is obtaining some points with an almost even distribution overall Pareto front. This algorithm is applied to six test problems with convex, non-convex, connected, and dis-connected Pareto fronts, and its results are compared with results of some famous algorithms. The results emphasize that MOP_MPS is effective and competitive in comparing with the other considered algorithms. In addition, it is shown that an optimal solution of a multiplicative programming problem is a properly Pareto optimal solution of an MOP. By considering this relation between MOPs and multiplicative programming problems (MPPs), another algorithm based on MOP_MPS, called MPP_MPS, is suggested for approximately solving non-linear MPPs in which functions multiplied are continuous and bounded from below. The computational results on seven problems of convex MPPs demonstrate that the algorithm is much better than a cut and bound algorithm presented by Shao and Ehrgott in terms of CPU time. [ABSTRACT FROM AUTHOR]

In this paper, we develop Newton's method for robust counterpart of an uncertain multiobjective optimization problem under an arbitrary finite uncertainty nonempty set. Here the robust counterpart of an uncertain multiobjective optimization problem is the minimum of objective wise worst case, which is the nonsmooth deterministic multiobjective optimization problem. To solve this robust counterpart with the help of Newton's method, a suproblem is constructed and solved to find a descent direction for robust counterpart. An Armijo type inexact line search technique is developed to find a suitable step length. With the help of the descent direction and step length, we present the Newton's algorithm for the robust counterpart. The convergence of the Newton's algorithm for the robust counterpart is obtained under some usual assumptions. We also prove that the algorithm converges with super linear and quadratic rate under different assumptions. Finally, we verify the algorithm and compare with the weighted sum method via some numerical problems. [ABSTRACT FROM AUTHOR]

In this paper, we study the classes of approximate Minty and Stampacchia type vector variational inequalities along with their local and weak versions on a Hadamard manifold, and a class of nonsmooth interval-valued multiobjective optimization problems, respectively. We obtain the equivalence between the solutions of considered approximate vector variational inequalities and LU-efficient solutions of nonsmooth interval-valued multiobjective optimization problems in which the cost function is assumed to be geodesic approximately LU-convex or geodesic LU-α-convex. [ABSTRACT FROM AUTHOR]

This paper proposes a new method to identify the near-optimal response to failures in water distribution networks in near real time. The response method is formulated as a two-objective optimization problem with objectives being the minimization of failure impacts and related operational costs. The new heuristics-based method is developed and used to solve this optimization problem. The method comprises three steps. In the first step, the initial list of available interventions is identified offline. In the second step (online), the narrowed-down list of interventions considered in the optimization is identified. Finally, in the last step (online), a novel heuristic algorithm is applied to identify near-optimal solutions in near real time. The new optimization method was validated and demonstrated in two case studies, a semireal case study based on a C-Town network and an assumed failure event (pipe burst), and a real UK case study involving a complex real pipe network and event caused by shutting down the Water Treatment Works. The Pareto front of response interventions identified by the new heuristics method approximates well the non-dominated sorting genetic algorithm II Pareto front in both cases with the largest differences measured in terms of end-impacts (between relevant solutions for the same cost) being 4% and 9%, respectively. In addition, the new heuristics method is able to identify near-optimal response solutions in a computationally fast manner (15 min and 1 h for the two cases). Therefore, the heuristics method can be used in near real time in real-life situations. [ABSTRACT FROM AUTHOR]

The green vehicle routing problem (GVRP) is a variant of the vehicle routing problem (VRP), which increasingly attracts many researchers in recent years due to the growing global environmental issues. As the transportation of the products grows, the number of vehicles in fleets and the pollutants caused by these vehicles also grow, which in turn negatively affects human health. In this paper, a biobjective GVRP was studied. The two objectives are minimizing the total distance and minimizing the total fuel consumption of all vehicle routes. As a solution method, an adaptive large neighborhood search was hybridized with two new local search heuristics. The proposed method was applied to two well‐known benchmark problem sets for VRPs and new approximate Pareto fronts were obtained for these benchmark sets. [ABSTRACT FROM AUTHOR]

A new type of approximate subdifferential was proposed for quasiconvex functions. Their properties were studied, and the approximate subdifferential was applied to the characterization of approximate solutions to quasiconvex multiobjective optimization problems. Firstly, the existing approximate subdifferentials were improved to get a new approximate subdifferential of the quasiconvex function, and their relationships and properties were given. Then, the optimality conditions for approximate efficient solutions and approximate properly efficient solutions to quasiconvex multiobjective optimization problems were obtained by means of the new approximate subdifferential. [ABSTRACT FROM AUTHOR]

The aim of this work is to study constrained optimization problems by means of (Φ, ρ)-convexity. We provide some sufficient conditions of optimality for a class of vectors of cuvilinear integrals by means of an adequate generalized convexity. Dual problems associated with this one are stated and developed, in terms of weak, strong, and converse duality results. The framework chosen here is one specific to the Riemannian geometry, namely that of first order jet bundles.

