In interplanetary trajectory optimization, events such as planetary gravitational-assist maneuvers (swingbys) and deep-space maneuvers can be added/removed from the trajectory plan to reduce the cost or the flight time. This renders the number of design variables in the optimization problem variable. Global optimization methods that optimize this type of multimodal objective function can only handle problems with a fixed number of design variables. This paper presents the structured-chromosome evolutionary algorithm framework that is developed to handle variable-size design space optimization problems. In this framework, a solution (chromosome) is represented by a hierarchical data structure where the genes in the chromosome are classified as dependent and nondependent genes. This structure provides the capability to apply genetic operations between solutions of different lengths, and thus to automatically determine the number of swingbys, the planets to swingby, launch and arrival dates, and the number of deep-space maneuvers, as well as their locations, magnitudes, and directions, in an optimal sense. This new method is applied to several interplanetary trajectory design problems. Results show that solutions obtained using this tool match known solutions for some complex problems. A comparison between genetic algorithms and differential evolution in the structured-chromosome framework is presented. Nomenclature a = first selected chromosome a = thrust acceleration vector b = second selected chromosome c = third selected chromosome F = fitness (cost function) F 0 = modified fitness (cost function) f = flight direction G = derating function h = pericenter altitude, km h = normalized swingby pericenter altitude iter = iteration m = number of swingby maneuvers NR = number of runs n = number of deep-space maneuvers in a single leg R = mean radius, km r = heliocentric position vector in inertial frame, km r = spacecraft position vector r = spacecraft acceleration vector SC = success counter SR = success rate sol = solution T = time of flight, days t = Julian date tmp = temporary chromosome u = solution feature v ∞ = hyperbolic velocity vector relative to the planet, km∕s w = differential weight ΔV x = x component of impulsive maneuver velocity ΔV y = y component of impulsive maneuver velocity ΔV z = z component of impulsive maneuver velocity Δv = impulsive maneuver velocity vector, km∕s Δv T = total mission cost, km∕s ε = epoch of a deep-space maneuver as a fraction of transfer time η = swingby plane rotation angle, rad μ = gravitational constant, km 3 ∕s 2 Subscripts a = arrival d = departure l = leg number p = swingby's planet ps = powered swingby req = required s∕c = spacecraft T = total Superscripts − = incoming = outgoing
Web applications employ key-value stores to cache the data that is most commonly accessed. The cache improves an web application's performance by serving its requests from memory, avoiding fetching them from the backend database. Since the memory space is limited, maximizing the memory utilization is a key to delivering the best performance possible. This has lead to the use of multi-tenant systems, allowing applications to share cache space. In addition, application data access patterns change over time, so the system should be adaptive in its memory allocation. In this thesis, we address both multi-tenancy (where a single cache is used for multiple applications) and dynamic workloads (changing access patterns) using a model that relates the cache size to the application miss ratio, known as a miss ratio curve. Intuitively, the larger the cache, the less likely the system will need to fetch the data from the database. Our efficient, online construction of the miss ratio curve allows us to determine a near optimal memory allocation given the available system memory, while adapting to changing data access patterns. We show that our model outperforms an existing state-of-the-art sharing model, Memshare, in terms of cache hit ratio and does so at a lower time cost. We show that average hit ratio is consistently 1 percentage point greater and 99.9th percentile latency is reduced by as much as 2.9% under standard web application workloads containing millions of requests. xv
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