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The extant supply chain management literature has not addressed the issue of coordination in supply chains involving risk‐averse agents. We take up this issue and begin with defining a coordinating contract as one that results in a Pareto‐optimal solution acceptable to each agent. Our definition generalizes the standard one in the risk‐neutral case. We then develop coordinating contracts in three specific cases: (i) the supplier is risk neutral and the retailer maximizes his expected profit subject to a downside risk constraint; (ii) the supplier and the retailer each maximizes his own mean‐variance trade‐off; and (iii) the supplier and the retailer each maximizes his own expected utility. Moreover, in case (iii), we show that our contract yields the Nash Bargaining solution. In each case, we show how we can find the set of Pareto‐optimal solutions, and then design a contract to achieve the solutions. We also exhibit a case in which we obtain Pareto‐optimal sharing rules explicitly, and outline a procedure to obtain Pareto‐optimal solutions.

A method for solving quasiconvex nondifferentiable unconstrained multiobjective optimization problems is proposed in this paper. This method extends to the multiobjective case of the classical subgradient method for real-valued minimization. Assuming the basically componentwise quasiconvexity of the objective components, full convergence (to Pareto optimal points) of all the sequences produced by the method is established.

Summary This paper formulates a new multi‐objective model for the optimal power flow (OPF) problem considering 3 non‐commensurable and contradictory objectives, namely cost, emission, and loss. The proposed multi‐objective OPF problem takes a complete model for power generators including valve‐point effects, ramp rate limits, prohibited operating zones, spinning reserve, and multi‐fuel operation. Considering these constraints results in a non‐convex and non‐linear optimization problem and requires powerful methods to cope with. In this regard, the present paper proposes a multi‐objective electromagnetism‐like algorithm (EMA) based on the Pareto dominance concept and external archive strategy to solve this problem. The original EMA has poor search space exploration ability; hence, this paper proposes an improved EMA with modified local search process, which increases both exploration and intensification capabilities of the algorithm. The feasibility and effectiveness of the proposed method are tested on the IEEE 30‐ and 118‐bus test systems and the obtained numerical results are compared with the results of the original EMA and other heuristic methods reported in the recent literature.

Purpose – The purpose of this paper is to present an approach to multiple criteria mechanical design problems, for cases where problem complexity precludes derivation of the whole Pareto front (PF). For such problems the authors propose to limit search, and hence also derivation, of the PF exclusively to regions of the direct designer’s interest, thus saving on computing efforts and gaining on tractable problem sizes. Design/methodology/approach – To achieve the purpose, the authors frame the decision making process (design) into a combination of three specific concepts, namely, decision maker’s preference capture, local PF search and approximate multiobjective optimization (MO) with assessments of the Pareto optimality gap. The authors illustrate the approach with two small design problems, namely, Pareto optimal round tube beam and Pareto optimal pneumatic high-speed machine drive selection. The authors solve these problems in a setting which can be regarded as representative for problem solving in real environment. Findings – On the decision making side, the proposed approach has turned out to be a versatile tool for selecting designs from the Pareto suboptimal ones, where each such a Pareto suboptimal design has an explicit assessment of the Pareto optimality gap. On the technical (optimization) side, it has been demonstrated that the approach seamlessly works with evolutionary computations, structured to the specific needs of the approach. Research limitations/implications – It has been shown that the navigation over the PF can be achieved with limited effort, both on the cognitive and the computing side. Moreover, navigation over the PF can be focussed from the very beginning of the design selection process on the regions of the PF which are of the direct designer’s interest. This eliminates the need to derive (or only approximate) the whole PF, a tangible asset as the derivation of that set is the main factor precluding scalability of design selection problems to higher dimensions (to higher problem sizes). Practical implications – Because of the general formulation of the Pareto optimal design selection problem considered in the paper, the absence of any assumptions on its form and easiness of implementation of the underlying procedure of the proposed approach, the paper offers a clear option to approaches based on classical optimization computations. Originality/value – The approach offers derivation of Pareto suboptimal designs with assessments of the Pareto optimality gap, whereas currently available multiobjective evolutionary optimization algorithms which derive Pareto suboptimal designs as well, offer no such assessments. Thus, the approach provides a firm ground to valuate designs resulting from approximate MO computations.