Antenna arrays can enhance the performance and reduce the overhead of the wireless communication systems. However, the beam pattern synthesis of antenna arrays are difficult problems since the optimization properties are usually trade‐offs that affect each other. In this paper, we formulate a multiobjective beam pattern optimization problem (MBPOP) to simultaneously reduce the maximum sidelobe level (SLL) and achieve the nulls of the antenna array beam pattern. The multiobjective evolutionary algorithm based on decomposition (MOEA/D) is a general and effective algorithm to solve the MOPs. However, it may be easy to lose population diversity and converge to local optimum. To overcome the issues above, we propose an improved MOEA/D (IMOEA/D) to deal with the formulated MBPOP. IMOEA/D introduces the normal distribution crossover operator (NDX), Lévy flight strategy and Euclidean distance‐based solution selection mechanism to enhance the performance of conventional MOEA/D to make it more suitable to solve the formulated MBPOP. Experiments are conducted and the results indicate that the proposed IMOEA/D has a better performance in terms of the convergence rate and population diversity compared to other algorithms for solving the formulated MBPOP. [ABSTRACT FROM AUTHOR]

This study presents the modeling of the multiobjective optimization problem in an intuitionistic fuzzy environment. The uncertain parameters are depicted as intuitionistic fuzzy numbers, and the crisp version is obtained using the ranking function method. Also, we have developed a novel interactive neutrosophic programming approach to solve multiobjective optimization problems. The proposed method involves neutral thoughts while making decisions. Furthermore, various sorts of membership functions are also depicted for the marginal evaluation of each objective simultaneously. The different numerical examples are presented to show the performances of the proposed solution approach. A case study of the cloud computing pricing problem is also addressed to reveal the real-life applications. The practical implication of the current study is also discussed efficiently. Finally, conclusions and future research scope are suggested based on the proposed work. [ABSTRACT FROM AUTHOR]

Problems in daily life can be modeled into mathematical forms, one of them is the optimization of the quadratic form where the objective functions are the quadratic function. There are many real problems involving variables that cannot be stated numerically so that fuzzy logic appears. The purpose of this research is to optimize the quadratic form with all its parameters in the form of a fuzzy number by using the method of a triangular fuzzy number. This research resulted in a new completion method by utilizing definitions and arithmetic on the triangular fuzzy numbers. The resulted method is by changing a single fuzzy quadratic program becomes a simple quadratic multiobjective program. By using Sum of Objective Method, the multiobjective problem can be changed into single optimization problem. This single optimization problem is then completed using Karush–Kuhn–Tucker method, resulting in three optimal values which will form optimal values in the form of triangular fuzzy numbers. [ABSTRACT FROM AUTHOR]

• Proposed an alternative method for big data optimization problems. • A hybrid between salp swarm algorithm and differential evolution is used as multi-objective for big data optimization. • A set of single objective and multi-objective problems from the 2015 big data optimization competition is used. • Experimental results show that the proposed method outperforms than other methods. This paper developed a multiobjective Big Data optimization approach based on a hybrid salp swarm algorithm and the differential evolution algorithm. The role of the differential evolution algorithm is to enhance the capability of the feature exploitation of the salp swarm algorithm because the operators of the differential evolution algorithm are used as local search operators. In general, the proposed method contains three stages. In the first stage, the population is generated, and the archive is initialized. The second stage updates the solutions using the hybrid salp swarm algorithm and the differential evolution algorithm, and the final stage determines the nondominated solutions and updates the archive. To assess the performance of the proposed approach, a series of experiments were performed. A set of single-objective and multiobjective problems from the 2015 Big Data optimization competition were tested; the dataset contained data with and without noise. The results of our experiments illustrated that the proposed approach outperformed other approaches, including the baseline nondominated sorting genetic algorithm, on all test problems. Moreover, for single-objective problems, the score value of the proposed method was better than that of the traditional multiobjective salp swarm algorithm. When compared with both algorithms, that is, the adaptive DE algorithm with external archive and the hybrid multiobjective firefly algorithm, its score was the largest. In contrast, for the multiobjective functions, the scores of the proposed algorithm were higher than that of the fireworks algorithm framework. [ABSTRACT FROM AUTHOR]