Experience from climate policy suggests that full cooperation among all countries is not a likely outcome. In this paper we therefore consider the case where only members of a subgroup of countries cooperate by reciprocally matching their public good contributions. In a two-stage game, matching rates are set at stage 1 then national contributions are chosen at stage 2. In the case of small coalitions, negative matching may result in the subgame-perfect equilibrium that decreases global public good provision and outsiders' welfare. Moreover, a growing number of countries may paradoxically entail a reduction of equilibrium public good supply.

The averaged Hausdorff distance ∆p is an inframetric, recently introduced in evolutionary multiobjective optimization (EMO) as a tool to measure the optimality of finite size approximations to the Pareto front associated to a multiobjective optimization problem (MOP). Tools of this kind are called performance indicators, and their quality depends on the useful criteria they provide to evaluate the suitability of different candidate solutions to a given MOP. We present here a purely theoretical study of the compliance of the ∆p -indicator to the notion of Pareto optimality. Since ∆p is defined in terms of a modified version of other well- known indicators, namely the generational distance GDp , and the inverted generational distance IGDp , specific criteria for the Pareto compliance of each one of them is discussed in detail. In doing so, we review some previously available knowledge on the behavior of these indicators, correcting inaccuracies found in the literature, and establish new and more general results, including detailed proofs and examples of illustrative situations.

A hot Markovian system can cool down faster than a colder one: this is known as the Mpemba effect. Here, we show that a non-equilibrium driving via stochastic reset can induce this phenomenon, when absent. Moreover, we derive an optimal driving protocol simultaneously optimizing the appearance time of the Mpemba effect, and the total energy dissipation into the environment, revealing the existence of a Pareto front. Building upon previous experimental results, our findings open up the avenue of possible experimental realizations of optimal cooling protocols in Markovian systems.

Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation-based algorithms. We also compare these algorithms based on different criteria such as metamodeling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive multiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.

Shaping global water and carbon cycles, plants lift water from roots to leaves through xylem conduits. The importance of xylem water conduction makes it crucial to understand how natural selection deploys conduit diameters within and across plants. Wider conduits transport more water but are likely more vulnerable to conductionb-locking gas embolisms and cost more for a plant to build, a tension necessarily shaping xylem conduit diameters along plant stems. We build on this expectation to present the Widened Pipe Model (WPM) of plant hydraulic evolution, testing it against a global dataset. The WPM predicts that xylem conduits should be narrowest at the stem tips, widening quickly before plateauing toward the stem base. This universal profile emerges from Pareto modeling of a trade-off between just two competing vectors of natural selection: one favoring rapid widening of conduits tip to base, minimizing hydraulic resistance, and another favoring slow widening of conduits, minimizing carbon cost and embolism risk. Our data spanning terrestrial plant orders, life forms, habitats, and sizes conform closely to WPM predictions. The WPM highlights carbon economy as a powerful vector of natural selection shaping plant function. It further implies that factors that cause resistance in plant conductive systems, such as conduit pit membrane resistance, should scale in exact harmony with tip-to-base conduit widening. Furthermore, the WPM implies that alterations in the environments of individual plants should lead to changes in plant height, for example, shedding terminal branches and resprouting at lower height under drier climates, thus achieving narrower and potentially more embolism-resistant conduits.

In this paper, we consider a multiobjective optimal control problem where the preference relation in the objective space is defined in terms of a pointed convex cone containing the origin, which defines generalized Pareto optimality. For this problem, we introduce the set-valued return function $V$ and provide a unique characterization for $V$ in terms of contingent derivative and coderivative for set-valued maps, which extends two previously introduced notions of generalized solution to the Hamilton--Jacobi equation for single objective optimal control problems. [PUBLICATION ABSTRACT]