The rapidly evolving industry standards and transformative advances in the field of Internet of Things are expected to create a tsunami of Big Data shortly. This, in turn, will demand real-time data analysis and processing from cloud computing platforms. A substantial part of the computing infrastructure is supported by large-scale and geographically distributed data centers (DCs). Nevertheless, these DCs impose a substantial cost in terms of rapidly growing energy consumption, which in turn adversely affects the environment. In this context, efficient resource utilization is seen as a potential candidate to enhance energy efficiency and minimize the load on the power sector. Nevertheless, in the majority of the public clouds, the resources are idle most of the time (i.e., under-utilized) as the load of the servers is unpredictable; thereby leading to a lofty increase in the energy utilization index and wastage of resources. Thus, it is highly essential to devise a precise and efficient resource management technique. Therefore, in this article, we leverage the advantages of software defined data centers (SDDCs) to minimize energy utilization levels. Precisely, SDDC refers to the process of programmatically abstracting the logical computing, network, and storage resources; and configuring them in real-time based on workload demands. In detail, we demonstrate the possibility of 1) designing a consolidated SDDC-based model to jointly optimize the process of virtual machine (VM) deployment and network bandwidth allocation for reduced energy consumption and guaranteed quality of service (QoS), particularly for heterogeneous computing infrastructures; 2) formulating a multiobjective optimization problem to deduce the optimal allocation of resources for both critical and noncritical applications; and 3) designing an efficient scheme based on heuristics to provide suboptimal results for the formulated multiobjective optimization problem. The proposed article presents a suboptimal approach based on first fit decreasing algorithm. Further, our empirical evaluations suggest that the proposed framework leads to almost 27.9% savings in terms of energy consumptions against the existing schemes with negligible QoS violations (approximately 0.33). [ABSTRACT FROM AUTHOR]

In this paper, an intelligent data-driven optimization scheme is proposed for finding the proper burden surface distribution, which exerts large influences on keeping blast furnace running smoothly in an energy-efficient state. In the proposed scheme, production indicators prediction models are first developed using a kernel extreme learning machine algorithm. To heel, burden surface decision is presented as a multiobjective optimization problem for the first time and solved by a modified two-stage intelligent optimization strategy to generate the initial setting values of burden surface. Furthermore, considering the existence of the approximation error of the created prediction models, feedback compensation is implemented to enhance the reliability of the results, in which an improved association rule mining method is developed to find the corrected values to compensate the initial setting values. Finally, we apply the proposed optimization scheme to determine the setting values of burden surface using actual data, and experimental results illustrate its effectiveness and feasibility. [ABSTRACT FROM AUTHOR]

When dealing with complex multiobjective problems, particle swarm optimization algorithm is easy to fall into local optimum and lead to uneven distribution. Therefore, this paper presents a hybrid multiobjective particle swarm optimization algorithm based on R2 indicator (R2HMOPSO) for solving multiobjective optimization problem. The proposed algorithm uses the sigmoid function mapping method to adjust the inertia weight and learning factors in order to tradeoffs the exploration and exploitation process effectively. In addition, simulation binary crossover operator is designed to reinitialize the particles to improve the search capability of the algorithm and to prevent particles from falling into local optimum and premature convergence. R2 indicator is incorporated into the R2HMOPSO algorithm so as to deal with the solutions of uneven distribution on the true Pareto front. Besides, polynomial mutation is used to maintain diversity in the external archive. The improved algorithm is evaluated on standard benchmarks. By comparing it with four state-of-the-art multiobjective optimization algorithms, the simulation results show that R2HMOPSO algorithm is competitive and effective in terms of convergence and distribution.

The steepest descent method for multiobjective optimization on Riemannian manifolds with lower bounded sectional curvature is analyzed. The aim of this study is twofold. First, an asymptotic analysis of the method is presented with three different finite procedures for determining the stepsize: Lipschitz, adaptive, and Armijo-type stepsizes. Second, by assuming the Lipschitz continuity of a Jacobian, iteration-complexity bounds for the method with these three stepsize strategies are presented. In addition, some examples that satisfy the hypotheses of the main theoretical results are provided. Finally, the aforementioned examples are presented through numerical experiments. [ABSTRACT FROM AUTHOR]

The relations between the robust efficient solutions and properly efficient solutions to multiobjective optimization problems were studied, and the optimality conditions for the robust efficient solutions were discussed. Firstly, the concept of weakly robust efficient solutions to multiobjective optimization problems was given. Then, the relations between the (weakly) robust efficient solutions and the properly efficient solutions were made clear. Several examples were given to illustrate the main results. Finally, the necessary and sufficient optimality conditions for the robust efficient solutions were established under the subconvexity and pseudoconvexity assumptions. [ABSTRACT FROM AUTHOR]

In this paper, by using the new concept of (ϱ,ψ,ω)-quasiinvexity associated with interval-valued path-independent curvilinear integral functionals, we establish some duality results for a new class of multiobjective variational control problems with interval-valued components. More concretely, we formulate and prove weak, strong, and converse duality theorems under (ϱ,ψ,ω)-quasiinvexity hypotheses for the considered class of optimization problems.